Arithmetic Expressions is a chapter in the CBSE Class 7 Mathematics syllabus from Ganita Prakash. This chapter hub brings together revision notes, practice questions, worksheets, flashcards, formula sheet to help students learn, practice, and revise Arithmetic Expressions effectively.

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Arithmetic Expressions

NCERT Class 7 Mathematics Chapter 2: Arithmetic Expressions (Pages 24–45)

Summary of Arithmetic Expressions

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Arithmetic Expressions at a Glance

Board

CBSE

Class

Class 7

Subject

Mathematics

Book

Ganita Prakash

Chapter

2

Pages

2445

Resources

7 study resources

Arithmetic Expressions Summary

In this chapter, students will learn about arithmetic expressions, which are mathematical phrases formed by numbers and operations like addition, subtraction, multiplication, and division. Understanding arithmetic expressions is essential as they form the foundation for problem-solving in mathematics. The chapter begins by explaining what an arithmetic expression is, providing examples like thirteen plus two or twenty minus four. Each expression has a value, which is the result of performing the operations involved. For example, when you add thirteen and two, the value is fifteen. Students will also learn the notation used to denote the equality of an expression and its value, using the equality sign. Next, the chapter explores different ways to express the same numerical value using various combinations of two numbers and the four basic operations. This shows students that there are often multiple methods to arrive at the same result. For instance, the number twelve can be expressed as ten plus two, fifteen minus three, three times four, or twenty-four divided by two. This part of the lesson encourages creativity and flexibility in thinking about numbers. Furthermore, the chapter discusses how to compare arithmetic expressions using equality and inequality signs. Students are taught to assess the values of different expressions and determine if one is greater than, less than, or equal to another. For example, they learn that the expression ten plus two is greater than seven plus one because both evaluate to the numerical values of twelve and eight, respectively. The chapter includes engaging activities where students fill in blanks to create equal expressions and arrange several expressions in increasing order of their values. This hands-on practice reinforces their understanding and helps them learn to work with expressions dynamically. To enhance comprehension, real-world scenarios are provided, allowing students to visualize the concept of greater than and less than through relatable situations. For instance, by imagining two characters, Raja and Joy, with different amounts of marbles, students deduce which has more based on arithmetic expressions corresponding to the situation. Overall, this chapter supports students as they develop their skills in handling arithmetic expressions, laying important groundwork for future mathematical learning and reasoning.

Arithmetic Expressions Revision Guide

Download the Arithmetic Expressions revision guide with key points, summaries, and quick revision notes for CBSE Class 7 Mathematics.

Key Points

1

Define arithmetic expressions.

Arithmetic expressions are mathematical phrases that represent values. Examples include 13 + 2 or 20 - 4.

2

Every expression has a value.

The value of an expression is the result of the calculations. For instance, 5 × 25 evaluates to 125.

3

Equality sign denotes value.

The '=' sign shows equality between an expression and its value, e.g., 13 + 2 = 15.

4

Understanding simple expressions.

Expressions simplify to a single value through operations: addition, subtraction, multiplication, and division.

5

Multiple expressions can equal the same value.

Different combinations can produce the same result. E.g., 10 + 2 and 15 - 3 both equal 12.

6

Comparing expressions.

Expressions can be compared using '<', '>', or '=' based on their evaluated values.

7

Example of comparison.

For instance, 10 + 2 (12) > 7 + 1 (8) shows how to compare arithmetic expressions.

8

Real-life applications of expressions.

Expressions represent scenarios, like calculating daily expenses, e.g. Mallika's weekly lunch expenses.

9

Filling in expressions.

Fill in blanks to create equivalent expressions, reinforcing understanding of value relationships.

10

Arranging expressions by value.

Practice ordering expressions based on their results to enhance comprehension of their values.

11

Use of imagination in comparisons.

Visualize scenarios to compare expressions without calculating, e.g., Raja and Joy's marbles.

12

Equivalence in subtraction.

Expressions can be equal even after subtraction, e.g., 113 - 25 = 112 - 24 shows equal results.

13

Identifying equal and unequal expressions.

Evaluate expressions for equality to understand their value differences better.

14

Daily life expressions.

Expressions help solve practical problems, like budgeting weekly expenses or calculating travel time.

15

Expressions using all operations.

Understand expressions can utilize addition, subtraction, multiplication, and division simultaneously.

16

Symbols for comparison.

'<', '>', '=' are essential to compare expressions based on values and define relationships.

17

Expressing the same value differently.

Create multiple expressions for the same value to practice flexibility in arithmetic thinking.

18

Understanding multiplication through addition.

Recognize multiplication as repeated addition, e.g., 4 × 3 = 3 + 3 + 3 + 3.

19

Simplifying complex expressions.

Simplifying large expressions into smaller components can help in faster calculation.

20

Evaluating expressions systematically.

Order of operations (PEMDAS/BODMAS) needs to be followed when calculating complex expressions.

21

Using number lines for comprehension.

Visual tools like number lines can help understand value comparisons and operations visually.

Arithmetic Expressions Practice Questions & Answers

Practice important questions and exam-style problems from Arithmetic Expressions. These questions cover key topics from the CBSE Class 7 Mathematics syllabus.

How to practice: Start with the questions below to test your understanding of Arithmetic Expressions. Use the revision guide to review concepts you find difficult, then come back and retry the questions for better retention.

View all 125 Arithmetic Expressions questions
Q9

Which expression is equivalent to 8 multiplied by 4?

Single Answer MCQ
Q-00123844
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Q10

If 3x = 12, what is the value of x?

Single Answer MCQ
Q-00123845
View explanation
Q11

Determine which is greater: 30 ÷ 3 or 5 × 5.

Single Answer MCQ
Q-00123846
View explanation
Q12

What is the value of the expression 4 × (2 + 3)?

Single Answer MCQ
Q-00123847
View explanation
Q13

Which of the following pairs of expressions are equal?

Single Answer MCQ
Q-00123848
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Q14

Which statement is true?

Single Answer MCQ
Q-00123849
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Q15

Which expression has the lowest value?

Single Answer MCQ
Q-00123850
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Q16

If an expression evaluates to 15, which of these could represent it?

Single Answer MCQ
Q-00123851
View explanation
Q17

Which statement correctly compares the two expressions: 9 - 3 and 2 × 3?

Single Answer MCQ
Q-00123852
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Q18

What is the result of 50 ÷ (5 + 5)?

Single Answer MCQ
Q-00123853
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Q19

What is greater: (5 + 5) × 2 or 20?

Single Answer MCQ
Q-00123854
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Q20

Which of the following is a common mistake when evaluating 2 × (3 + 5)?

Single Answer MCQ
Q-00123855
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Q21

Which expression has the value of 24?

Single Answer MCQ
Q-00123856
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Q22

Which expression shows that 20 is less than the sum of 15 and 10?

Single Answer MCQ
Q-00123857
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Q23

Which of these statements is true?

Single Answer MCQ
Q-00123858
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Q24

What is the value of 18 ÷ 3 × 2?

Single Answer MCQ
Q-00123859
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Q25

Which expression results in a value smaller than both 10 and 20?

Single Answer MCQ
Q-00123860
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Q26

If x + 7 = 15, what is the value of x?

Single Answer MCQ
Q-00123861
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Q27

Which statement is true about the expressions: 12 ÷ 3 and 6 × 2?

Single Answer MCQ
Q-00123862
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Q28

Which of the following correctly represents the expression for 'three times the sum of 2 and 4'?

Single Answer MCQ
Q-00123863
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Q29

If a = 2, which is greater: 3a + 4 or 5 + 2a?

Single Answer MCQ
Q-00123864
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Q30

Which expression mistakenly uses distributive property?

Single Answer MCQ
Q-00123865
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Q31

What is the value of the expression 8 + 7?

Single Answer MCQ
Q-00123866
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Q32

Which of the following expressions represents the total cost of 4 books costing ₹50 each?

Single Answer MCQ
Q-00123867
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Q33

Which operation gives a smaller value: 15 – 8 or 5 × 2?

Single Answer MCQ
Q-00123868
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Q34

Which of the following pairs of expressions are equal?

Single Answer MCQ
Q-00123869
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Q35

What expression represents Raja having 100 marbles and losing 25?

Single Answer MCQ
Q-00123870
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Q36

If Mallika spends ₹25 each day, how can we express her total spending over 7 days?

Single Answer MCQ
Q-00123871
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Q37

Which of the following expressions is equivalent to the expression 9 + 3 × 2?

Single Answer MCQ
Q-00123872
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Q38

If 4 × 9 = 36, which of the following expressions is not true?

Single Answer MCQ
Q-00123873
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Q39

What is the result of the expression 60 ÷ (2 + 1)?

Single Answer MCQ
Q-00123874
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Q40

Which of the following shows the correct use of the equality sign?

Single Answer MCQ
Q-00123875
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Q41

What is greater, 30 – 10 or 5 × 4?

Single Answer MCQ
Q-00123876
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Q42

Which expression represents the number 5 using multiplication?

Single Answer MCQ
Q-00123877
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Q43

What expression would you use to describe three times a number x?

Single Answer MCQ
Q-00123878
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Q44

Which arithmetic expression evaluates to 18?

Single Answer MCQ
Q-00123879
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Q45

In the expression 4 + (5 × 2), what should be calculated first?

Single Answer MCQ
Q-00123880
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Q46

What is the value of the expression 15 + 7?

Single Answer MCQ
Q-00123881
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Q47

Which expression is equivalent to 5 × 6?

Single Answer MCQ
Q-00123882
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Q48

If x = 3, what is the value of 2x + 5?

Single Answer MCQ
Q-00123883
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Q49

Which of the following expressions is greater: 12 + 9 or 24 ÷ 2?

Single Answer MCQ
Q-00123884
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Q50

What is the result of the expression 90 - (5 × 3)?

Single Answer MCQ
Q-00123885
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Q51

If 4a = 32, what is the value of a?

Single Answer MCQ
Q-00123886
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Q52

Which is the correct expression that represents 'three times a number n decreased by 4'?

Single Answer MCQ
Q-00123887
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Q53

What is the value of (20 ÷ 5) + (6 × 2)?

Single Answer MCQ
Q-00123888
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Q54

Which expression represents the result of reducing 100 by 15?

Single Answer MCQ
Q-00123889
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Q55

What is the value of 2 × (3 + 4)?

Single Answer MCQ
Q-00123890
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Q56

Which of the following statements is true: 18 ÷ 2 < 10 + 1?

Single Answer MCQ
Q-00123891
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Q57

If m = 10, what is the value of 3(m - 2)?

Single Answer MCQ
Q-00123892
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Q58

What is the expression for the product of a number x and 7, decreased by 5?

Single Answer MCQ
Q-00123893
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Q59

Which of the following evaluates to 0? 8 - 8, 5 ÷ 1, 10 - 10, or 6 - 6?

Single Answer MCQ
Q-00123894
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Q60

If the expression 9 - x is equal to 5, what is x?

Single Answer MCQ
Q-00123895
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Q61

What is the simplified form of 4(2x + 3)?

Single Answer MCQ
Q-00123896
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Q62

What is the value of the expression 3 × (4 + 2)?

Single Answer MCQ
Q-00123897
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Q63

If 5 × (x + 3) = 40, what is the value of x?

Single Answer MCQ
Q-00123898
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Q64

Which of the following expressions is equivalent to (x + 1) + (2 + x)?

Single Answer MCQ
Q-00123899
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Q65

Evaluate (6 + 4) ÷ 2 × 5.

Single Answer MCQ
Q-00123900
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Q66

Which expression equals 70?

Single Answer MCQ
Q-00123901
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Q67

What is the simplified form of 2 × (3 + 5) - 4?

Single Answer MCQ
Q-00123902
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Q68

Which of the following represents (a + b) × (a - b) correctly?

Single Answer MCQ
Q-00123903
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Q69

If (x + 5) - (3 - x) = 10, what is the value of x?

Single Answer MCQ
Q-00123904
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Q70

What is the result of 3 × (2 × 4) + 5?

Single Answer MCQ
Q-00123905
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Q71

How do you express 'the sum of x and 4, multiplied by 3' using brackets?

Single Answer MCQ
Q-00123906
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Q72

Which of the following is true regarding the expression (x - 2) + (2 - x)?

Single Answer MCQ
Q-00123907
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Q73

Simplify the expression 4 × (x + 3) - 2 × (x - 2).

Single Answer MCQ
Q-00123908
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Q74

If you add 5 × (2 + 3) and 3 × (4 - 1), what is the result?

Single Answer MCQ
Q-00123909
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Q75

Solve for y in the expression 2(y + 4) = 16.

Single Answer MCQ
Q-00123910
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Q76

What is the simplified result of (8 - (3 + 2)) × 2?

Single Answer MCQ
Q-00123911
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Q77

Which expression is equal to 15?

Single Answer MCQ
Q-00123912
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Q78

What is the value of the expression 5 × (2 + 3)?

Single Answer MCQ
Q-00123913
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Q79

If 8 × x = 64, what is the value of x?

Single Answer MCQ
Q-00123914
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Q80

Which expression is greater: 15 - 3 or 2 × 6?

Single Answer MCQ
Q-00123915
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Q81

Simplify the expression: 8 + 3 × 2.

Single Answer MCQ
Q-00123916
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Q82

If 5x + 3 = 28, what is the value of x?

Single Answer MCQ
Q-00123917
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Q83

Which expression is equal to 35?

Single Answer MCQ
Q-00123918
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Q84

Which of the following expressions is less than 20?

Single Answer MCQ
Q-00123919
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Q85

What is the value of 18 ÷ (6 ÷ 3)?

Single Answer MCQ
Q-00123920
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Q86

Which of the following pairs of expressions are equal? 7 + 5 and 10 - 3; 9 - 3 and 3 × 2; 6 × 2 and 12 - 2:

Single Answer MCQ
Q-00123921
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Q87

If an expression gives the same result as another when their values are switched (swapping), what property is being utilized?

Single Answer MCQ
Q-00123922
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Q88

In comparison of expressions, which sign shows that the left expression is less than the right expression?

Single Answer MCQ
Q-00123923
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Q89

Evaluate the expression: (3 × 4) + (5 - 2).

Single Answer MCQ
Q-00123924
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Q90

Identify the arithmetic expression that represents the total amount spent if a person spends ₹10 each day for 7 days.

Single Answer MCQ
Q-00123925
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Q91

Which expression simplifies to 50?

Single Answer MCQ
Q-00123926
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Q92

What is the value of the expression 14 + 8?

Single Answer MCQ
Q-00123927
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Q93

Which expressions result in the same value?

Single Answer MCQ
Q-00123928
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Q94

What is the expression that represents '7 less than 12'?

Single Answer MCQ
Q-00123929
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Q95

How can you express the total cost of 3 items priced at ₹45 each?

Single Answer MCQ
Q-00123930
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Q96

Which of the following is greater? 50 - 8 or 40 + 5?

Single Answer MCQ
Q-00123931
View explanation
Q97

If x = 3, what is the value of the expression 2x + 6?

Single Answer MCQ
Q-00123932
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Q98

What is the value of the expression 45 ÷ (5 + 4)?

Single Answer MCQ
Q-00123933
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Q99

Which expression equals 30 when simplified?

Single Answer MCQ
Q-00123934
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Q100

Which of the following is equal to the expression 9 - (3 × 2)?

Single Answer MCQ
Q-00123935
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Q101

If a = 2 and b = 5, what is the value of the expression a × b + 3?

Single Answer MCQ
Q-00123936
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Q102

Which expression correctly represents the phrase 'double a number and then add 10'?

Single Answer MCQ
Q-00123937
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Q103

What is the comparison of the expression 15 + 15 to 30?

Single Answer MCQ
Q-00123938
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Q104

Which expression is equivalent to 4 × (2 + 3)?

Single Answer MCQ
Q-00123939
View explanation
Q105

Simplify the expression: 70 - (30 - 10).

Single Answer MCQ
Q-00123940
View explanation
Q106

Which one of the following is NOT an arithmetic expression?

Single Answer MCQ
Q-00123941
View explanation
Q107

If x = 4, what is the value of 5x - 6?

Single Answer MCQ
Q-00123942
View explanation
Q108

Which of the following represents the sum of three consecutive integers?

Single Answer MCQ
Q-00123943
View explanation
Q109

If the expression 2x + 3y = 12 holds true, what could be the value of x if y = 2?

Single Answer MCQ
Q-00123944
View explanation
Q110

What is the value of the expression 7 + (3 + 4)?

Single Answer MCQ
Q-00123945
View explanation
Q111

Which expression simplifies to 9?

Single Answer MCQ
Q-00123946
View explanation
Q112

What is the result of 10 - (2 × 3)?

Single Answer MCQ
Q-00123947
View explanation
Q113

Simplify the expression (5 + 3) × 2.

Single Answer MCQ
Q-00123948
View explanation
Q114

If 8 + (x - 3) = 12, what is the value of x?

Single Answer MCQ
Q-00123949
View explanation
Q115

What is simplified form of 20 - (5 + 2)?

Single Answer MCQ
Q-00123950
View explanation
Q116

What is the value of 4 × (2 + 6) - 8?

Single Answer MCQ
Q-00123951
View explanation
Q117

Which of the following simplifies to 0?

Single Answer MCQ
Q-00123952
View explanation
Q118

What is the result of (4 + 6) - (3 + 1)?

Single Answer MCQ
Q-00123953
View explanation
Q119

Which of these statements is true about expressions?

Single Answer MCQ
Q-00123954
View explanation
Q120

If (x + 5) = 12, what is x?

Single Answer MCQ
Q-00123955
View explanation
Q121

Which expression equals 15?

Single Answer MCQ
Q-00123956
View explanation
Q122

What is the final value of 5 × (6 - 4) + 3?

Single Answer MCQ
Q-00123957
View explanation
Q123

Evaluate the expression 8 - (1 + 3) × 2.

Single Answer MCQ
Q-00123958
View explanation
Q124

If (x + 7) - 3 = 10, what is the value of x?

Single Answer MCQ
Q-00123959
View explanation
Q125

What is the value of the expression (10 - 5) + (3 × 4)?

Single Answer MCQ
Q-00123960
View explanation

Arithmetic Expressions Practice Worksheets

Download and practice Arithmetic Expressions worksheets to improve problem-solving accuracy and speed for CBSE Class 7 Mathematics exams.

Arithmetic Expressions - Practice Worksheet

This worksheet covers essential long-answer questions to help you build confidence in Arithmetic Expressions from Ganita Prakash for Class 7 (Mathematics).

Practice

Questions

1

Define an arithmetic expression and provide an example of how it is used in everyday life.

An arithmetic expression is a combination of numbers, variables, and operators (such as +, -, ×, ÷) that represent a value. For example, the expression 5 × 20 represents the total cost of 5 items priced at ₹20 each. We can evaluate this expression by multiplying, yielding ₹100.

2

Create five different arithmetic expressions that each equal the same value of your choice. Explain how each expression can be derived.

If I choose the value 12, I can create: 10 + 2, 15 - 3, 3 × 4, 24 ÷ 2, and 6 + 6. Each of these expressions uses different operations but ultimately they evaluate to 12. For instance, 3 × 4 calculates to 12 using multiplication.

3

Compare the expressions 23 + 9 and 30 + 2. Determine which is greater and explain your reasoning.

To compare, we evaluate both expressions: 23 + 9 = 32 and 30 + 2 = 32. Thus, they are equal. We can also think about the values before adding: 23 is less than 30, but 9 is equal to 2 added to 30, leading to the same total.

4

Explain how you would fill in the blanks to make the expressions equal, such as 13 + 4 = ____ + 6.

To find the blank, we first evaluate 13 + 4 to get 17. Then we want to find a number that, when added to 6, equals 17. Thus, 17 - 6 = 11. The completed expression is: 13 + 4 = 11 + 6.

5

Discuss the steps to arrange the expressions 67 – 19, 67 – 20, and 5 × 11 in ascending order based on their values.

First, we calculate each expression: 67 - 19 = 48, 67 - 20 = 47, and 5 × 11 = 55. To arrange them in ascending order, we list them by their values: 67 - 20 < 67 - 19 < 5 × 11 resulting in 47 < 48 < 55.

6

What is the difference between arithmetic expressions and numerical values? Provide examples.

Arithmetic expressions are combinations of numbers and operators, like 12 + 7, while numerical values are the results of evaluating those expressions, like 19. For instance, 10 - 3 is an arithmetic expression that evaluates to 7.

7

Show how the expression 113 – 25 can be compared to 112 – 24, illustrating with a real-world context.

Evaluating both gives 113 - 25 = 88 and 112 - 24 = 88 as well. Imagine Raja losing marbles versus Joy. Despite starting with different amounts, both lost amounts put them at equal values. Thus, they have the same number of marbles.

8

Construct an arithmetic expression that represents the total amount spent by a family on groceries, given they spend ₹50 every week for four weeks. Explain the process.

I can write the expression as 4 × 50 to find the total expenditure. Multiplying 4 (weeks) by 50 (spending each week) results in ₹200. This shows how to combine repeated amounts into one computation.

9

Create an expression that would need to be solved in order to find if someone has more apples, 15 + 5 or 14 + 7. Explain how you arrived at your answer.

We evaluate: 15 + 5 = 20 and 14 + 7 = 21. To notice which has more, we simply calculate both values. Thus, after evaluating, 14 + 7 is greater than 15 + 5.

10

Reflect on the importance of understanding arithmetic expressions in mathematical problem solving and decision making.

Understanding arithmetic expressions allows individuals to evaluate situations clearly, such as budgeting or processing information in grades. Not only do we learn operations, but we apply them to scenarios. For example, deciding which purchase is more affordable involves evaluating the right expressions.

Arithmetic Expressions - Mastery Worksheet

This worksheet challenges you with deeper, multi-concept long-answer questions from Arithmetic Expressions to prepare for higher-weightage questions in Class 7.

Mastery

Questions

1

Mallika spends ₹25 daily for lunch. Write an expression for her total spending for a week, and then create two different expressions that equal the same total spending. Explain your reasoning.

Total spending = 5 × 25 = ₹125. Alternate expressions: 100 + 25 or 150 - 25. Each represents the same total amount using different operations.

2

Ensure that the expressions below are equal by filling in the blanks: 13 + 4 = ____ + 6. What values can replace the blanks, and why do they result in equality?

Fill in the blank with 11: 13 + 4 = 11 + 6. Both simplify to 17. Use the property of equality to understand that both sides must yield the same value.

3

Compare the expressions 67 – 19 and 5 × 11. Determine which is greater and justify your answer with calculations.

67 - 19 = 48; 5 × 11 = 55. Since 55 > 48, 5 × 11 is greater. Students often misinterpret this by not performing the calculations properly.

4

Write down the various expressions that equal the value 12 using any of the four operations. Analyze why they are equivalent and provide at least three different examples.

Examples: 10 + 2, 15 - 3, 3 × 4. Despite different operations, they yield the same result. This highlights the commutative and associative properties.

5

Evaluate which is greater: 1023 + 125 or 1022 + 128. Provide a detailed explanation of your thought process using the details provided in the story context.

1023 + 125 = 1148; 1022 + 128 = 1150. Hence, 1022 + 128 > 1023 + 125 based on the incremental values. Key is recognizing how small changes affect totals.

6

Simplify the expressions 34 – ____ = 25 and determine the value of the blank. What method did you use to find this?

To simplify, 34 - x = 25 implies x = 9. This shows understanding of balance in an equation. The variable can shift based on the operation applied.

7

Design a problem where the two expressions 113 - 25 and 112 - 24 are equal, then explain why the equality holds. What mathematical properties support your reasoning?

Both simplify to 88. This demonstrates the conservation of value when one number is added and another subtracted equivalently. Being aware of this can prevent incorrect assumptions.

8

Create a two-step expression from the following data: If a shopping cart has 5 items, each costing ₹20 and a discount of ₹10 is offered. Write and simplify the expression then evaluate.

Expression: (5 × 20) - 10 = 100 - 10 = ₹90. Understanding multi-step problems is essential in arithmetic to arrive at the correct conclusion.

9

Analyze how the expressions 120 ÷ 3 and 67 – 20 compare in value. After calculating, discuss common misconceptions students might have.

120 ÷ 3 = 40; 67 - 20 = 47. Here, 67 - 20 > 120 ÷ 3. Many mistake subtraction seeing it as less impactful, while division can also yield smaller totals.

10

Formulate different expressions that yield the value of 25 using all four arithmetic operations. Explain each expression.

Examples include: 20 + 5, 30 - 5, 5 × 5, 100 ÷ 4. Understanding how to represent the same numerical value through various forms is key in algebra.

Arithmetic Expressions - Challenge Worksheet

The final worksheet presents challenging long-answer questions that test your depth of understanding and exam-readiness for Arithmetic Expressions in Class 7.

Challenge

Questions

1

Evaluate the implications of using expressions with negative numbers in real-life budgeting scenarios.

Explore how negative values affect total expenditure and savings. Provide examples such as debts and discounts.

2

Discuss how different arithmetic expressions can lead to the same result and the importance of this concept in mathematical problem-solving.

Demonstrate with various expressions equating to the same number. Analyze why understanding these variations enhances flexibility in problem-solving.

3

Analyze the importance of parentheses in arithmetic expressions by comparing results with and without them.

Present different expressions, one with parentheses and one without. Discuss variations in results and their implications.

4

Evaluate a scenario where you need to prove which of two complex arithmetic expressions is greater without calculating their final values.

Use logical reasoning or inequality properties to derive the answer. Provide clear step-by-step reasoning.

5

Reflect on how arithmetic expressions can model real life situations such as planning a party budget. Create different expressions for various expenses.

Write expressions for food, venue, and decorations. Discuss how simplifying these expressions can reveal insightful information about costs.

6

Explore the concept of balancing equations. If two expressions are equal, can you derive other related expressions that are also equal?

Provide an original equation, and create at least three new equations by manipulating it. Discuss validity.

7

Investigate the role of arithmetic expressions in calculating areas of geometric shapes. Provide examples with variable lengths.

Formulate expressions for area calculations. Analyze how altering dimensions affects area and which scenarios benefit from this approach.

8

Discuss the significance of expressing rational numbers in different forms (e.g., fractions, decimals) through arithmetic expressions.

Provide examples illustrating how converting between forms can solve various computational problems effectively.

9

Create a mathematical justification for why the order of numbers affects the computation in arithmetic expressions, providing examples.

Use the commutative and associative properties to explain your reasoning. Support with operational changes yielding different results.

10

Evaluate how algebraic linear expressions can simplify complex problems; apply to real-world contexts such as travel distance calculations.

Generate and manipulate expressions based on scenarios such as time taken at different speeds. Discuss effectiveness and efficiency.

Arithmetic Expressions Formula Sheet

Use this Class 7 Mathematics Arithmetic Expressions Formula Sheet for quick revision before school exams and CBSE exams. It brings together the important formulas, key concepts, and worked examples in one place so students can revise faster and download a printable PDF for offline study.

Important Formulas

1

Sum: a + b

a and b are numbers. This formula is used to calculate the total when two or more numbers are combined. For example, the sum of 2 and 3 is 5.

2

Difference: a - b

a and b are numbers. It represents the result of subtracting b from a. For instance, 7 - 2 equals 5.

3

Product: a × b

a and b are factors. This formula shows how to calculate the total of multiple equal groups, such as 3 groups of 4, which equals 12.

4

Quotient: a ÷ b

a is the dividend, and b is the divisor. This formula computes how many times b fits into a. For example, 20 ÷ 5 equals 4.

5

Equality: a = b

Indicates that a and b have the same value. For instance, when 10 + 2 = 12, it shows equality.

6

Comparative Operation: a < b or a > b

These symbols indicate that a is less than or greater than b. Useful for comparing values, such as 3 < 5 or 8 > 6.

7

Expressions with variables: ax + by = c

a, b are coefficients; x, y are variables, and c is a constant. This represents a linear relation between variables, common in algebra.

8

Combined Operations: a + b - c

Used to calculate an expression that involves multiple operations. For example, 5 + 3 - 1 evaluates to 7.

9

Order of Operations: PEMDAS

Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right). It determines the sequence in which operations are performed.

10

Distributive Property: a(b + c) = ab + ac

This shows that multiplying a number by a sum is the same as doing each multiplication separately. An example is 2(3 + 4) = 2×3 + 2×4.

Worked Examples

1

1 + 1 = 2

Demonstrates basic addition, showing that combining one and one results in two.

2

5 - 3 = 2

Illustrates subtraction, where subtracting three from five yields two.

3

4 × 3 = 12

Displays multiplication, indicating that four sets of three equal twelve.

4

15 ÷ 3 = 5

Shows division, where dividing fifteen by three equals five.

5

10 + 5 > 8

Indicates that the sum of ten and five is greater than eight, which is a comparison expression.

6

3 × 4 < 20

Indicates that twelve is less than twenty, demonstrating the use of multiplication in comparisons.

7

x + 3 = 7

A simple algebraic equation showing that adding three to x results in seven.

8

2x = 10

Indicates that multiplying x by two gives ten, leading to the conclusion that x = 5.

9

y - 4 = 6

Shows that if y subtracts four, the result equals six, so y must equal ten.

10

5 + x = 12

Indicates that adding five to x results in twelve, allowing for the interpretation that x = 7.

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Arithmetic Expressions Frequently Asked Questions

Master the fundamentals of arithmetic expressions in Class 7 Mathematics with insights from Ganita Prakash. Learn to evaluate, compare, and analyze mathematical expressions.

An arithmetic expression is a mathematical phrase made up of numbers, operators like +, -, ×, ÷, and sometimes variables. It describes operations that yield a specific value. For instance, '13 + 2' is an expression that evaluates to 15.
To evaluate an arithmetic expression, perform the operations in the correct order, often following PEMDAS/BODMAS rules (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction). For example, for '3 + 5 × 2', you multiply first to get 10, then add 3 to arrive at 13.
Yes, different arithmetic expressions can yield the same value. For instance, the expressions '10 + 2', '15 - 3', and '24 ÷ 2' all evaluate to the value of 12, illustrating that multiple combinations can express the same result.
Expressions can be compared using equality symbols: '=', '<', and '>'. These symbols indicate whether one expression equals, is greater than, or is less than another. For example, '10 + 2 > 7 + 1' shows that the first expression has a greater value.
Writing simple expressions involves using numbers and basic arithmetic operators to represent a mathematical situation. For example, if a person spends ₹25 daily for lunches, the total weekly spending can be expressed as '5 × 25'.
Brackets in expressions dictate the order of operations. They indicate which calculations should be performed first. For example, in the expression '(2 + 3) × 4', the addition within the brackets is performed first, resulting in 5, which is then multiplied by 4 to yield 20.
Terms in expressions are individual parts separated by '+' or '−' symbols. For instance, in the expression '3x + 5y - 2', '3x', '5y', and '−2' are all distinct terms. Understanding terms helps in simplifying and calculating expressions correctly.
Removing brackets from expressions involves applying the appropriate operations according to the distributive property. For instance, in '2 × (3 + 4)', you would multiply each term inside the bracket by 2, resulting in '6 + 8' or '14'.
Comparing expressions allows us to understand relative values and make informed decisions based on mathematical arguments. It helps in solving problems and understanding scenarios where one value may be more significant than another.
To arrange expressions in order of value, evaluate each expression first and then compare their results. For example, to arrange '(67 – 19)', '(67 – 20)', '(35 + 25)', '(5 × 11)', and '(120 ÷ 3)', evaluate each to find their respective values and sort them from least to greatest.
Further exploration of expressions involves examining more complex or creative ways to formulate and manipulate expressions. This might include identifying patterns, solving equations involving multiple expressions, or even applying expressions to real-world problems.
In comparing '1023 + 125' and '1022 + 128', understand the scenario behind it. Raja has more marbles initially but Joy receives more more than Raja today. Therefore, by reasoning, we find that '1022 + 128' exceeds '1023 + 125' based on their respective growths.
The value of an expression is influenced by the numbers and operations involved. For instance, changing any number or operator can yield a different value. For example, changing '3 + 5' to '3 × 5' changes the value from 8 to 15.
Students can practice writing expressions by creating real-life scenarios involving quantities. For example, if a student knows they have 10 apples and gives away 2, they can write the expression '10 - 2' to represent the remaining apples.
The equality sign '=' indicates that both sides of an expression have the same value. It highlights relationships in mathematics, allowing for comparisons. For example, in '13 + 2 = 15', it shows that both quantities represent the same amount.
Arithmetic operators are symbols used to perform mathematical operations. Common operators include addition (+), subtraction (−), multiplication (×), and division (÷). Each operator serves a specific function in evaluating and simplifying expressions.
Numerical values are the outcomes of evaluating expressions. For instance, for the expression '5 + 3', the numerical value is obtained by performing the addition, resulting in the value of 8, which represents the summed total of both numbers.
Expressions can vary based on the number of terms and operations involved. A simple expression might only involve two numbers and one operator, like '8 + 5', while a complex expression could combine several operations and brackets, like '(3 + 2) × (4 - 1)'.
Brackets in numerical calculations dictate the order of operations, ensuring certain calculations are prioritized. For example, in the expression '2 × (3 + 4)', the calculation inside the brackets must be done first, affecting the final result.
Students can use various tools to assist in learning expressions, such as calculators for evaluating expressions, algebra tiles for visualizing terms and operations, and educational websites that offer practice problems and interactive lessons.
Understanding arithmetic expressions is vital for developing problem-solving and analytical skills in mathematics. These principles form the groundwork for higher-level mathematics, enabling students to confidently tackle more complex equations and real-world applications.
Strategies for learning to evaluate expressions include practicing with concrete examples, using visual aids like charts, applying the order of operations consistently, and performing step-by-step calculations to ensure clarity and accuracy throughout the process.

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Arithmetic Expressions Flashcards

Revise key terms and definitions from Arithmetic Expressions with interactive flashcards. Quick recall practice for CBSE Class 7 Mathematics.

These flash cards cover important concepts from Arithmetic Expressions in Ganita Prakash for Class 7 (Mathematics).

1/19

Define arithmetic expression.

1/19

An arithmetic expression is a mathematical phrase that combines numbers and operations (like +, -, ×, ÷) to represent a value.

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2/19

What is the value of 13 + 2?

2/19

The value of the expression 13 + 2 is 15.

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3/19

What does the '=' sign represent?

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3/19

The '=' sign denotes equality, showing that an arithmetic expression equals its value, e.g., 13 + 2 = 15.

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4/19

How to express total lunch expense in a week?

4/19

Mallika's total lunch expense from Monday to Friday is expressed as 5 × 25 (5 days × ₹25 per day).

5/19

How can you express the number 12?

5/19

The number 12 can be expressed as 10 + 2, 15 - 3, 3 × 4, and 24 ÷ 2.

6/19

What signs are used to compare expressions?

6/19

Expressions can be compared using '=', '>', and '<' based on their values.

7/19

Which is greater: 10 + 2 or 7 + 1?

7/19

10 + 2 (value is 12) is greater than 7 + 1 (value is 8).

8/19

Which is less: 13 - 2 or 4 × 3?

8/19

13 - 2 (value is 11) is less than 4 × 3 (value is 12).

9/19

Complete: 13 + 4 = ____ + 6.

9/19

The answer is 11, because 13 + 4 = 17 and 11 + 6 = 17.

10/19

Order these expressions: 67 - 19, 67 - 20, 35 + 25.

10/19

In ascending order: 67 - 20, 67 - 19, 35 + 25.

11/19

How do scenarios help compare expressions?

11/19

By imagining real situations, we can compare expressions without calculating, such as comparing marbles.

12/19

Which is greater: 1023 + 125 or 1022 + 128?

12/19

1023 + 125 is less than 1022 + 128, because Joy ends up with more marbles.

13/19

Which is equal: 113 - 25 or 112 - 24?

13/19

Both expressions equal to 88, showing they are equal.

14/19

What operations are used in arithmetic expressions?

14/19

The four basic operations are addition (+), subtraction (-), multiplication (×), and division (÷).

15/19

Why can different expressions have the same value?

15/19

Different combinations of numbers and operations can result in the same numerical value.

16/19

What does 5 × 25 represent?

16/19

It represents '5 times 25', equaling ₹125, Mallika's total lunch expense in a week.

17/19

What does 7 + 1 > 10 + 2 indicate?

17/19

It indicates that 7 + 1 is greater than 10 + 2, based on their calculated values.

18/19

What does '<' signify?

18/19

'<' signifies that one expression evaluates to a lesser value than another.

19/19

What's a common mistake in expressions?

19/19

A common mistake is miscalculating values; always check your arithmetic!

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