Arithmetic Expressions – Formula & Equation Sheet
Essential formulas and equations from Ganita Prakash, tailored for Class 7 in Mathematics.
This one-pager compiles key formulas and equations from the Arithmetic Expressions chapter of Ganita Prakash. Ideal for exam prep, quick reference, and solving time-bound numerical problems accurately.
Formulas
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.
Difference: a - b
a and b are numbers. It represents the result of subtracting b from a. For instance, 7 - 2 equals 5.
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.
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.
Equality: a = b
Indicates that a and b have the same value. For instance, when 10 + 2 = 12, it shows equality.
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.
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.
Combined Operations: a + b - c
Used to calculate an expression that involves multiple operations. For example, 5 + 3 - 1 evaluates to 7.
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.
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.
Equations
1 + 1 = 2
Demonstrates basic addition, showing that combining one and one results in two.
5 - 3 = 2
Illustrates subtraction, where subtracting three from five yields two.
4 × 3 = 12
Displays multiplication, indicating that four sets of three equal twelve.
15 ÷ 3 = 5
Shows division, where dividing fifteen by three equals five.
10 + 5 > 8
Indicates that the sum of ten and five is greater than eight, which is a comparison expression.
3 × 4 < 20
Indicates that twelve is less than twenty, demonstrating the use of multiplication in comparisons.
x + 3 = 7
A simple algebraic equation showing that adding three to x results in seven.
2x = 10
Indicates that multiplying x by two gives ten, leading to the conclusion that x = 5.
y - 4 = 6
Shows that if y subtracts four, the result equals six, so y must equal ten.
5 + x = 12
Indicates that adding five to x results in twelve, allowing for the interpretation that x = 7.
