Working with Fractions

Q-00124418

If a car travels 2/5 kilometers in 1 hour, how far will it travel in 2 hours?

Q-00124419

What is the result of multiplying 5 by 4/7?

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How much is 3/4 of 1/2?

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A tortoise moves 1/6 kilometer in one hour. How far will it travel in 4 hours?

Q-00124422

What is the product of 7/8 and 2?

Q-00124423

A chef uses 3/5 of a cup of sugar for one cake. How much sugar is needed for 3 cakes?

Q-00124424

If you multiply 1/3 by 9, what is the result?

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View all 46 Working with Fractions questions

What is 5/6 multiplied by 4/5?

How much is 3/8 multiplied by 16?

A runner completes 3/10 of the marathon in 1 hour. How far does he run in 4 hours?

If an employee works 3/5 of an hour at a task, how much time is spent in 10 hours of tasks?

Calculate the value of 2/3 × 3/4.

A student answered 3/5 of the questions correctly. If there were 50 questions, how many did he get right?

What is the result of 5/8 × 2/3?

What do you get when you multiply 7/9 by 3/4?

What is the result of dividing 1/2 by 1/4?

How do you solve 3/5 ÷ 2?

If you have 3/4 of a pizza and you want to divide it among 3 friends, how much does each friend get?

Which is equivalent to 1 ÷ 1/3?

Find the result of 5 ÷ 1/5.

What is the answer to (2/3) ÷ (1/4)?

When you divide 7/10 by 2/5, what do you get?

If a recipe requires 3/4 cup of sugar and you want to make half the recipe, how much sugar do you need?

Which of the following is the same as 1/2 ÷ 1/8?

If you divide 1/3 by 1/6, what is the result?

What does 4 ÷ (3/8) equal?

Calculate the result of dividing 5/6 by 2/3.

How much is 2/5 ÷ 1/2?

If a car travels 2/3 mile in 1/6 hour, how far does it travel in one hour?

Divide 9/10 by 3/5. What is the result?

If a farmer has 5 acres of land and distributes 2/5 acre to each of his 7 grandchildren, how much land does he distribute in total?

A worker is paid ₹150 for 1 hour of work. How much will he earn for 2/3 of an hour?

A school distributes 1/4 cake to each of its 8 students. How much cake do they use in total?

If Aaron walks 3 km in 1 hour, how far will he walk in 1/3 hour?

A recipe requires 2/3 cup of sugar. If you want to make 4 batches, how much sugar will you need?

If a tortoise walks 1/4 km in an hour, how far does it walk in 5 hours?

How much distance does Aaron cover in 3/5 hours if he walks at 3 km per hour?

How much will 1 1/2 hours of internet time cost if 1 hour costs ₹12?

Which is the equivalent of 2/3 of 9?

What is the distance Aaron would cover in 1 1/4 hours if he walks at a speed of 4 km/h?

If a car travels 3 km in 1/4 hour, how far does it travel in 1 hour?

A gardener planted 5 seeds and estimated each seed would produce 2/5 of a flower. How many flowers will there be in total?

If Jenny drank 2/3 of a liter of water each day, how much will she drink in 5 days?

How much did 2 hours and 1/2 hour of a service cost if the service costs ₹60 per hour?

If a cyclist travels at a speed of 12 km/h, how far will she travel in 1/2 hour?

Q-00124463

Practice Questions Worksheets Revision Notes Flashcards Download PDFs

Working with Fractions Practice Worksheets

Download and practice Working with Fractions worksheets to improve problem-solving accuracy and speed for CBSE Class 7 Mathematics exams.

Working with Fractions - Mastery Worksheet

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

Mastery

Questions

If Aaron walks 3 km in 1 hour and his tortoise walks 1/4 km in 1 hour, how much further does Aaron walk than his tortoise in 5 hours? Show your calculations and reasoning.

Distance Aaron walks in 5 hours = 5 × 3 = 15 km. Distance tortoise walks in 5 hours = 5 × 1/4 = 5/4 km = 1.25 km. Difference = 15 km - 1.25 km = 13.75 km.

A farmer distributes 2/3 acre of land to each of her 5 grandchildren. If one grandchild decides to give back 1/3 of the land he received, how much land does he end up with? Include all steps in your calculations.

Land distributed to each grandchild = 2/3 acre. Total land for 5 grandchildren = 5 × 2/3 = 10/3 acres. Land returned by one grandchild = (1/3) of (2/3) = 2/9 acres. Total land left with that grandchild = 2/3 - 2/9 = 6/9 - 2/9 = 4/9 acres.

If Aaron can walk 3 km in 1 hour, how far can he walk in 1 1/4 hours? Convert the mixed number to an improper fraction and show all calculations.

Convert 1 1/4 hours to improper fraction: 1 1/4 = 5/4 hours. Distance in 5/4 hours = 5/4 × 3 = 15/4 km = 3.75 km.

For a running event, a participant runs at a speed of 2/3 of a km in 2/5 of an hour. How much distance can he cover in 1 hour? Use multiplication of fractions to find your answer.

Speed = 2/3 km in 2/5 hours. To find speed per hour, calculate = (2/3) ÷ (2/5) = (2/3) × (5/2) = 5/3 km/hour.

During a school event, a cake is divided into 12 equal pieces, where 1/4 of the cake is left over. How many pieces were eaten? Show both the fraction and whole number representations.

Total cake = 12 pieces. Leftover = 1/4 of full cake = 3 pieces (12 × 1/4). Pieces eaten = 12 - 3 = 9 pieces.

A shopkeeper sells a chocolate bar for ₹8. If he sells 1/3 of a bar for ₹X, what will be the total earnings if he sells 4 such pieces? Express X in terms of 8.

Price for 1 bar = ₹8, thus price for 1/3 bar = 8/3. Selling 4 pieces gives total earnings = 4 × (8/3) = 32/3 = ₹10.67.

In a fruit garden, a tree gives 1/6 of its apples every week. If there are 48 apples on a tree, how many apples are left after 3 weeks? Use fractions in your calculations.

Apples per week = 1/6 of 48 = 8 apples. After 3 weeks = 3 × 8 = 24 apples taken. Apples left = 48 - 24 = 24 apples.

If a teacher spends 1/2 of an hour grading papers and 1/3 of an hour conducting a quiz, how much total time does she spend? Find a common denominator to show your solution.

Common denominator for 1/2 and 1/3 is 6. Thus, 1/2 = 3/6 and 1/3 = 2/6. Total time = 3/6 + 2/6 = 5/6 hours.

A school project requires 3/4 of a liter of paint for each mural. If there are 4 murals and each has a different requirement, how much paint is needed in total for all? Present your workings.

Total paint needed = 4 × (3/4) = 3 liters since = 4 × 3 = 12/4 = 3 liters.

If a product costs ₹120 and there’s a discount of 1/4 on it, what will be the final price after applying the discount? Show all calculations to find the final price.

Discount = 1/4 of ₹120 = ₹30. Final price = ₹120 - ₹30 = ₹90.

Working with Fractions - Challenge Worksheet

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

Challenge

Questions

Aaron walks 3 kilometers in 1 hour. If he decides to walk at a pace of 4/5 of his usual speed for 2 hours, how far will he walk? Discuss implications of speed variation in real-life scenarios.

Evaluate the adjusted speed and relate it to distance covered. Discuss scenarios where speed fluctuation is critical, like emergencies.

A farmer distributes 1/2 acre of land among 4 grandchildren. If each grandchild gets an additional 1/4 acre, calculate the total land distributed. Evaluate this distribution process.

Outline the calculation steps and analyze the fairness of land distribution compared to each child's needs.

Lucy buys 3/4 kg of flour and uses 1/2 kg for a cake. How much flour is left? Discuss the importance of understanding measurements in cooking.

Show calculations clearly and explain why precise measurements are crucial for successful recipes.

If a tortoise walks 1/3 km in 1 hour, how far can it walk in 4 1/2 hours? Analyze how patience can be a virtue in both literal and metaphorical journeys.

Calculate total distance and discuss how persistence leads to gradual achievements in life.

In the context of a recipe, if 2/3 cup of sugar is needed for a cake, how much would be needed for 5 cakes? Debate the effects of altering ingredient quantities on taste.

Perform the necessary calculations and evaluate how ingredient proportions influence final product quality.

An internet service costs ₹12 per hour. If a user utilizes 1 1/3 hours, calculate the total cost. Discuss how managing internet usage can reflect budgeting skills.

Demonstrate calculations and evaluate financial management strategies that promote effective spending.

A recipe requires 1/4 cup of oil for a single batch. If a chef prepares 7 batches, how much oil will he need? Assess implications of ingredient scaling up in cooking.

Outline total oil calculations and discuss scaling recipes in different contexts.

A runner completes 5 km in 1 hour. If she increases her pace by 1/4 km/hr, how long will it take her to run 15 km? Evaluate how small changes can impact long-term goals.

Calculate the new time and discuss how marginal improvements contribute significantly in the long run.

If 2/5 of a tank is filled with water and then you add 3/10 of the tank’s capacity, how much is filled? Explore the concept of addition of fractions using different denominators.

Discuss calculation steps and relate this to the importance of understanding fractions in everyday situations.

A student saves 1/6 of his pocket money weekly. If he aims to save ₹60 for a video game, how many weeks will he need to save? Discuss the value of saving and financial planning.

Calculate the total number of weeks and analyze financial literacy and the implications of saving.

Working with Fractions - Practice Worksheet

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

Practice

Questions

Define the multiplication of fractions and explain the process involved with an example.

Multiplying fractions involves taking the product of the numerators and the product of the denominators. For example, to find 2/3 × 3/4, multiply 2 × 3 = 6 (numerators) and 3 × 4 = 12 (denominators), yielding 6/12, which simplifies to 1/2. This method provides a systematic approach to fraction multiplication.

How can you explain to a classmate how to find the distance walked by Aaron in 2/5 hours?

To find the distance walked by Aaron in 2/5 hours, start by noting he walks 3 km in 1 hour. Calculate the distance for 1/5 hour: 3/5 km. Then for 2/5 hours, multiply by 2: 2 × 3/5 = 6/5 km. Thus, Aaron walks 6/5 km, or 1 1/5 km.

Explain the significance of converting mixed numbers to improper fractions using the example of 1 1/4 hours.

Converting mixed numbers helps simplify calculations in fraction multiplication. For 1 1/4 hours, convert it to an improper fraction: 1 × 4 + 1 = 5/4. This is used to compute cost by multiplying against the rate. Understanding this process aids in effectively handling fractional calculations.

A farmer distributed 2/3 acre of land to each of his 5 grandchildren. Calculate the total land given and explain your reasoning.

Total land = 5 × 2/3 = 10/3 acres. This means the farmer gave each grandchild 2/3 acre, and by multiplying with the number of grandchildren, you utilize the multiplication of fractions method. This total is an improper fraction, which can be interpreted in whole parts.

Discuss how to calculate the cost of 1 1/4 hours of internet time if 1 hour costs ₹8.

First convert 1 1/4 to 5/4. The cost is then calculated as (5/4) × 8 = 5 × 2 = ₹10. Understanding the conversion of mixed numbers streamlines multiplication and cost calculations, providing practical knowledge.

What does it mean to divide fractions? Illustrate with the example of dividing 1/2 by 1/3.

Dividing fractions involves multiplying by the reciprocal. To divide 1/2 by 1/3, multiply 1/2 by 3/1: (1 × 3)/(2 × 1) = 3/2. This result indicates how many halves fit into a third. It's crucial for understanding relative sizes of fractions.

Generate a real-world scenario for multiplying a fraction by a whole number.

For instance, if a chef uses 3/4 of a cup of sugar for one batch of cookies and makes 5 batches, the total sugar used is 5 × 3/4 = 15/4 cups, or 3 3/4 cups. This real-world application exemplifies the practical usage of multiplying fractions, aiding comprehension.

Explain how to add two fractions with different denominators and provide an example.

To add fractions like 1/4 and 1/3, you must find a common denominator, which is 12 in this case. Convert them: 1/4 = 3/12 and 1/3 = 4/12, leading to 3/12 + 4/12 = 7/12. This approach emphasizes why a common denominator is necessary for addition.

Introduce the concept of reciprocals and demonstrate with an example.

The reciprocal of a number is 1 divided by that number. For example, the reciprocal of 2/5 is 5/2. This concept is crucial when dividing fractions, as understanding how to form and use reciprocals facilitates many operations involving fractions.

Describe a method for simplifying fractions and why it is important.

Simplifying fractions involves dividing both the numerator and denominator by their greatest common divisor (GCD). For 8/12, both can be divided by 4, simplifying it to 2/3. Simplification makes calculations easier and is essential for providing clean, understandable answers.

Working with Fractions Formula Sheet

Use this Class 7 Mathematics Working with Fractions 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

Distance = Speed × Time

Distance (km) is found by multiplying Speed (km/h) by Time (h). Useful in determining how far an object travels given its speed and time of travel.

Distance covered in t hours = t × (S)

Where S is speed (km/h) and t is time (h). This formula calculates the total distance based on speed and time.

Distance for fractions: Distance = (Fraction of Time) × (Speed)

For calculating distance when time is a fraction, multiply the fraction by speed.

Cost = Rate × Time

Cost (₹) is determined by multiplying Rate (₹/h) by Time (h). Useful for budgeting expenses based on time spent.

Conversion: Mixed Number to Improper Fraction

Convert by multiplying the whole number by the denominator and adding the numerator. Example: 1 1/4 = (1×4 + 1)/4 = 5/4.

Multiplying a Whole Number by a Fraction

When multiplying a whole number by a fraction a/b, use (Whole Number × a)/b to find the product.

a/b × c/d = (a × c) / (b × d)

This formula describes how to multiply two fractions together, where a, b, c, d are integers.

Adding Fractions: a/b + c/d = (ad + bc) / (bd)

To add fractions, find a common denominator and adjust the numerators accordingly.

Subtracting Fractions: a/b - c/d = (ad - bc) / (bd)

Similar to addition, but subtract the numerators after finding a common denominator.

Cost of services: Total Cost = Number of Units × Cost per Unit

This formula helps calculate the total expenditure on services based on the quantity and cost per unit.

Worked Examples

Distance in 5 hours: 5 × 3 = 15 km

If a person walks 3 km in 1 hour, in 5 hours the total distance will be 5 times this value.

Distance in 3 hours for Tortoise: 3 × 1/4 = 3/4 km

Calculates the distance a tortoise can walk if its speed is 1/4 km/h over 3 hours.

Distance in 1/5 hours: 1/5 × 3 = 3/5 km

Shows how to calculate the distance covered when the time is a fraction of an hour.

Total Distance in 2/5 hours: 2/5 × 3 = 6/5 km

Calculates the total distance when walking time is a multiple of a fraction.

Total Land = 5 × 2/3 = 10/3 acres

Calculates the total land distributed to grandchildren if each gets 2/3 acre.

Cost of Internet Time: Cost = 8 × (5/4) = 10 ₹

Determines the cost for 1 1/4 hours of internet given a rate of ₹8 per hour.

Cost = Units × Rate (Rate = 8 ₹)

General formula for calculating costs when the price per unit is known.

a/b × c = (a × c) / b

Describes the multiplication of a fraction by a whole number, adjusting the numerator.

Cost of n hours = n × (Rate)

If Rate is given, this formula allows for quick calculation of total cost for n hours.

Total Distance = Sum of Parts = 3 + 3 + ... (n times)

Utilized for calculating the total distance as a repeated sum of constant speed over time.

Explore More Working with Fractions Resources

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Working with Fractions Frequently Asked Questions

Discover the chapter 'Working with Fractions' for Class 7 in Ganita Prakash, focusing on multiplication and division of fractions with real-life applications. Ideal for students to master fundamental math skills.

QWhat is the multiplication of fractions?

Multiplication of fractions involves multiplying the numerators together and the denominators together. For example, if you want to multiply 3/4 by 2/3, you calculate (3 × 2) / (4 × 3) = 6/12, which simplifies to 1/2.

QHow do you calculate the distance traveled when given a fraction of time?

To find the distance traveled given a fraction of time, multiply the rate of travel by the fraction of time. For instance, if someone walks at 3 km per hour for 1/5 of an hour, you calculate 3 × (1/5) = 3/5 km.

QCan we multiply a whole number by a fraction?

Yes, you can multiply a whole number by a fraction. This involves treating the whole number as a fraction, such as 5 being 5/1, and then applying the multiplication rules for fractions. For example, 5 × 2/3 = (5 × 2) / 3 = 10/3.

QWhat is an example of dividing fractions?

To divide fractions, you multiply the first fraction by the reciprocal of the second. For instance, to divide 1/2 by 1/4, you multiply 1/2 by 4/1, resulting in (1 × 4) / (2 × 1) = 4/2, which simplifies to 2.

QHow can word problems help with understanding fractions?

Word problems provide context that helps students visualize how fractions are used in real life. They can illustrate practical applications, like distributing land or calculating costs, helping students grasp the relevance and importance of fractions.

QWhat does 1/4 of a kilometer represent?

1/4 of a kilometer represents a distance that is a quarter of the full kilometer, equal to 250 meters. It is often used in scenarios where smaller measurements are necessary, such as walking distances.

QHow do you convert a mixed fraction like 1 1/4 to an improper fraction?

To convert a mixed fraction like 1 1/4 to an improper fraction, multiply the whole number by the denominator and add the numerator. For 1 1/4, it would be (1 × 4 + 1) / 4 = 5/4.

QWhat steps do you take to multiply fractions by whole numbers?

To multiply a fraction by a whole number, convert the whole number into a fraction (e.g., 5 becomes 5/1), then multiply the numerators to get the new numerator and the denominators remain the same. For example, 5 × 2/3 = 10/3.

QWhat's the importance of understanding fractions in real life?

Understanding fractions is crucial in practical situations like cooking, budgeting, and measuring. It enhances problem-solving skills, allowing individuals to manage ratios, proportions, and quantities effectively in everyday life.

QHow do you add fractions with the same denominator?

To add fractions with the same denominator, simply add the numerators while keeping the denominator unchanged. For example, 2/5 + 3/5 = (2 + 3)/5 = 5/5, which simplifies to 1.

QWhat are some common mistakes when working with fractions?

Common mistakes include forgetting to simplify results, incorrectly converting between mixed and improper fractions, and misapplying the rules of operations such as the addition of unlike fractions. Care and practice help avoid these errors.

QWhat does it mean to simplify a fraction?

Simplifying a fraction means reducing it to its simplest form, where the numerator and denominator have no common factors other than 1. This makes the fraction easier to understand and work with, for example, 6/8 simplifies to 3/4.

QHow do you subtract fractions?

To subtract fractions, ensure they have a common denominator. Subtract the numerators and keep the denominator the same. For instance, 4/5 - 1/5 = (4 - 1)/5 = 3/5.

QCan fractions be used to measure quantities?

Yes, fractions are often used to measure quantities, whether it’s dividing a whole into parts (like splitting 1 kg of fruit), or indicating a portion of an amount needed for recipes or budget calculations.

QHow does understanding fractions aid in calculation of area?

Understanding fractions is critical in calculating area, especially in composite shapes. When determining areas of rectangles and triangles, fractions help in dividing and combining calculations effectively.

QWhat is the relationship between fractions and decimals?

Fractions and decimals represent the same values in different forms. For example, 1/2 as a decimal is 0.5. Understanding both aids in mathematical flexibility and problem-solving across various contexts.

QHow can I practice working with fractions?

Practicing with fractions can be done through various methods such as worksheets, online quizzes, and real-world problem-solving scenarios. Engaging with different types of problems helps reinforce understanding and application.

QWhy is it important to learn about ratios with fractions?

Learning about ratios with fractions is essential as it helps understand relationships between quantities. This knowledge aids in making informed decisions in situations like cooking and financial planning where proportionality is key.

QWhat is a reciprocal in fractions?

A reciprocal of a fraction is obtained by flipping its numerator and denominator. For example, the reciprocal of 2/3 is 3/2. Reciprocals are particularly important in division of fractions.

QWhat's an example of using fractions in budgeting?

In budgeting, fractions may be used to allocate funds. For instance, if 1/3 of your budget is for food, and your total budget is $300, you'd allocate $100 for food (1/3 of $300 = $100).

QHow do you find the least common denominator?

To find the least common denominator (LCD), list the multiples of the denominators and determine the smallest common multiple. For example, for 1/4 and 1/6, the LCD is 12.

QWhat is the significance of fractions in cooking?

Fractions play a crucial role in cooking as ingredients often need to be measured in parts. Recipes frequently require fractions to denote portions, making it essential for precise culinary results.

QHow can I check if my fraction work is correct?

To check fraction work, re-evaluate calculations by following the same steps, simplifying results, and applying estimation for reasonableness. If the re-calculated result closely matches the original, it's likely correct.

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