Working with Fractions - Mastery Worksheet
Advance your understanding through integrative and tricky questions.
This worksheet challenges you with deeper, multi-concept long-answer questions from Working with Fractions to prepare for higher-weightage questions in Class 7.
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
Push your limits with complex, exam-level long-form questions.
The final worksheet presents challenging long-answer questions that test your depth of understanding and exam-readiness for Working with Fractions in Class 7.
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.
