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Quizzes > High School Quizzes > Mathematics

Word Problems: Dividing Whole Numbers by Fractions Quiz

Excel at fraction divided by whole number problems today

Difficulty: Moderate
Grade: Grade 5
Study OutcomesCheat Sheet
Colorful paper art promoting the Fraction Division Challenge for middle school students.

Samantha has 12 cups of water. If a science experiment uses 1/4 cup of water per trial, how many trials can she perform?
48
12
24
36
Dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, 12 multiplied by 4 equals 48, which is the number of trials.
John has 10 pies. If each pie is divided into pieces that are 1/2 of a whole pie, how many pieces can he get?
20
10
15
25
Dividing 10 by 1/2 is the same as multiplying 10 by 2. Thus, John gets 20 pieces in total.
A baker with 9 cups of milk makes pudding servings that require 1/3 cup of milk each. How many servings can be made?
27
18
24
21
Dividing by 1/3 is equivalent to multiplying by 3. Therefore, 9 multiplied by 3 equals 27 servings.
If a rope is 7 yards long and it is cut into pieces each measuring 1/7 yard, how many pieces are there?
49
14
21
28
Dividing by 1/7 means multiplying 7 by 7, resulting in 49 pieces. This illustrates the usefulness of reciprocals in fraction division.
A car travels 100 miles on a trip. If each lap around the track is 1/10 mile, how many laps did the car complete?
1000
100
500
1100
Dividing 100 by 1/10 is the same as multiplying 100 by 10. Thus, the car completes 1000 laps.
If there are 24 cupcakes and each serving is 3/8 of a cupcake, how many servings can you get?
64
56
72
48
To solve 24 divided by 3/8, multiply 24 by the reciprocal 8/3, resulting in 64 servings.
A gardener has 18 meters of ribbon. If each flower arrangement uses 2/3 meter of ribbon, how many arrangements can be made?
27
24
30
21
Multiplying 18 by the reciprocal of 2/3 (which is 3/2) gives 27 arrangements. This conversion is key in fraction division.
Carlos has 16 pencils. If each art project requires 2/5 of a pencil, how many projects can be completed?
40
32
35
45
Dividing 16 by 2/5 results in 16 multiplied by 5/2, which equals 40 projects. Multiplying by the reciprocal simplifies the operation.
A water tank holds 48 liters. If each watering can holds 2/3 liters, how many watering cans can be filled?
72
64
68
78
By multiplying 48 by the reciprocal of 2/3 (which is 3/2), you get 72. This shows how many cans can be filled.
In a recycling drive, 40 bottles are collected. If each artwork requires 4/5 of a bottle, how many artworks can be made?
50
45
55
60
Divide 40 by 4/5 by multiplying 40 by 5/4, which results in 50 artworks. Understanding reciprocal multiplication is crucial here.
A teacher has 36 cookies to share. If each student receives 1/6 of a cookie, how many students receive cookies?
216
180
200
192
Dividing 36 by 1/6 is equivalent to multiplying 36 by 6, resulting in 216 students receiving cookies.
A gardener has 20 feet of fencing. If each section of the fence is 1/5 foot long, how many sections can be built?
100
90
80
110
Multiplying 20 by 5 (the reciprocal of 1/5) gives 100 sections. This problem illustrates the utility of dividing by a fraction.
A painter has 27 cans of paint. If each art piece requires 3/5 can of paint, how many art pieces can be painted?
45
40
42
50
Dividing 27 by 3/5 is the same as multiplying 27 by 5/3, which equals 45 art pieces. The reciprocal is key in solving this problem.
Lilly is making ribbon garlands. If she has 48 yards of ribbon and uses 3/8 yard per section, how many sections can she make?
128
120
136
144
Multiplying 48 by the reciprocal of 3/8 (which is 8/3) gives 128 sections. This is a straightforward application of dividing by a fraction.
A music teacher has 84 notes to distribute. If each student gets 2/7 of a note, how many students can be given a note?
294
280
300
312
Dividing 84 by 2/7 is done by multiplying 84 by 7/2, resulting in 294 students. This emphasizes the idea of using reciprocals in division.
A restaurant uses 30 pounds of cheese to make mini pizzas. If each mini pizza requires 5/8 pound of cheese, how many mini pizzas can be made?
48
40
42
52
To find the number of mini pizzas, divide 30 by 5/8, which is the same as multiplying 30 by 8/5, yielding 48.
Linda has 54 slices of bread to make sandwiches. If each sandwich uses 2/3 slice of bread, how many sandwiches can she prepare?
81
72
75
90
Dividing 54 by 2/3 is equivalent to multiplying 54 by 3/2, which equals 81 sandwiches.
A cyclist rides a total distance of 64 miles. If each lap of his circuit is 1/4 mile, how many laps did he complete?
256
240
252
260
Dividing by 1/4 is the same as multiplying by 4. Thus, 64 miles divided by 1/4 mile per lap equals 256 laps.
A machine fills containers with 90 liters of juice. If each container holds 3/10 liter, how many containers can be filled?
300
270
280
310
Multiplying 90 by the reciprocal of 3/10 (which is 10/3) gives 300 containers. This operation shows the straightforward approach to dividing by a fraction.
During a book drive, 72 boxes of supplies are donated. If each classroom receives 2/9 of a box, how many classrooms can be served?
324
288
300
336
Dividing 72 by 2/9 means multiplying 72 by the reciprocal 9/2, which results in 324. This shows how many classrooms can be served.
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Study Outcomes

  1. Analyze word problems to identify the appropriate strategy for dividing whole numbers by fractions.
  2. Apply fraction division rules to convert division problems into multiplication problems.
  3. Solve division problems involving fractions with accuracy and efficiency.
  4. Interpret the steps involved in converting word problems into mathematical expressions.
  5. Evaluate solutions to ensure correctness in the context of real-world scenarios.

Quiz: Dividing Whole Numbers by Fractions Cheat Sheet

  1. Grasp the Big Picture of Fraction Division - Dividing a whole number by a fraction is all about finding out how many of those fractional pieces fit inside your starting amount. Imagine slicing a chocolate bar into halves and counting each piece - that's exactly how it works! This approach builds strong number sense and confidence. Divide Fractions Word Problems
  2. Use the Reciprocal Trick - To divide a whole number by a fraction, simply multiply by its reciprocal: flip the fraction upside down and switch ÷ to ×. For example, 6 ÷ 2/3 becomes 6 × 3/2, turning division into a familiar multiplication task. This swap‑and‑flip method makes the process quick and painless! Whole Number‑Fraction Division Worksheet
  3. Leverage Visual Models - Visual aids like fraction bars and circles transform abstract problems into clear, colorful pictures. By drawing out how many slices fit into your whole, you'll see the answer right before your eyes! This hands‑on strategy cements your understanding. Visual Models Guide
  4. Apply Real‑World Scenarios - Turn dry math into real fun by dividing pizzas, candy bars, or backpacks of supplies among friends. You'll see how 8 ÷ 3/4 actually plays out at lunchtime or during a party. These relatable examples make fraction division stick! Divide Whole Numbers Word Problems
  5. Master the Keep‑Change‑Flip Method - Remember: Keep the whole number, Change the division sign to multiplication, and Flip the fraction to its reciprocal. This catchy phrase is your secret weapon for any fraction division problem. Say it out loud and watch your mistakes vanish! Keep‑Change‑Flip Trick
  6. Always Simplify Your Answers - After multiplying, reduce your fraction to the simplest form so it's neat and easy to use. Simplifying ensures you present answers like 9/4 as 2 ¼, which is much friendlier. Neat fractions make you look like a math pro! Simplify Your Fractions
  7. Tackle Word Problems Strategically - Read carefully, spot the whole number and the fraction, then set up your division equation step by step. Underline key numbers and draw quick sketches to avoid mix‑ups. A clear plan turns tricky word problems into easy wins! Word Problem Strategies
  8. Build Confidence with Unit Fractions - Start by dividing whole numbers by unit fractions (fractions with a 1 on top) to get comfortable. Once you ace problems like 7 ÷ 1/5, you'll breeze through more complex divisions. It's like leveling up in your favorite game! Unit Fractions Practice
  9. Check with Estimation - Use quick rounding to see if your answer makes sense. For instance, dividing 10 by 1/4 should give a big number - around 40 - so you know you're on track. Estimation is your fast check for silly slip‑ups! Estimation Check
  10. Practice, Practice, Practice - The more problems you solve, the sharper your skills become. Challenge yourself with timed drills, quizzes, and online games to keep the fun going. Before you know it, dividing whole numbers by fractions will feel like second nature! IXL Practice Problems
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