Grade 5 · Fractions · MAT-05-NF-014
Solve Fraction Division Word Problems
Represent and solve solve fraction division word problems problems using accurate mathematical models, notation, and reasoning.
Learning objectives
What you should be able to do
- Represent and solve solve fraction division word problems problems using accurate mathematical models, notation, and reasoning.
- Explain why a strategy for solve fraction division word problems works and verify the result with an independent check.
Prerequisite check
Make sure the foundation is ready.
The new lesson builds directly on this prior concept, so the prerequisite should be usable rather than merely familiar.
Learn
Build the idea from meaning, not memorization.
Meaning and structure
Solve Fraction Division Word Problems depends on treating fractions as numbers built from equal-sized units. The numerator counts those units and the denominator defines their size; operations are valid only when the units being combined are compatible.
Represent the idea
The Math Box uses fraction model as the primary representation. Translate the situation into numbers or geometry first, identify what stays fixed, then change one quantity at a time and observe which relationships remain invariant.
Reason, calculate, and verify
A convincing solution names the quantities, shows the mathematical relationship, computes accurately, and includes a reasonableness check rather than relying on an unsupported answer.
Math Box · Interactive lesson
Touch the math. Change it. See what stays true.
Use the interactive model before and after the worked examples. Change the inputs, make a prediction, then use the model to test whether your reasoning holds.
Equal-Share Lab
Keep the whole fixed and change how many equal shares it contains.
- Build one example of solve fraction division word problems in the Math Box.
- Change one input and predict the effect before moving the control.
- Explain which mathematical relationship stayed invariant after the change.
Worked examples
Twenty different ways to see the concept work.
How many pieces of size 1/2 fit into 1 whole units?
1 ÷ 1/2 = 2Each whole contains 2 pieces of size 1/2; 1 wholes contain 2 pieces.
How many pieces of size 1/3 fit into 2 whole units?
2 ÷ 1/3 = 6Each whole contains 3 pieces of size 1/3; 2 wholes contain 6 pieces.
How many pieces of size 1/4 fit into 3 whole units?
3 ÷ 1/4 = 12Each whole contains 4 pieces of size 1/4; 3 wholes contain 12 pieces.
How many pieces of size 1/5 fit into 4 whole units?
4 ÷ 1/5 = 20Each whole contains 5 pieces of size 1/5; 4 wholes contain 20 pieces.
How many pieces of size 1/6 fit into 5 whole units?
5 ÷ 1/6 = 30Each whole contains 6 pieces of size 1/6; 5 wholes contain 30 pieces.
How many pieces of size 1/7 fit into 6 whole units?
6 ÷ 1/7 = 42Each whole contains 7 pieces of size 1/7; 6 wholes contain 42 pieces.
How many pieces of size 1/8 fit into 1 whole units?
1 ÷ 1/8 = 8Each whole contains 8 pieces of size 1/8; 1 wholes contain 8 pieces.
How many pieces of size 1/2 fit into 2 whole units?
2 ÷ 1/2 = 4Each whole contains 2 pieces of size 1/2; 2 wholes contain 4 pieces.
How many pieces of size 1/3 fit into 3 whole units?
3 ÷ 1/3 = 9Each whole contains 3 pieces of size 1/3; 3 wholes contain 9 pieces.
How many pieces of size 1/4 fit into 4 whole units?
4 ÷ 1/4 = 16Each whole contains 4 pieces of size 1/4; 4 wholes contain 16 pieces.
How many pieces of size 1/5 fit into 5 whole units?
5 ÷ 1/5 = 25Each whole contains 5 pieces of size 1/5; 5 wholes contain 25 pieces.
How many pieces of size 1/6 fit into 6 whole units?
6 ÷ 1/6 = 36Each whole contains 6 pieces of size 1/6; 6 wholes contain 36 pieces.
How many pieces of size 1/7 fit into 1 whole units?
1 ÷ 1/7 = 7Each whole contains 7 pieces of size 1/7; 1 wholes contain 7 pieces.
How many pieces of size 1/8 fit into 2 whole units?
2 ÷ 1/8 = 16Each whole contains 8 pieces of size 1/8; 2 wholes contain 16 pieces.
How many pieces of size 1/2 fit into 3 whole units?
3 ÷ 1/2 = 6Each whole contains 2 pieces of size 1/2; 3 wholes contain 6 pieces.
How many pieces of size 1/3 fit into 4 whole units?
4 ÷ 1/3 = 12Each whole contains 3 pieces of size 1/3; 4 wholes contain 12 pieces.
How many pieces of size 1/4 fit into 5 whole units?
5 ÷ 1/4 = 20Each whole contains 4 pieces of size 1/4; 5 wholes contain 20 pieces.
How many pieces of size 1/5 fit into 6 whole units?
6 ÷ 1/5 = 30Each whole contains 5 pieces of size 1/5; 6 wholes contain 30 pieces.
How many pieces of size 1/6 fit into 1 whole units?
1 ÷ 1/6 = 6Each whole contains 6 pieces of size 1/6; 1 wholes contain 6 pieces.
How many pieces of size 1/7 fit into 2 whole units?
2 ÷ 1/7 = 14Each whole contains 7 pieces of size 1/7; 2 wholes contain 14 pieces.
Practice
Guided practice with hints
01How many pieces of size 1/8 fit into 3 whole units?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 3 ÷ 1/8 = 24
02How many pieces of size 1/2 fit into 4 whole units?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 4 ÷ 1/2 = 8
03How many pieces of size 1/3 fit into 5 whole units?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 5 ÷ 1/3 = 15
04How many pieces of size 1/4 fit into 6 whole units?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 6 ÷ 1/4 = 24
05How many pieces of size 1/5 fit into 1 whole units?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 1 ÷ 1/5 = 5
06How many pieces of size 1/6 fit into 2 whole units?
Hint: Name the quantities and representation first; then choose the operation or comparison that preserves their meaning.
Answer: 2 ÷ 1/6 = 12
Practice
Independent practice
01How many pieces of size 1/7 fit into 3 whole units?
Answer: 3 ÷ 1/7 = 21
02How many pieces of size 1/8 fit into 4 whole units?
Answer: 4 ÷ 1/8 = 32
03How many pieces of size 1/2 fit into 5 whole units?
Answer: 5 ÷ 1/2 = 10
04How many pieces of size 1/3 fit into 6 whole units?
Answer: 6 ÷ 1/3 = 18
05How many pieces of size 1/4 fit into 1 whole units?
Answer: 1 ÷ 1/4 = 4
06How many pieces of size 1/5 fit into 2 whole units?
Answer: 2 ÷ 1/5 = 10
07How many pieces of size 1/6 fit into 3 whole units?
Answer: 3 ÷ 1/6 = 18
08How many pieces of size 1/7 fit into 4 whole units?
Answer: 4 ÷ 1/7 = 28
Common mistakes
Learn to catch the error, not just the answer.
Track the size of the fractional unit first; fractions can be combined only when the units are compatible.
Compare complete fraction values with a model, benchmark, common denominator, or cross-product reasoning.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Scale recipes, measurements, money, and data while preserving the meaning of the unit.
- Compare quantities that are not whole numbers in science, construction, shopping, and measurement.
Challenge problems
How many pieces of size 1/8 fit into 5 whole units?
5 ÷ 1/8 = 40
How many pieces of size 1/2 fit into 6 whole units?
6 ÷ 1/2 = 12
How many pieces of size 1/3 fit into 1 whole units?
1 ÷ 1/3 = 3
How many pieces of size 1/4 fit into 2 whole units?
2 ÷ 1/4 = 8
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 4
Game mode
Grade 5 Math Strategy Sprint
Solve and explain solve fraction division word problems problems accurately, then check each result with a second method.
Practice
Mastery check
01How many pieces of size 1/5 fit into 3 whole units?
Answer: 3 ÷ 1/5 = 15
02How many pieces of size 1/6 fit into 4 whole units?
Answer: 4 ÷ 1/6 = 24
03How many pieces of size 1/7 fit into 5 whole units?
Answer: 5 ÷ 1/7 = 35
04How many pieces of size 1/8 fit into 6 whole units?
Answer: 6 ÷ 1/8 = 48
05How many pieces of size 1/2 fit into 1 whole units?
Answer: 1 ÷ 1/2 = 2
06How many pieces of size 1/3 fit into 2 whole units?
Answer: 2 ÷ 1/3 = 6
07How many pieces of size 1/4 fit into 3 whole units?
Answer: 3 ÷ 1/4 = 12
08How many pieces of size 1/5 fit into 4 whole units?
Answer: 4 ÷ 1/5 = 20
Terminology
Words to know
- numerator
- The number of selected equal parts or unit fractions.
- denominator
- The number of equal parts that make one whole.
- equivalent fractions
- Different fraction names for the same numerical value.
- benchmark
- A familiar reference value such as 0, 1/2, or 1 used for comparison.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Mathematics Framework (2023)
Grade-level instructional guidance, mathematical practices, and coherent progression.Common Core State Standards for Mathematics — Grades 4–5
Grade-level expectations for operations, number and fraction work, measurement, data, and geometry.Principles to Actions: Ensuring Mathematical Success for All
Evidence-based emphasis on reasoning, representations, discourse, and conceptual understanding.