Fraction Multiplication Basics
What is 2/3 x 4?
2 2/3
What does 4 ÷ 1/2 mean in words?
How many 1/2s are in 4?
OR
How many half-units fit into 4 whole units?
Which model best represents 2 x 3/4:
An area model OR a number line?
Why?
An AREA MODEL because it clearly shows 2 groups of 3/4 and how they combine.
Each serving of granola is 1/2 cup.
How many servings are in 3 cups?
3 ÷ 1/2 = 6 servings
1/4 × 8 = 8 ÷ 4.
Is this TRUE or FALSE?
Explain why.
This is TRUE.
Multiplying by 1/4 is the same as dividing by 4.
Find the product: 3 x 5/6
2 1/2
Solve 6 ÷ 3/4.
8
Draw or describe a model that represents 3/4 x 2/3.
An area model split into thirds one way and fourths the other, with 2 of the 3 parts shaded.
Total shaded parts = 6/12 or 1/2.
A recipe uses 3/4 cup of sugar per batch.
How much sugar is needed for 4 batches?
4 x 3/4 = 3 cups of sugar
Why does multiplying by a fraction less than 1 make the product smaller?
A fraction less than 1 represents part of a whole, so taking a part makes the result smaller.
Multiply 4/5 x 3/4. Simplify your answer.
Which is larger:
3 ÷ 1/3 OR 3 x 1/3
Explain why.
3 ÷ 1/3 is larger because dividing by 1/3 asking how many thirds are in 3, which equals 9. Multplying gives you an answer of 1.
A rectangle is split into 5 equal parts.
3 of those parts are shaded.
What fraction of the rectangle is shaded?
How does this relate to multiplication?
3/5 of the rectangle is shaded.
A ribbon is 5 meters long.
Each piece is 2/5 meters.
How many pieces can be cut?
5 ÷ 2/3 = 12 1/2 pieces
A student solves: 2 ÷ 1/4 = 2/4
What did the student misunderstand?
What is the correct answer?
The student treated the division like multiplication.
The correct answer is 2 ÷ 1/4 = 8.
True or False:
Multiplying a whole number by a fraction always makes the product smaller.
Explain your reasoning.
False! Multiplying by a fraction greater than 1 makes the product larger. Example: 4 x 5/4 = 5.
Write a word problem that could be represented by 5 ÷ 1/2.
Example Answer:
You have 5 cups of flour. Each serving is 1/2 cup. How many servings can you make?
Use a tape diagram to explain 4 ÷ 2/3.
The tape diagram shows 4 wholes partitioned into thirds.
There are 6 groups of 2/3.
4 ÷ 2/3 = 6.
A cyclist rides 3/4 km every minute.
How far will they ride in 8 minutes?
Write an equation and explain your thinking.
8 x 3/4 = 6 km
Each minute adds another 3/4 km.
Explain why dividing by 1/2 is the same as multiplying by 2.
Dividing by 1/2 asks how many halves are in a number.
Each whole contains 2 halves, so the amount doubles.
A student says:
“To multiply 2/3 x 3/5, you add the numerators and add the denominators.”
Is the student correct?
Explain the mistake AND show the correct solution.
The student is INCORRECT. When multiplying fractions, you multiply numerators and multiply denominators, not add.
The correct solution is: 2/3 x 3/5 = 6/15 = 2/5
A student claims:
“Dividing by a fraction makes the answer smaller.”
Is this statement TRUE or FALSE?
Use TWO examples to prove or disprove this statement.
The statement is FALSE. The size of the divisor matters.
Example #1: 4 ÷ 1/2 = 8 (answer gets larger).
Example #2: 1/2 ÷ 2 = 1/4 (answer gets smaller).
Create two different models (visual representations) to show the division problem 4 ÷ 2/3.
Explanation: Both models show measurement division by counting how many groups of size 2/3 fit into 4 wholes.
Model 1: Tape Diagram
Represent 4 wholes as a bar
Partition each whole into thirds
Count how many groups of 23\frac{2}{3}32 fit into 4
Result: 6 groups
Model 2: Area or Number Line Model
Show 4 units on a number line marked in thirds
Group every 2/3 interval
Count the number of intervals
Result: 6 intervals
A baker has 6 cups of flour.
Each batch of bread uses 3/4 cup of flour.
How many full batches of bread can the baker make?
How much flour is left over after making those batches?
Explain how both division and multiplication are used to solve this problem.
1. 6 ÷ 3/4 = 8
2. There is no flour left over.
3. For question 1, you solve 6 ÷ 3/4 = 8. For question 2, you solve 6 x 3/4 = 6.
Compare and contrast:
3/4 × 4 and 4 ÷ 3/4
How are the strategies similar?
How are they different?
3/4 × 4 = 3
4 ÷ 3/4 =5 1/3
Similarities
Both involve fractions and whole numbers
Both can be represented with tape diagrams or area models
Both involve thinking about groups and scaling
Differences
Multiplication finds a part of a whole (4 groups of 3/4)
Division asks how many 3/4 groups fit into 4
Multiplication results in a smaller or equal value
Division results in a larger value in this case