Mathematics
Grade 5
15 min
Multiply fractions by whole numbers using models
Multiply fractions by whole numbers using models
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Introduction & Learning Objectives
Learning Objectives
Represent fractions and whole numbers using visual models.
Use area models to multiply a fraction by a whole number.
Use number line models to multiply a fraction by a whole number.
Write a multiplication expression that matches a given model of a fraction multiplied by a whole number.
Calculate the product of a fraction and a whole number by interpreting visual models.
Explain how multiplying a fraction by a whole number is related to repeated addition.
Simplify the resulting fraction from a multiplication problem, if necessary.
Ever wonder how many slices of pizza you'd have if everyone at your party ate 1/4 of a pizza, and there were 3 people? 🍕 Let's find out how to solve problems like this using pictures!
In this lesson, you'll lea...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number that represents a part of a whole or a part of a collection. It is written as a numerator over a denominator.In the fraction 3/4, '3' is the numerator (parts we have) and '4' is the denominator (total equal parts in the whole).
Whole NumberA number without fractions or decimals, used for counting. It represents a complete unit or a collection of complete units.Numbers like 1, 2, 3, 10, 100 are whole numbers.
MultiplicationA mathematical operation that represents repeated addition of the same number. It can also be thought of as finding the total number of items in equal groups.3 × 1/4 means adding 1/4 three times: 1/4 + 1/4 + 1/4.
Area ModelA visual representation of multiplication using rectangles or squares divided into equal pa...
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Core Formulas
Multiplication as Repeated Addition
$$n \times \frac{a}{b} = \frac{a}{b} + \frac{a}{b} + ... + \frac{a}{b} \text{ (n times)}$$
This rule shows that multiplying a fraction by a whole number is the same as adding that fraction to itself 'n' number of times. Models like number lines clearly demonstrate this repeated addition.
Multiplying Whole Number by Numerator
$$n \times \frac{a}{b} = \frac{n \times a}{b}$$
When multiplying a whole number by a fraction, you multiply the whole number by the numerator of the fraction and keep the denominator the same. This is because you are finding 'n' groups of 'a' parts, where each part is 'b' of a whole. Models help visualize why the denominator stays the same (the size of the parts doesn't chan...
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Challenging
Maya practices piano for 3/4 of an hour every day. She wants to find the total time she practices in 4 days. Which expression and model description correctly represent this problem?
A.Expression: 4 × 3/4. Model: 3 jumps of 4/4 on a number line.
B.Expression: 3 × 4/3. Model: 3 rectangles, each with 4 of 3 parts shaded.
C.Expression: 4 + 3/4. Model: A number line starting at 3/4 and adding a jump of 4.
D.Expression: 4 × 3/4. Model: 4 rectangles, each divided into 4 parts with 3 parts shaded.
Challenging
An area model shows a total shaded area equivalent to 12/5. This was created by multiplying a whole number by a fraction. Which of the following expressions could NOT have resulted in this total?
A.3 × 4/5
B.4 × 3/5
C.6 × 2/5
D.2 × 7/5
Challenging
When using a model to multiply 3 × 2/5, why does the denominator (5) stay the same in the product 6/5?
A.Because the whole number 3 is smaller than the denominator 5.
B.Because the denominator represents the total number of equal parts in each whole, and the size of those parts doesn't change.
C.Because you are only supposed to multiply the numerators in any fraction problem.
D.Because the denominator is a prime number and cannot be changed.
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