Mathematics
Grade 5
15 min
Multiply fractions by whole numbers using models
Multiply fractions by whole numbers using models
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1
Introduction & Learning Objectives
Learning Objectives
Represent fractions and whole numbers using visual models.
Explain the concept of multiplying a fraction by a whole number as repeated addition.
Use area models to solve multiplication problems involving fractions and whole numbers.
Use number line models to solve multiplication problems involving fractions and whole numbers.
Write a multiplication sentence to represent a given model of a fraction multiplied by a whole number.
Find the product of a fraction and a whole number using models and simplify the result.
Solve real-world problems involving multiplying fractions by whole numbers using models.
Have you ever shared a pizza or baked cookies? 🍕 Sometimes, you need to figure out how much of an ingredient you need if you're making multiple batch...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA number that represents a part of a whole or a part of a collection. It has a numerator (top number) and a denominator (bottom number).In the fraction $\frac{3}{4}$, 3 is the numerator and 4 is the denominator. It means 3 out of 4 equal parts.
Whole NumberA number without fractions or decimals. It represents a complete quantity.0, 1, 2, 3, 4, 5, and so on are whole numbers.
NumeratorThe top number in a fraction that tells you how many parts of the whole you have.In $\frac{2}{5}$, the numerator is 2, meaning you have 2 parts.
DenominatorThe bottom number in a fraction that tells you how many equal parts the whole is divided into.In $\frac{2}{5}$, the denominator is 5, meaning the whole is divided into 5 equal parts.
ProductThe answer to a multiplication probl...
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Core Formulas
Multiplication as Repeated Addition
$n \times \frac{a}{b} = \frac{a}{b} + \frac{a}{b} + ... + \frac{a}{b}$ (n times)
Multiplying a fraction by a whole number is the same as adding that fraction to itself 'n' times. Models help us visualize these repeated additions.
Multiplying Numerator by Whole Number
$n \times \frac{a}{b} = \frac{n \times a}{b}$
When multiplying a fraction by a whole number, you multiply the whole number by the numerator and keep the denominator the same. This rule comes directly from the repeated addition concept shown by models.
Simplifying the Product
If the product is an improper fraction (numerator is greater than or equal to the denominator), convert it to a mixed number. Always simplify fractions to their simplest form.
After multi...
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Challenging
The final result of a multiplication problem is modeled by two fully shaded circles and one circle that is 1/4 shaded. Which multiplication problem does this model represent the product of?
A.4 x 1/2
B.3 x 3/4
C.9 x 1/4
D.2 x 1/4
Challenging
Imagine a number line used to model the problem 6 x 2/5. If you start at 0, how would you describe the jumps and the final landing point?
A.You would make 6 jumps, each 2/5 long, and land on 12/5 or 2 and 2/5.
B.You would make 2 jumps, each 6/5 long, and land on 12/5 or 2 and 2/5.
C.You would make 6 jumps, each 2/5 long, and land on 12/30 or 2/5.
D.You would make 5 jumps, each 2/6 long, and land on 10/6 or 1 and 4/6.
Challenging
Which of the following problems would NOT result in a product that can be modeled as exactly 3 whole units?
A.6 x 1/2
B.4 x 3/4
C.5 x 3/4
D.9 x 1/3
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