Mathematics
Grade 5
15 min
Multiply unit fractions by whole numbers using models
Multiply unit fractions by whole numbers using models
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1
Introduction & Learning Objectives
Learning Objectives
Identify and represent unit fractions.
Explain what it means to multiply a unit fraction by a whole number.
Use visual models (like fraction strips, number lines, or area models) to represent multiplication of unit fractions by whole numbers.
Write multiplication expressions that correspond to visual models.
Calculate the product of a unit fraction and a whole number using models and relate it to repeated addition.
Convert improper fractions to mixed numbers when the product is greater than one.
Have you ever shared a pizza or a cake? 🍕 What if you ate 1/8 of a pizza every day for 3 days? How much pizza would you have eaten in total?
In this lesson, you'll learn how to multiply unit fractions by whole numbers. We'll use fun pictures and models...
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Key Concepts & Vocabulary
TermDefinitionExample
Unit FractionA fraction where the numerator (top number) is 1. It represents one part of a whole that has been divided into equal parts.1/2, 1/3, 1/4, 1/8 are all unit fractions.
Whole NumberA number without fractions or decimals. It represents a complete quantity.0, 1, 2, 3, 10, 100 are all whole numbers.
MultiplicationA mathematical operation that represents repeated addition of the same number. When we multiply a fraction by a whole number, it means we have that many 'groups of' the fraction.3 x 1/4 means '3 groups of 1/4' or '1/4 + 1/4 + 1/4'.
ModelA visual representation (like a drawing, diagram, or physical object) used to help understand and solve a math problem.Fraction strips, number lines, and area models are types of models us...
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Core Formulas
Multiplication Rule for Unit Fractions
$$n \times \frac{1}{d} = \frac{n \times 1}{d} = \frac{n}{d}$$
To multiply a whole number ($n$) by a unit fraction (1/d), you multiply the whole number by the numerator (which is always 1) and keep the denominator the same. This tells you how many 'unit fraction' pieces you have in total.
Repeated Addition Connection
$$n \times \frac{1}{d} = \frac{1}{d} + \frac{1}{d} + ... + \frac{1}{d} \text{ (n times)}$$
Multiplying a unit fraction by a whole number is the same as adding that unit fraction to itself 'n' times. This helps visualize the total amount when using models.
Modeling Principle
Each whole number 'n' represents 'n' groups, and each group contains the unit fraction '1/d'. Com...
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Challenging
A multiplication problem using a unit fraction and a whole number has a product between 3 and 4. Which of the following problems and corresponding models could represent this?
A.6 × 1/3, which results in 2.
B.10 × 1/4, which results in 2 and 1/2.
C.7 × 1/2, which results in 3 and 1/2.
D.12 × 1/3, which results in 4.
Challenging
The product of n × 1/d is exactly 5. If 'n' is a whole number and '1/d' is a unit fraction, which of these is a possible pair of values for n and d?
A.n = 10, d = 3
B.n = 5, d = 1
C.n = 15, d = 3
D.n = 5, d = 5
Challenging
A baker uses 1/4 cup of flour for a single muffin. He wants to bake a batch of 'n' muffins. He uses a total of 3 and 1/4 cups of flour. Which model and equation correctly identifies 'n'?
A.model showing 4 jumps of 1/4, so n=4.
B.model showing 3 and 1/4 shaded circles, so n=3.
C.model showing 13 shaded 1/4 pieces, so n=13.
D.model showing 1/4 of 13 rectangles, so n=1/4.
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