Mathematics
Grade 5
15 min
Multiply fractions by whole numbers using number lines
Multiply fractions by whole numbers using number lines
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1
Introduction & Learning Objectives
Learning Objectives
Represent a given fraction on a number line.
Understand multiplication of a fraction by a whole number as repeated addition.
Model multiplying a fraction by a whole number using jumps on a number line.
Determine the product of a fraction and a whole number by interpreting the final position on a number line.
Convert improper fractions to mixed numbers when the product exceeds one whole.
Solve word problems involving multiplying fractions by whole numbers using number lines.
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In this lesson, you'll learn how to multiply fractions by whole numbers. We'll use number lines to make this concept easy to see a...
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Key Concepts & Vocabulary
TermDefinitionExample
FractionA part of a whole, represented as a numerator over a denominator. The numerator tells how many parts you have, and the denominator tells how many equal parts make up the whole.1/2 means 1 out of 2 equal parts; 3/4 means 3 out of 4 equal parts.
Whole NumberA counting number (0, 1, 2, 3, ...). These numbers do not have fractional or decimal parts.5, 10, 100 are whole numbers.
Number LineA visual representation of numbers in order, extending infinitely in both directions. It helps us see the value and position of numbers, including fractions.A line with markings for 0, 1/4, 1/2, 3/4, 1, 1 1/4, etc.
Unit FractionA fraction with a numerator of 1, representing one single part of a whole that has been divided into equal parts.1/4, 1/8, 1/10 are unit fractions.
Repea...
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Core Formulas
Multiplication as Repeated Addition for Fractions
$a \times \frac{b}{c} = \frac{b}{c} + \frac{b}{c} + \dots \text{ (a times)}$
This rule shows that multiplying a fraction by a whole number is the same as adding that fraction to itself 'a' times. On a number line, this means making 'a' jumps, each of size 'b/c'.
Multiplying Numerator by Whole Number
$a \times \frac{b}{c} = \frac{a \times b}{c}$
To multiply a fraction by a whole number, multiply the whole number by the numerator of the fraction and keep the denominator the same. This is the arithmetic shortcut after understanding the number line model.
Converting Improper Fractions to Mixed Numbers
$\frac{\text{Numerator}}{\text{Denominator}} = \text{Whole Number} \frac{\text{Remainder}}{\te...
5 more steps in this tutorial
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Challenging
Consider two problems: Problem A is 6 x 1/2 and Problem B is 4 x 3/4. Which statement is true when you model them on a number line?
A.The final point for Problem A is further from zero than Problem B.
B.The final point for Problem B is further from zero than Problem A.
C.The final points for both problems are the same.
D.The jumps in Problem A are larger than the jumps in Problem B.
Challenging
The final position on a number line after modeling a multiplication problem is 3 1/2. Which of the following problems could this model represent?
A.7 x 1/2
B.3 x 1/2
C.7 x 1/3
D.2 x 3 1/2
Challenging
You are modeling 5 x 3/8 on a number line. If you change the problem to 10 x 3/8, what happens on the number line?
A.The size of each jump doubles.
B.The number of divisions between whole numbers doubles.
C.The size of each jump is halved, and the final position is the same.
D.The number of jumps doubles, and the final position is twice as far from zero.
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