Mathematics
Grade 7
15 min
Multiply unit fractions by whole numbers using number lines (Tutorial)
Multiply unit fractions by whole numbers using number lines (Tutorial)
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Introduction & Learning Objectives
Learning Objectives
Identify and define unit fractions and whole numbers.
Accurately partition a number line to represent unit fractions.
Model the multiplication of a unit fraction by a whole number using repeated jumps on a number line.
Determine the product of a unit fraction and a whole number by locating the final position on a number line.
Connect the visual representation on a number line to the symbolic multiplication equation.
Solve word problems involving the multiplication of unit fractions by whole numbers using number lines.
Ever wonder how many steps it takes to walk a certain fraction of a mile multiple times? 🚶♀️
In this lesson, you'll learn a visual way to multiply unit fractions by whole numbers using number lines. This skill helps you understand fr...
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Key Concepts & Vocabulary
TermDefinitionExample
Unit FractionA fraction where the numerator (the top number) is 1, representing one part of a whole.1/2, 1/5, 1/10
Whole NumberAny non-negative integer (0, 1, 2, 3, ...).3, 7, 12
Number LineA visual representation of numbers as points on a straight line, ordered by value.A line with equally spaced marks for 0, 1, 2, 3
Multiplication as Repeated AdditionUnderstanding that multiplying a fraction by a whole number is equivalent to adding that fraction to itself the specified number of times.3 × 1/4 is the same as 1/4 + 1/4 + 1/4
ProductThe result obtained when two or more numbers are multiplied together.In 3 × 1/4 = 3/4, the product is 3/4
DenominatorThe bottom number in a fraction, indicating the total number of equal parts into which the whole is divided.In 1/5, the d...
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Core Formulas
Multiplication of a Unit Fraction by a Whole Number
$n \times \frac{1}{d} = \frac{n}{d}$
To multiply a whole number ($n$) by a unit fraction ($\frac{1}{d}$), multiply the whole number by the numerator (which is 1) and keep the denominator the same. This simplifies to placing the whole number as the new numerator over the original denominator.
Repeated Addition Principle for Number Lines
$n \times \frac{1}{d} = \underbrace{\frac{1}{d} + \frac{1}{d} + \dots + \frac{1}{d}}_{n \text{ times}}$
When modeling multiplication on a number line, each jump represents adding the unit fraction. You make 'n' jumps, each of size $\frac{1}{d}$, starting from zero. The final landing spot is the product.
Number Line Partitioning Rule
To represent $\frac{1}{d}$ on a number line,...
5 more steps in this tutorial
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Challenging
The product of a whole number 'n' and a unit fraction \frac{1}{d} is \frac{11}{6}. Based on the number line modeling rules, what must be the values of 'n' and 'd'?
A.n = 6, d = 11
B.n = 11, d = 6
C.n = 1, d = 11/6
D.n = 11, d = 11
Challenging
A student is asked to solve $6 \times \frac{1}{4}$. They draw a number line, partition each whole unit into 6 parts, and then make 4 jumps. They arrive at the answer \frac{4}{6}. Which two fundamental errors did they make?
A.They started at 1 and multiplied the denominator.
B.They confused the roles of the whole number and the denominator for both partitioning and the number of jumps.
C.They should have simplified the fraction and they misread the final landing spot.
D.They used repeated subtraction instead of addition and partitioned incorrectly.
Challenging
A number line model shows 'k' jumps of size \frac{1}{m}, starting from 0. The final landing point is greater than 3 but less than 4. Which inequality must be true?
A.k/m > 4
B.3 < k/m < 4
C.m/k > 3
D.k < m
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