
- Multiply and Divide Fractions
- Home
- Product of a Unit Fraction and a Whole Number
- Product of a Fraction and a Whole Number: Problem Type 1
- Introduction to Fraction Multiplication
- Fraction Multiplication
- Product of a Fraction and a Whole Number Problem Type 2
- Determining if a Quantity is Increased or Decreased When Multiplied by a Fraction
- Modeling Multiplication of Proper Fractions
- Multiplication of 3 Fractions
- Word Problem Involving Fractions and Multiplication
- The Reciprocal of a Number
- Division Involving a Whole Number and a Fraction
- Fraction Division
- Fact Families for Multiplication and Division of Fractions
- Modeling Division of a Whole Number by a Fraction
- Word Problem Involving Fractions and Division
Product of a Fraction and a Whole Number: Problem Type 2
In this lesson, we solve problems where we find the product of a fraction and a whole number.
Rules for finding the product of a fraction and a whole number
We first write the whole number as a fraction, i.e., we write it divided by one; for example 5 is written as 5/1.
We then multiply the numerators and then the denominators of both fractions to get the product fraction.
If any simplification or cross cancelling is required, it is done and final answer is written.
Example
Multiply $\frac{3}{8}$ × 5
SolutionStep 1:
First, we write the whole number 5 as a fraction $\frac{5}{1}$
Step 2:
$\frac{3}{8}$ × 5 = $\frac{3}{8}$ × $\frac{5}{1}$
Step 3:
Multiply the numerators and denominators of both fractions as follows.
$\frac{3}{8}$ × $\frac{5}{1}$ = $\frac{(3 × 5)}{(8 × 1)}$ = $\frac{15}{8}$
Step 4:
So $\frac{3}{8}$ × 5 = $\frac{15}{8}$
Multiply $\frac{2}{15}$ × 5
Solution
Step 1:
First, we write the whole number 5 as a fraction $\frac{5}{1}$
$\frac{2}{15}$ × 5 = $\frac{2}{15}$ × $\frac{5}{1}$
Step 2:
As 5 and 15 are multiples of 5, cross cancelling 5 and 15, we get
$\frac{2}{3}$ × $\frac{1}{1}$
Step 3:
Multiply the numerators and denominators of both fractions as follows.
$\frac{2}{3}$ × $\frac{1}{1}$ = $\frac{(2 × 1)}{(3 × 1)}$ = $\frac{2}{3}$
Step 4:
So $\frac{2}{15}$ × 5 = $\frac{2}{3}$
Multiply $\frac{3}{7}$ × 2
Solution
Step 1:
First, we write the whole number 2 as a fraction $\frac{2}{1}$
$\frac{3}{7}$ × 2 = $\frac{3}{7}$ × $\frac{2}{1}$
Step 2:
Multiply the numerators and denominators of both fractions as follows.
$\frac{3}{7}$ × $\frac{2}{1}$ = $\frac{(3 × 2)}{(7 × 1)}$ = $\frac{6}{7}$
Step 3:
So $\frac{3}{7}$ × 2 = $\frac{6}{7}$