# Multiplying proper fractions

### Multiplying proper fractions

Unlike the previous sections, this section will only deal with multiplications with fractions only, specifically proper fractions. To do so, we will need to multiply the numerators together and then the denominators together. We also will learn the trick of simplifying fractions in order to reduce the answers to the lowest form.

#### Lessons

In this lesson, we will learn:

• Multiplying Single-digit Proper Fractions
• Word Problems: Multiplying Proper Fractions
• Multiplying Proper Fractions Involving Multiple-digit Numbers and Negative Numbers

• Proper fractions:
• Fractions in which the values of the numerators are less than that of the denominators.
• Fractions that are greater than 0 but less than 1.
• The product of two proper fractions must also be a proper fraction.
• Introduction
a)
Simplify fractions: Method A - By using greatest common factors

b)
Simplify fractions: Method B - By using common factors

c)
How to multiply fractions with cross-cancelling?

d)
How to multiply proper fractions?

• 1.
Multiplying Single-digit Proper Fractions
Estimate and solve. Give the answers in the lowest form.
a)
$\frac{1}{4} \times \frac{3}{4}$

b)
$\frac{2}{7} \times \frac{5}{8}$

c)
$\frac{5}{7} \times \frac{7}{{10}}$

• 2.
Word Problems: Multiplying Proper Fractions
In April last year, $\frac{2}{5}$ of the month has records of rainfall. $\frac{1}{4}$ of these rainy days fell on weekends.
a)
What fraction of rainfall happened on weekends in April last year?

b)
How many of these rainy days were on weekends?