# Multiplying improper fractions and mixed numbers

### Multiplying improper fractions and mixed numbers

Improper fractions are fractions that their numerators are larger than or equal to their denominators. On the other hand, mixed numbers, also known as compound fractions, are numbers that have both a whole number and a fraction. In this section, a model will be used as a way to multiply mixed numbers and improper fractions. We will also practice questions of multiplying improper fractions and mixed numbers algebraically.

#### Lessons

• 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 convert between mixed numbers and improper fractions?

• 1.
Use a model to find each product.
a)
$\frac{1}{3} \times 2\frac{1}{3}$

b)
$1\frac{1}{4} \times 1\frac{1}{2}$

c)
$2\frac{1}{5} \times 1\frac{1}{6}$

• 2.
Estimate and calculate each product.
a)
$3\frac{2}{3} \times 1\frac{1}{4}$

b)
$\frac{7}{4} \times \frac{{13}}{8}$

c)
$2\frac{2}{5} \times 6$

• 3.
Three and a half rolls of wrapping paper are needed to wrap 10 presents. How many rolls of wrapping paper are needed to wrap 25 presents?