# 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

In this lesson, we will learn:

• Multiplying Improper Fractions and Mixed Numbers Using Area Models
• Multiply Improper Fractions and Mixed Numbers Involving Single-digit Numbers
• Word Problems: Multiplying Improper Fractions and Mixed Numbers
• Multiply Improper Fractions and Mixed Numbers Involving Multiple-digit Numbers and Negatives
• Steps to multiplying fractions involving mixed numbers:
1. Convert all the mixed numbers into improper fractions.
2. Multiply the improper fractions.
3. Reduce the answer to the lowest terms.
4. Convert the answer back to a mixed number.
• 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?

e)
How to multiply improper fractions and mixed numbers?

• 1.
Multiplying Improper Fractions and Mixed Numbers Using Area Models
Use an area 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.
Multiply Improper Fractions and Mixed Numbers Involving Single-digit Numbers
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.
Word Problems: Multiplying Improper Fractions and Mixed Numbers
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?