
- Mixed numbers
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- Writing a mixed number and an improper fraction for a shaded region
- Writing an improper fraction as a mixed number
- Writing a mixed number as an improper fraction
- Mixed number multiplication
- Multiplication of a mixed number and a whole number
- Division with a mixed number and a whole number
- Mixed number division
- Word problem involving multiplication or division with mixed numbers
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Mixed number division
In this lesson, we are dealing with division involving mixed numbers and fractions and division involving two mixed numbers.
Rules for mixed number division
The mixed number is converted into an improper fraction and division of the fractions is carried out as follows.
The division operation is written as a multiplication operation by multiplying the top fraction with the reciprocal of the bottom fraction.
The resulting fraction, if required, is written as a mixed number in simplest form.
Formula
If a mixed number (as improper fraction a/b) is being divided by another fraction(c/d), then
$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$
Divide. Write your answer as a mixed number in simplest form.
$3\frac{1}{2} \div \frac{3}{4}$
Solution
Step 1:
First, we write the mixed number $3\frac{1}{2}$ as an improper fraction
$3\frac{1}{2} = \frac{\left ( 3 \times 2 + 1 \right )}{2} = \frac{7}{2}$
Step 2:
$3\frac{1}{2} \div \frac{3}{4} = \frac{7}{2} \div \frac{3}{4} = \frac{7}{2} \times \frac{4}{3} $
Step 3:
Multiplying numerators and denominators
$\frac{7}{2} \times \frac{4}{3} = \frac{(7 \times 4)}{(2 \times 3)} = \frac{28}{6} = \frac{14}{3}$
Step 4:
Writing the improper fraction as a mixed number
$\frac{14}{3} = 4\frac{2}{3}$
Step 5:
So, $3\frac{1}{2} \div \frac{3}{4} = 4\frac{2}{3}$
Divide. Write your answer as a mixed number in simplest form.
$\frac{2}{3} \div 7\frac{1}{2}$
Solution
Step 1:
First, we write the mixed number $7\frac{1}{2}$ as an improper fraction
$7\frac{1}{2} = \frac{\left ( 7 \times 2 + 1 \right )}{2} = \frac{15}{2}$
Step 2:
$\frac{2}{3} \div 7\frac{1}{2} = \frac{2}{3} \div \frac{15}{2} = \frac{2}{3} \times \frac{2}{15}$
Step 3:
Multiplying numerators and denominators
$\frac{2}{3} \times \frac{2}{15} = \frac{(2 \times 2)}{(3 \times 15)} = \frac{4}{45}$
Step 4:
So, $\frac{2}{3} \div 7\frac{1}{2} = \frac{4}{45}$
Divide. Write your answer as a mixed number in simplest form.
$5\frac{1}{2} \div 1\frac{3}{4}$
Solution
Step 1:
First, we write the mixed numbers as improper fractions
$5\frac{1}{2} = \frac{\left ( 5 \times 2 + 1 \right )}{2} = \frac{11}{2}$
$1\frac{3}{4} = \frac{\left ( 1 \times 4 + 3 \right )}{4} = \frac{7}{4}$
Step 2:
$5\frac{1}{2} \div 1\frac{3}{4} = \frac{11}{2} \div \frac{7}{4} = \frac{11}{2} \times \frac{4}{7}$
Step 3:
Multiplying numerators and denominators
$\frac{11}{2} \times \frac{4}{7} = \frac{(11 \times 4)}{(2 \times 7)} = \frac{44}{14} = \frac{22}{7}$
Step 4:
Writing the improper fraction as a mixed number
$\frac{22}{7} = 3\frac{1}{7}$
Step 5:
So, $5\frac{1}{2} \div 1\frac{3}{4} = 3\frac{1}{7}$