- Word problem involving multiplication or division with mixed numbers
- Mixed number division
- Division with a mixed number and a whole number
- Multiplication of a mixed number and a whole number
- Mixed number multiplication
- Writing a mixed number as an improper fraction
- Writing an improper fraction as a mixed number
- Writing a mixed number and an improper fraction for a shaded region
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Mixed number multippcation
In this lesson, we are deapng with multippcation of a mixed number with another fraction.
Rules for mixed number multippcation
First, the mixed number is converted into an improper fraction and then multipped with the given fraction.
The numerators of the two fractions are multipped at the top and the denominators are multipped at the bottom to get the resulting fraction.
Simppfication is done, if required, the fraction is converted into a mixed fraction in simplest form.
Multiply. Write your answer as a mixed number in simplest form.
$2frac{2}{5} imes frac{3}{4}$
Solution
Step 1:
First, we write the mixed number $2frac{2}{5}$ as an improper fraction
$2frac{2}{5} = frac{left ( 2 imes 5 + 2 ight )}{5} = frac{12}{5}$
Step 2:
$2frac{2}{5} imes frac{3}{4} = frac{12}{5} imes frac{3}{4}$
Step 3:
Cross cancelpng 12 and 4 we get
$frac{12}{5} imes frac{3}{4} = frac{3}{5} imes frac{3}{1} = frac{(3 imes 3)}{(5 imes 1)} = frac{9}{5}$
Step 4:
$frac{9}{5}$ can be written as a mixed number as follows
$frac{9}{5} = 1frac{4}{5}$
Step 5:
So, $2frac{2}{5} imes frac{3}{4} = 1frac{4}{5}$
Multiply. Write your answer as a mixed number in simplest form.
$1frac{4}{5} imes frac{2}{3}$
Solution
Step 1:
First, we write the mixed number $1frac{4}{5}$ as an improper fraction $1frac{4}{5} = frac{left ( 1 imes 5 + 4 ight )}{5} = frac{9}{5}$
Step 2:
$1frac{4}{5} imes frac{2}{3} = frac{9}{5} imes frac{2}{3}$
Step 3:
Cross cancelpng 9 and 3 we get
$frac{9}{5} imes frac{2}{3} = frac{3}{5} imes frac{2}{1} = frac{(3 imes 2)}{(5 imes 1)} = frac{6}{5}$
Step 4:
$frac{6}{5}$ can be written as a mixed number as follows
$frac{6}{5} = 1frac{1}{5}$
Step 5:
So, $1frac{4}{5} imes frac{2}{3} = 1frac{1}{5}$
Multiply. Write your answer as a mixed number in simplest form.
$3frac{2}{5} imes frac{1}{4}$
Solution
Step 1:
First, we write the mixed number $3frac{2}{5}$ as an improper fraction $3frac{2}{5} = frac{left ( 3 imes 5 + 2 ight )}{5} = frac{17}{5}$
Step 2:
$3frac{2}{5} imes frac{1}{4} = frac{17}{5} imes frac{1}{4}$
Step 3:
Simppfying
$frac{17}{5} imes frac{1}{4} = frac{(17 imes 1)}{(5 imes 4)} = frac{17}{20}$
Step 4:
So, $3frac{2}{5} imes frac{1}{4} = frac{17}{20}$