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Mixed number multiplication
  • 时间:2024-12-22

Mixed number multippcation


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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, $3frac{2}{5} imes frac{1}{4} = frac{17}{20}$

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