Mixed number spanision

In this lesson, we are deapng with spanision involving mixed numbers and fractions and spanision involving two mixed numbers.

Rules for mixed number spanision

The mixed number is converted into an improper fraction and spanision of the fractions is carried out as follows.

The spanision operation is written as a multippcation 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 spanided by another fraction(c/d), then

$frac{a}{b} span frac{c}{d} = frac{a}{b} imes frac{d}{c}$

Divide. Write your answer as a mixed number in simplest form.

$3frac{1}{2} span frac{3}{4}$

Solution

Step 1:

First, we write the mixed number $3frac{1}{2}$ as an improper fraction

$3frac{1}{2} = frac{left ( 3 imes 2 + 1 ight )}{2} = frac{7}{2}$

Step 2:

$3frac{1}{2} span frac{3}{4} = frac{7}{2} span frac{3}{4} = frac{7}{2} imes frac{4}{3} $

Step 3:

Multiplying numerators and denominators

$frac{7}{2} imes frac{4}{3} = frac{(7 imes 4)}{(2 imes 3)} = frac{28}{6} = frac{14}{3}$

Step 4:

Writing the improper fraction as a mixed number

$frac{14}{3} = 4frac{2}{3}$

Step 5:

So, $3frac{1}{2} span frac{3}{4} = 4frac{2}{3}$

Divide. Write your answer as a mixed number in simplest form.

$frac{2}{3} span 7frac{1}{2}$

Solution

Step 1:

First, we write the mixed number $7frac{1}{2}$ as an improper fraction

$7frac{1}{2} = frac{left ( 7 imes 2 + 1 ight )}{2} = frac{15}{2}$

Step 2:

$frac{2}{3} span 7frac{1}{2} = frac{2}{3} span frac{15}{2} = frac{2}{3} imes frac{2}{15}$

Step 3:

Multiplying numerators and denominators

$frac{2}{3} imes frac{2}{15} = frac{(2 imes 2)}{(3 imes 15)} = frac{4}{45}$

Step 4:

So, $frac{2}{3} span 7frac{1}{2} = frac{4}{45}$

Divide. Write your answer as a mixed number in simplest form.

$5frac{1}{2} span 1frac{3}{4}$

Solution

Step 1:

First, we write the mixed numbers as improper fractions

$5frac{1}{2} = frac{left ( 5 imes 2 + 1 ight )}{2} = frac{11}{2}$

$1frac{3}{4} = frac{left ( 1 imes 4 + 3 ight )}{4} = frac{7}{4}$

Step 2:

$5frac{1}{2} span 1frac{3}{4} = frac{11}{2} span frac{7}{4} = frac{11}{2} imes frac{4}{7}$

Step 3:

Multiplying numerators and denominators

$frac{11}{2} imes frac{4}{7} = frac{(11 imes 4)}{(2 imes 7)} = frac{44}{14} = frac{22}{7}$

Step 4:

Writing the improper fraction as a mixed number

$frac{22}{7} = 3frac{1}{7}$

Step 5:

So, $5frac{1}{2} span 1frac{3}{4} = 3frac{1}{7}$