22 1/5 - 9 8/9 — all steps free

⚠ 22 1/5 is read as the mixed number 22 + 1/5■9 8/9 is read as the mixed number 9 + 8/9

Let's evaluate:

22 + \frac{1}{5} - (9 + \frac{8}{9})

ⓘ A minus sign before a parenthesis changes the sign of each of its terms:

- (9 + \frac{8}{9})

- 9 - \frac{8}{9}

22

+ \frac{1}{5}

- 9

- \frac{8}{9}

ⓘ Start from

22

and move back

9

on the number line:

22 - 9

13

13 + \frac{1}{5} - \frac{8}{9}

ⓘ Add fractions by using a common denominator and then adding their numerators. We choose

45

, the least common multiple of

5

and

9

. Multiplying the numerator and the denominator by the same number does not change the fraction:

\frac{1}{5} - \frac{8}{9}

\frac{1 \times 9}{5 \times 9} - \frac{8 \times 5}{9 \times 5}

\frac{1 \times 9 - 8 \times 5}{5 \times 9}

\frac{9 - 8 \times 5}{5 \times 9}

13 + \frac{9 - 8 \times 5}{5 \times 9}

ⓘ Perform multiplications before additions and subtractions:

8 \times 5

40

ⅰ

5 \times 9

45

13 + \frac{9 - 40}{45}

ⓘ Calculate the numerator and denominator before dividing:

9 - 40

-31

13 - \frac{31}{45}

▶Result:

12

\frac{14}{45}

ⓘ Since the fraction

- \frac{31}{45}

is negative, borrow

1

from the whole part so that the fraction lies between 0 and 1:

13 - \frac{31}{45}

13 - \frac{45 - 14}{45}

13 - \frac{45}{45} + \frac{14}{45}

13 - 1 + \frac{14}{45}

12 + \frac{14}{45}

The numeric value of:

12 + \frac{14}{45}

is:

12 + \approx 0.3111

▷

\approx 12.3111

22 1/5 - 9 8/9