explain 11 1/9 + 22 4/5 + 12 2/15 — step-by-step solution

⚠ 11 1/9 is read as the mixed number 11 + 1/9

⚠ 22 4/5 is read as the mixed number 22 + 4/5

Let's calculate:

11

+ \frac{1}{9}

+ 22

+ \frac{4}{5}

+ 12

+ \frac{2}{15}

ⓘTo add fractions, put them over the same denominator, then add the numerators:

\frac{4}{5} + \frac{2}{15}

\frac{3 \times 4 + 2}{15}

ℹ

11 + 22

33

33

+ \frac{1}{9}

+ \frac{3 \times 4 + 2}{15}

+ 12

ⓘMultiplications are done before additions and subtractions:

3 \times 4

12

ℹ

33 + 12

45

45 + \frac{1}{9} + \frac{12 + 2}{15}

ⓘThe numerator and the denominator are computed before the division:

12 + 2

14

45 + \frac{1}{9} + \frac{14}{15}

ℹ

\frac{1}{9} + \frac{14}{15}

\frac{1 \times 5 + 14 \times 3}{9 \times 5}

45 + \frac{1 \times 5 + 14 \times 3}{9 \times 5}

ⓘ

14 \times 3

(10 + 4) \times 3

10 \times 3 + 4 \times 3

30 + 12

42

ℹ

1 \times 5

5

‖

9 \times 5

45

45 + \frac{5 + 42}{45}

ℹ

5 + 42

47

45 + \frac{47}{45}

ⓘThe fraction

\frac{47}{45}

is greater than 1: add its integer part

1

to the whole part:

\frac{47}{45} + 45

46 + \frac{2}{45}

▶Result:

46

\frac{2}{45}

The numeric value of:

46 + \frac{2}{45}

is:

46 + \approx 4.4444 \times 10^{- 2}

▷

\approx 46.0444