11 1/9 + 22 4/5 + 12 2/15

⚠ 11 1/9 is read as the mixed number 11 + 1/9■22 4/5 is read as the mixed number 22 + 4/5■12 2/15 is read as the mixed number 12 + 2/15

Let's evaluate:

11

+ \frac{1}{9}

+ 22

+ \frac{4}{5}

+ 12

+ \frac{2}{15}

ⓘ Start from

11

and move forward

22

on the number line:

11 + 22

33

■Add fractions by using a common denominator and then adding their numerators:

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

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

33

+ \frac{1}{9}

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

+ 12

ⓘ Perform multiplications before additions and subtractions:

3 \times 4

12

■Start from

33

and move forward

12

on the number line:

33 + 12

45

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

ⓘ Calculate the numerator and denominator before dividing:

12 + 2

14

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

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

45

, the least common multiple of

9

and

15

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

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

\frac{1 \times 5}{9 \times 5} + \frac{14 \times 3}{15 \times 3}

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

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

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

ⓘ Perform multiplications before additions and subtractions:

14 \times 3

(10 + 4) \times 3

10 \times 3 + 4 \times 3

30 + 12

42

ⅰ

9 \times 5

45

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

ⓘ Calculate the numerator and denominator before dividing:

5 + 42

47

45 + \frac{47}{45}

▶Result:

46

\frac{2}{45}

ⓘ Since the fraction

\frac{47}{45}

exceeds 1, take

1

out of it and add it to the whole part:

45 + \frac{47}{45}

45 + \frac{45 + 2}{45}

45 + \frac{45}{45} + \frac{2}{45}

45 + 1 + \frac{2}{45}

46 + \frac{2}{45}

The numeric value of:

46 + \frac{2}{45}

is:

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

▷

\approx 46.0444

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