20 9/10 + 11 5/8 + 22 4/7

⚠ 20 9/10 is read as the mixed number 20 + 9/10■11 5/8 is read as the mixed number 11 + 5/8■22 4/7 is read as the mixed number 22 + 4/7

1) Let's calculate:

20

+ \frac{9}{10}

+ 11

+ \frac{5}{8}

+ 22

+ \frac{4}{7}

ⓘ Start from

20

and move forward

11

on the number line:

20 + 11

31

31

+ \frac{9}{10}

+ \frac{5}{8}

+ 22

+ \frac{4}{7}

ⓘ Start from

31

and move forward

22

on the number line:

31 + 22

53

53

+ \frac{9}{10}

+ \frac{5}{8}

+ \frac{4}{7}

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

40

, the least common multiple of

10

and

8

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

\frac{9}{10} + \frac{5}{8}

\frac{9 \times 4}{10 \times 4} + \frac{5 \times 5}{8 \times 5}

\frac{9 \times 4 + 5 \times 5}{10 \times 4}

53 + \frac{9 \times 4 + 5 \times 5}{10 \times 4} + \frac{4}{7}

ⓘ Multiplications are done before additions and subtractions:

9 \times 4

36

5 \times 5

25

ⅰ

10 \times 4

40

53 + \frac{36 + 25}{40} + \frac{4}{7}

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

36 + 25

61

53 + \frac{61}{40} + \frac{4}{7}

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

280

, the least common multiple of

40

and

7

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

\frac{61}{40} + \frac{4}{7}

\frac{61 \times 7}{40 \times 7} + \frac{4 \times 40}{7 \times 40}

\frac{61 \times 7 + 4 \times 40}{40 \times 7}

53 + \frac{61 \times 7 + 4 \times 40}{40 \times 7}

ⓘ Multiplications are done before additions and subtractions:

61 \times 7

(60 + 1) \times 7

60 \times 7 + 7

420 + 7

427

4 \times 40

160

ⅰ

40 \times 7

280

53 + \frac{427 + 160}{280}

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

427 + 160

587

53 + \frac{587}{280}

▶Result:

55

\frac{27}{280}

ⓘ Since the fraction

\frac{587}{280}

exceeds 1, take

2

out of it and add it to the whole part:

53 + \frac{587}{280}

53 + \frac{560 + 27}{280}

53 + \frac{560}{280} + \frac{27}{280}

53 + 2 + \frac{27}{280}

55 + \frac{27}{280}

2) The numeric value of:

55 + \frac{27}{280}

equals:

55 + \approx 9.6429 \times 10^{- 2}

▷

\approx 55.0964

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