2 9/20 + 9 8/9 + 21 7/9

⚠ 2 9/20 is read as the mixed number 2 + 9/20■9 8/9 is read as the mixed number 9 + 8/9■21 7/9 is read as the mixed number 21 + 7/9

Let's evaluate:

2

+ \frac{9}{20}

+ 9

+ \frac{8}{9}

+ 21

+ \frac{7}{9}

ⓘ Start from

2

and move forward

9

on the number line:

2 + 9

11

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

\frac{8}{9} + \frac{7}{9}

\frac{8 + 7}{9}

11

+ \frac{9}{20}

+ \frac{8 + 7}{9}

+ 21

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

8 + 7

15

11

+ \frac{9}{20}

+ \frac{15}{9}

+ 21

ⓘ Start from

11

and move forward

21

on the number line:

11 + 21

32

■Simplify the fraction by dividing the numerator and the denominator by

3

, their greatest common divisor:

\frac{15}{9}

\frac{5 \times 3}{3 \times 3}

\frac{5}{3}

32 + \frac{9}{20} + \frac{5}{3}

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

60

, the least common multiple of

20

and

3

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

\frac{9}{20} + \frac{5}{3}

\frac{9 \times 3}{20 \times 3} + \frac{5 \times 20}{3 \times 20}

\frac{9 \times 3 + 5 \times 20}{20 \times 3}

32 + \frac{9 \times 3 + 5 \times 20}{20 \times 3}

ⓘ Multiplications are done before additions and subtractions:

9 \times 3

27

5 \times 20

100

ⅰ

20 \times 3

60

32 + \frac{27 + 100}{60}

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

27 + 100

127

32 + \frac{127}{60}

▶Result:

34

\frac{7}{60}

ⓘ Since the fraction

\frac{127}{60}

exceeds 1, take

2

out of it and add it to the whole part:

32 + \frac{127}{60}

32 + \frac{120 + 7}{60}

32 + \frac{120}{60} + \frac{7}{60}

32 + 2 + \frac{7}{60}

34 + \frac{7}{60}

The numeric value of:

34 + \frac{7}{60}

equals:

34 + \approx 0.1167

▷

\approx 34.1167

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