16 2/15 + 8 1/16 + 8 7/12

⚠ 16 2/15 is read as the mixed number 16 + 2/15■8 1/16 is read as the mixed number 8 + 1/16■8 7/12 is read as the mixed number 8 + 7/12

1) Let's evaluate:

16

+ \frac{2}{15}

+ 8

+ \frac{1}{16}

+ 8

+ \frac{7}{12}

ⓘ Start from

16

and move forward

8

on the number line:

16 + 8

24

24

+ \frac{2}{15}

+ \frac{1}{16}

+ 8

+ \frac{7}{12}

ⓘ Start from

24

and move forward

8

on the number line:

24 + 8

32

32

+ \frac{2}{15}

+ \frac{1}{16}

+ \frac{7}{12}

ⓘ To add fractions, put them over the same denominator, then add the numerators. We choose

240

, the least common multiple of

15

and

16

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

\frac{2}{15} + \frac{1}{16}

\frac{2 \times 16}{15 \times 16} + \frac{1 \times 15}{16 \times 15}

\frac{2 \times 16 + 1 \times 15}{15 \times 16}

\frac{2 \times 16 + 15}{15 \times 16}

32 + \frac{2 \times 16 + 15}{15 \times 16} + \frac{7}{12}

ⓘ Perform multiplications before additions and subtractions:

2 \times 16

2 \times (10 + 6)

2 \times 10 + 2 \times 6

20 + 12

32

ⅰ

15 \times 16

(10 + 5) \times 16

10 \times 16 + 5 \times 16

160 + 80

240

32 + \frac{32 + 15}{240} + \frac{7}{12}

ⓘ Calculate the numerator and denominator before dividing:

32 + 15

47

32 + \frac{47}{240} + \frac{7}{12}

ⓘ To add fractions, put them over the same denominator, then add the numerators. We choose

240

, the least common multiple of

240

and

12

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

\frac{47}{240} + \frac{7}{12}

\frac{47}{240} + \frac{7 \times 20}{12 \times 20}

\frac{47 + 7 \times 20}{240}

32 + \frac{47 + 7 \times 20}{240}

ⓘ Perform multiplications before additions and subtractions:

7 \times 20

140

32 + \frac{47 + 140}{240}

ⓘ Calculate the numerator and denominator before dividing:

47 + 140

187

32 + \frac{187}{240}

▶Result:

32

\frac{187}{240}

2) The numeric value of:

32 + \frac{187}{240}

equals:

32 + \approx 0.7792

▷

\approx 32.7792

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