17 15/16 + 8 2/9 + 23 6/7

⚠ 17 15/16 is read as the mixed number 17 + 15/16■8 2/9 is read as the mixed number 8 + 2/9■23 6/7 is read as the mixed number 23 + 6/7

1) Let's evaluate:

17

+ \frac{15}{16}

+ 8

+ \frac{2}{9}

+ 23

+ \frac{6}{7}

ⓘ Start from

17

and move forward

8

on the number line:

17 + 8

25

25

+ \frac{15}{16}

+ \frac{2}{9}

+ 23

+ \frac{6}{7}

ⓘ Start from

25

and move forward

23

on the number line:

25 + 23

48

48

+ \frac{15}{16}

+ \frac{2}{9}

+ \frac{6}{7}

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

144

, the least common multiple of

16

and

9

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

\frac{15}{16} + \frac{2}{9}

\frac{15 \times 9}{16 \times 9} + \frac{2 \times 16}{9 \times 16}

\frac{15 \times 9 + 2 \times 16}{16 \times 9}

48 + \frac{15 \times 9 + 2 \times 16}{16 \times 9} + \frac{6}{7}

ⓘ Perform multiplications before additions and subtractions:

15 \times 9

(10 + 5) \times 9

10 \times 9 + 5 \times 9

90 + 45

135

2 \times 16

2 \times (10 + 6)

2 \times 10 + 2 \times 6

20 + 12

32

ⅰ

16 \times 9

(10 + 6) \times 9

10 \times 9 + 6 \times 9

90 + 54

144

48 + \frac{135 + 32}{144} + \frac{6}{7}

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

135 + 32

167

48 + \frac{167}{144} + \frac{6}{7}

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

1008

, the least common multiple of

144

and

7

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

\frac{167}{144} + \frac{6}{7}

\frac{167 \times 7}{144 \times 7} + \frac{6 \times 144}{7 \times 144}

\frac{167 \times 7 + 6 \times 144}{144 \times 7}

48 + \frac{167 \times 7 + 6 \times 144}{144 \times 7}

ⓘ Perform multiplications before additions and subtractions:

167 \times 7

(100 + 60 + 7) \times 7

100 \times 7 + 60 \times 7 + 7 \times 7

700 + 420 + 49

1169

6 \times 144

6 \times (100 + 40 + 4)

6 \times 100 + 6 \times 40 + 6 \times 4

600 + 240 + 24

864

ⅰ

144 \times 7

(100 + 40 + 4) \times 7

100 \times 7 + 40 \times 7 + 4 \times 7

700 + 280 + 28

1008

48 + \frac{1169 + 864}{1008}

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

1169 + 864

2033

48 + \frac{2033}{1008}

▶Result:

50

\frac{17}{1008}

ⓘ The fraction

\frac{2033}{1008}

is greater than 1: extract

2

from it and add it to the whole part:

48 + \frac{2033}{1008}

48 + \frac{2016 + 17}{1008}

48 + \frac{2016}{1008} + \frac{17}{1008}

48 + 2 + \frac{17}{1008}

50 + \frac{17}{1008}

2) The numeric value of:

50 + \frac{17}{1008}

equals:

50 + \approx 1.6865 \times 10^{- 2}

▷

\approx 50.0169

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