8 4/5 + 6 11/16 + 23 2/3

⚠ 8 4/5 is read as the mixed number 8 + 4/5■6 11/16 is read as the mixed number 6 + 11/16■23 2/3 is read as the mixed number 23 + 2/3

1) Let's evaluate:

8

+ \frac{4}{5}

+ 6

+ \frac{11}{16}

+ 23

+ \frac{2}{3}

ⓘ Start from

8

and move forward

6

on the number line:

8 + 6

14

14

+ \frac{4}{5}

+ \frac{11}{16}

+ 23

+ \frac{2}{3}

ⓘ Start from

14

and move forward

23

on the number line:

14 + 23

37

37

+ \frac{4}{5}

+ \frac{11}{16}

+ \frac{2}{3}

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

80

, the least common multiple of

5

and

16

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

\frac{4}{5} + \frac{11}{16}

\frac{4 \times 16}{5 \times 16} + \frac{11 \times 5}{16 \times 5}

\frac{4 \times 16 + 11 \times 5}{5 \times 16}

37 + \frac{4 \times 16 + 11 \times 5}{5 \times 16} + \frac{2}{3}

ⓘ Multiplications are done before additions and subtractions:

4 \times 16

4 \times (10 + 6)

4 \times 10 + 4 \times 6

40 + 24

64

11 \times 5

(10 + 1) \times 5

10 \times 5 + 5

50 + 5

55

ⅰ

5 \times 16

5 \times (10 + 6)

5 \times 10 + 5 \times 6

50 + 30

80

37 + \frac{64 + 55}{80} + \frac{2}{3}

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

64 + 55

119

37 + \frac{119}{80} + \frac{2}{3}

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

240

, the least common multiple of

80

and

3

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

\frac{119}{80} + \frac{2}{3}

\frac{119 \times 3}{80 \times 3} + \frac{2 \times 80}{3 \times 80}

\frac{119 \times 3 + 2 \times 80}{80 \times 3}

37 + \frac{119 \times 3 + 2 \times 80}{80 \times 3}

ⓘ Multiplications are done before additions and subtractions:

119 \times 3

(100 + 10 + 9) \times 3

100 \times 3 + 10 \times 3 + 9 \times 3

300 + 30 + 27

357

2 \times 80

160

ⅰ

80 \times 3

240

37 + \frac{357 + 160}{240}

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

357 + 160

517

37 + \frac{517}{240}

▶Result:

39

\frac{37}{240}

ⓘ Since the fraction

\frac{517}{240}

exceeds 1, take

2

out of it and add it to the whole part:

37 + \frac{517}{240}

37 + \frac{480 + 37}{240}

37 + \frac{480}{240} + \frac{37}{240}

37 + 2 + \frac{37}{240}

39 + \frac{37}{240}

2) The numeric value of:

39 + \frac{37}{240}

is:

39 + \approx 0.1542

▷

\approx 39.1542

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