23 5/6 + 24 3/4 + 17 8/9

⚠ 23 5/6 is read as the mixed number 23 + 5/6■24 3/4 is read as the mixed number 24 + 3/4■17 8/9 is read as the mixed number 17 + 8/9

1) Let's evaluate:

23

+ \frac{5}{6}

+ 24

+ \frac{3}{4}

+ 17

+ \frac{8}{9}

ⓘ Start from

23

and move forward

24

on the number line:

23 + 24

47

47

+ \frac{5}{6}

+ \frac{3}{4}

+ 17

+ \frac{8}{9}

ⓘ Start from

47

and move forward

17

on the number line:

47 + 17

64

64

+ \frac{5}{6}

+ \frac{3}{4}

+ \frac{8}{9}

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

12

, the least common multiple of

6

and

4

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

\frac{5}{6} + \frac{3}{4}

\frac{5 \times 2}{6 \times 2} + \frac{3 \times 3}{4 \times 3}

\frac{5 \times 2 + 3 \times 3}{6 \times 2}

64 + \frac{5 \times 2 + 3 \times 3}{6 \times 2} + \frac{8}{9}

ⓘ Multiplications are done before additions and subtractions:

5 \times 2

10

3 \times 3

9

ⅰ

6 \times 2

12

64 + \frac{10 + 9}{12} + \frac{8}{9}

ⓘ Calculate the numerator and denominator before dividing:

10 + 9

19

64 + \frac{19}{12} + \frac{8}{9}

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

36

, the least common multiple of

12

and

9

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

\frac{19}{12} + \frac{8}{9}

\frac{19 \times 3}{12 \times 3} + \frac{8 \times 4}{9 \times 4}

\frac{19 \times 3 + 8 \times 4}{12 \times 3}

64 + \frac{19 \times 3 + 8 \times 4}{12 \times 3}

ⓘ Multiplications are done before additions and subtractions:

19 \times 3

(10 + 9) \times 3

10 \times 3 + 9 \times 3

30 + 27

57

8 \times 4

32

ⅰ

12 \times 3

(10 + 2) \times 3

10 \times 3 + 2 \times 3

30 + 6

36

64 + \frac{57 + 32}{36}

ⓘ Calculate the numerator and denominator before dividing:

57 + 32

89

64 + \frac{89}{36}

▶Result:

66

\frac{17}{36}

ⓘ Since the fraction

\frac{89}{36}

exceeds 1, take

2

out of it and add it to the whole part:

64 + \frac{89}{36}

64 + \frac{72 + 17}{36}

64 + \frac{72}{36} + \frac{17}{36}

64 + 2 + \frac{17}{36}

66 + \frac{17}{36}

2) The numeric value of:

66 + \frac{17}{36}

equals:

66 + \approx 0.4722

▷

\approx 66.4722

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