23 13/15 + 10 9/20 + 8 7/16

⚠ 23 13/15 is read as the mixed number 23 + 13/15■10 9/20 is read as the mixed number 10 + 9/20■8 7/16 is read as the mixed number 8 + 7/16

1) Let's calculate:

23

+ \frac{13}{15}

+ 10

+ \frac{9}{20}

+ 8

+ \frac{7}{16}

ⓘ Start from

23

and move forward

10

on the number line:

23 + 10

33

33

+ \frac{13}{15}

+ \frac{9}{20}

+ 8

+ \frac{7}{16}

ⓘ Start from

33

and move forward

8

on the number line:

33 + 8

41

41

+ \frac{13}{15}

+ \frac{9}{20}

+ \frac{7}{16}

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

60

, the least common multiple of

15

and

20

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

\frac{13}{15} + \frac{9}{20}

\frac{13 \times 4}{15 \times 4} + \frac{9 \times 3}{20 \times 3}

\frac{13 \times 4 + 9 \times 3}{15 \times 4}

41 + \frac{13 \times 4 + 9 \times 3}{15 \times 4} + \frac{7}{16}

ⓘ Perform multiplications before additions and subtractions:

13 \times 4

(10 + 3) \times 4

10 \times 4 + 3 \times 4

40 + 12

52

9 \times 3

27

ⅰ

15 \times 4

(10 + 5) \times 4

10 \times 4 + 5 \times 4

40 + 20

60

41 + \frac{52 + 27}{60} + \frac{7}{16}

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

52 + 27

79

41 + \frac{79}{60} + \frac{7}{16}

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

240

, the least common multiple of

60

and

16

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

\frac{79}{60} + \frac{7}{16}

\frac{79 \times 4}{60 \times 4} + \frac{7 \times 15}{16 \times 15}

\frac{79 \times 4 + 7 \times 15}{60 \times 4}

41 + \frac{79 \times 4 + 7 \times 15}{60 \times 4}

ⓘ Perform multiplications before additions and subtractions:

79 \times 4

(70 + 9) \times 4

70 \times 4 + 9 \times 4

280 + 36

316

7 \times 15

7 \times (10 + 5)

7 \times 10 + 7 \times 5

70 + 35

105

ⅰ

60 \times 4

240

41 + \frac{316 + 105}{240}

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

316 + 105

421

41 + \frac{421}{240}

▶Result:

42

\frac{181}{240}

ⓘ Since the fraction

\frac{421}{240}

exceeds 1, take

1

out of it and add it to the whole part:

41 + \frac{421}{240}

41 + \frac{240 + 181}{240}

41 + \frac{240}{240} + \frac{181}{240}

41 + 1 + \frac{181}{240}

42 + \frac{181}{240}

2) The numeric value of:

42 + \frac{181}{240}

is:

42 + \approx 0.7542

▷

\approx 42.7542

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