15 14/15 + 10 11/12 + 15 13/20

⚠ 15 14/15 is read as the mixed number 15 + 14/15■10 11/12 is read as the mixed number 10 + 11/12■15 13/20 is read as the mixed number 15 + 13/20

1) Let's calculate:

15

+ \frac{14}{15}

+ 10

+ \frac{11}{12}

+ 15

+ \frac{13}{20}

ⓘ Start from

15

and move forward

10

on the number line:

15 + 10

25

25

+ \frac{14}{15}

+ \frac{11}{12}

+ 15

+ \frac{13}{20}

ⓘ Start from

25

and move forward

15

on the number line:

25 + 15

40

40

+ \frac{14}{15}

+ \frac{11}{12}

+ \frac{13}{20}

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

60

, the least common multiple of

15

and

12

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

\frac{14}{15} + \frac{11}{12}

\frac{14 \times 4}{15 \times 4} + \frac{11 \times 5}{12 \times 5}

\frac{14 \times 4 + 11 \times 5}{15 \times 4}

40 + \frac{14 \times 4 + 11 \times 5}{15 \times 4} + \frac{13}{20}

ⓘ Multiplications are done before additions and subtractions:

14 \times 4

(10 + 4) \times 4

10 \times 4 + 4 \times 4

40 + 16

56

11 \times 5

(10 + 1) \times 5

10 \times 5 + 5

50 + 5

55

ⅰ

15 \times 4

(10 + 5) \times 4

10 \times 4 + 5 \times 4

40 + 20

60

40 + \frac{56 + 55}{60} + \frac{13}{20}

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

56 + 55

111

40 + \frac{111}{60} + \frac{13}{20}

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

60

, the least common multiple of

60

and

20

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

\frac{111}{60} + \frac{13}{20}

\frac{111}{60} + \frac{13 \times 3}{20 \times 3}

\frac{111 + 13 \times 3}{60}

40 + \frac{111 + 13 \times 3}{60}

ⓘ Multiplications are done before additions and subtractions:

13 \times 3

(10 + 3) \times 3

10 \times 3 + 3 \times 3

30 + 9

39

40 + \frac{111 + 39}{60}

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

111 + 39

150

40 + \frac{150}{60}

We divide the numerator and denominator of

\frac{150}{60}

by the common factor:

30

, which gives the new fraction:

\frac{5}{2}

40 + \frac{5}{2}

▶Result:

42

\frac{1}{2}

ⓘ Since the fraction

\frac{5}{2}

exceeds 1, take

2

out of it and add it to the whole part:

40 + \frac{5}{2}

40 + \frac{4 + 1}{2}

40 + \frac{4}{2} + \frac{1}{2}

40 + 2 + \frac{1}{2}

42 + \frac{1}{2}

2) The numeric value of:

42 + \frac{1}{2}

is:

42 + 0.5

▷

42.5

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