explain 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

Let's evaluate:

15

+ \frac{14}{15}

+ 10

+ \frac{11}{12}

+ 15

+ \frac{13}{20}

ℹ

15 + 10

25

25

+ \frac{14}{15}

+ \frac{11}{12}

+ 15

+ \frac{13}{20}

ℹ

25 + 15

40

40

+ \frac{14}{15}

+ \frac{11}{12}

+ \frac{13}{20}

ⓘTo add fractions, put them over the same denominator, then add the numerators:

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

\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

‖

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}

ℹ

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

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

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

ⓘ

13 \times 3

(10 + 3) \times 3

10 \times 3 + 3 \times 3

30 + 9

39

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

ℹ

111 + 39

150

40 + \frac{150}{60}

We divide

\frac{150}{60}

by the common factor:

30

, which gives the new quotient:

\frac{5}{2}

ⓘWe simplify the fraction by dividing the numerator and the denominator by the number

30

\frac{150}{60}

\frac{5 \times 30}{2 \times 30}

\frac{5}{2}

40 + \frac{5}{2}

ⓘThe fraction

\frac{5}{2}

is greater than 1: add its integer part

2

to the whole part:

\frac{5}{2} + 40

42 + \frac{1}{2}

▶Result:

42

\frac{1}{2}

The numeric value of:

42 + \frac{1}{2}

equals:

42 + 0.5

▷

42.5