14 5/16 + 20 13/15 + 21 11/12

⚠ 14 5/16 is read as the mixed number 14 + 5/16■20 13/15 is read as the mixed number 20 + 13/15■21 11/12 is read as the mixed number 21 + 11/12

1) Let's calculate:

14

+ \frac{5}{16}

+ 20

+ \frac{13}{15}

+ 21

+ \frac{11}{12}

ⓘ Start from

14

and move forward

20

on the number line:

14 + 20

34

34

+ \frac{5}{16}

+ \frac{13}{15}

+ 21

+ \frac{11}{12}

ⓘ Start from

34

and move forward

21

on the number line:

34 + 21

55

55

+ \frac{5}{16}

+ \frac{13}{15}

+ \frac{11}{12}

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

240

, the least common multiple of

16

and

15

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

\frac{5}{16} + \frac{13}{15}

\frac{5 \times 15}{16 \times 15} + \frac{13 \times 16}{15 \times 16}

\frac{5 \times 15 + 13 \times 16}{16 \times 15}

55 + \frac{5 \times 15 + 13 \times 16}{16 \times 15} + \frac{11}{12}

ⓘ Perform multiplications before additions and subtractions:

5 \times 15

5 \times (10 + 5)

5 \times 10 + 5 \times 5

50 + 25

75

13 \times 16

(10 + 3) \times 16

10 \times 16 + 3 \times 16

160 + 48

208

ⅰ

16 \times 15

16 \times (10 + 5)

16 \times 10 + 16 \times 5

160 + 80

240

55 + \frac{75 + 208}{240} + \frac{11}{12}

ⓘ Calculate the numerator and denominator before dividing:

75 + 208

283

55 + \frac{283}{240} + \frac{11}{12}

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

240

, the least common multiple of

240

and

12

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

\frac{283}{240} + \frac{11}{12}

\frac{283}{240} + \frac{11 \times 20}{12 \times 20}

\frac{283 + 11 \times 20}{240}

55 + \frac{283 + 11 \times 20}{240}

ⓘ Perform multiplications before additions and subtractions:

11 \times 20

(10 + 1) \times 20

10 \times 20 + 20

200 + 20

220

55 + \frac{283 + 220}{240}

ⓘ Calculate the numerator and denominator before dividing:

283 + 220

503

55 + \frac{503}{240}

▶Result:

57

\frac{23}{240}

ⓘ Since the fraction

\frac{503}{240}

exceeds 1, take

2

out of it and add it to the whole part:

55 + \frac{503}{240}

55 + \frac{480 + 23}{240}

55 + \frac{480}{240} + \frac{23}{240}

55 + 2 + \frac{23}{240}

57 + \frac{23}{240}

2) The numeric value of:

57 + \frac{23}{240}

equals:

57 + \approx 9.5833 \times 10^{- 2}

▷

\approx 57.0958

100% free