7 7/16 + 6 11/12 + 14 6/7

⚠ 7 7/16 is read as the mixed number 7 + 7/16■6 11/12 is read as the mixed number 6 + 11/12■14 6/7 is read as the mixed number 14 + 6/7

1) Let's calculate:

7

+ \frac{7}{16}

+ 6

+ \frac{11}{12}

+ 14

+ \frac{6}{7}

ⓘ Start from

7

and move forward

6

on the number line:

7 + 6

13

13

+ \frac{7}{16}

+ \frac{11}{12}

+ 14

+ \frac{6}{7}

ⓘ Start from

13

and move forward

14

on the number line:

13 + 14

27

27

+ \frac{7}{16}

+ \frac{11}{12}

+ \frac{6}{7}

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

48

, the least common multiple of

16

and

12

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

\frac{7}{16} + \frac{11}{12}

\frac{7 \times 3}{16 \times 3} + \frac{11 \times 4}{12 \times 4}

\frac{7 \times 3 + 11 \times 4}{16 \times 3}

27 + \frac{7 \times 3 + 11 \times 4}{16 \times 3} + \frac{6}{7}

ⓘ Perform multiplications before additions and subtractions:

7 \times 3

21

11 \times 4

(10 + 1) \times 4

10 \times 4 + 4

40 + 4

44

ⅰ

16 \times 3

(10 + 6) \times 3

10 \times 3 + 6 \times 3

30 + 18

48

27 + \frac{21 + 44}{48} + \frac{6}{7}

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

21 + 44

65

27 + \frac{65}{48} + \frac{6}{7}

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

336

, the least common multiple of

48

and

7

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

\frac{65}{48} + \frac{6}{7}

\frac{65 \times 7}{48 \times 7} + \frac{6 \times 48}{7 \times 48}

\frac{65 \times 7 + 6 \times 48}{48 \times 7}

27 + \frac{65 \times 7 + 6 \times 48}{48 \times 7}

ⓘ Perform multiplications before additions and subtractions:

65 \times 7

(60 + 5) \times 7

60 \times 7 + 5 \times 7

420 + 35

455

6 \times 48

6 \times (40 + 8)

6 \times 40 + 6 \times 8

240 + 48

288

ⅰ

48 \times 7

(40 + 8) \times 7

40 \times 7 + 8 \times 7

280 + 56

336

27 + \frac{455 + 288}{336}

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

455 + 288

743

27 + \frac{743}{336}

▶Result:

29

\frac{71}{336}

ⓘ Since the fraction

\frac{743}{336}

exceeds 1, take

2

out of it and add it to the whole part:

27 + \frac{743}{336}

27 + \frac{672 + 71}{336}

27 + \frac{672}{336} + \frac{71}{336}

27 + 2 + \frac{71}{336}

29 + \frac{71}{336}

2) The numeric value of:

29 + \frac{71}{336}

is:

29 + \approx 0.2113

▷

\approx 29.2113

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