12 2/3 + 7 3/16 + 5 3/7

⚠ 12 2/3 is read as the mixed number 12 + 2/3■7 3/16 is read as the mixed number 7 + 3/16■5 3/7 is read as the mixed number 5 + 3/7

1) Let's calculate:

12

+ \frac{2}{3}

+ 7

+ \frac{3}{16}

+ 5

+ \frac{3}{7}

ⓘ Start from

12

and move forward

7

on the number line:

12 + 7

19

19

+ \frac{2}{3}

+ \frac{3}{16}

+ 5

+ \frac{3}{7}

ⓘ Start from

19

and move forward

5

on the number line:

19 + 5

24

24

+ \frac{2}{3}

+ \frac{3}{16}

+ \frac{3}{7}

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

48

, the least common multiple of

3

and

16

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

\frac{2}{3} + \frac{3}{16}

\frac{2 \times 16}{3 \times 16} + \frac{3 \times 3}{16 \times 3}

\frac{2 \times 16 + 3 \times 3}{3 \times 16}

24 + \frac{2 \times 16 + 3 \times 3}{3 \times 16} + \frac{3}{7}

ⓘ Multiplications are done before additions and subtractions:

2 \times 16

2 \times (10 + 6)

2 \times 10 + 2 \times 6

20 + 12

32

3 \times 3

9

ⅰ

3 \times 16

3 \times (10 + 6)

3 \times 10 + 3 \times 6

30 + 18

48

24 + \frac{32 + 9}{48} + \frac{3}{7}

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

32 + 9

41

24 + \frac{41}{48} + \frac{3}{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{41}{48} + \frac{3}{7}

\frac{41 \times 7}{48 \times 7} + \frac{3 \times 48}{7 \times 48}

\frac{41 \times 7 + 3 \times 48}{48 \times 7}

24 + \frac{41 \times 7 + 3 \times 48}{48 \times 7}

ⓘ Multiplications are done before additions and subtractions:

41 \times 7

(40 + 1) \times 7

40 \times 7 + 7

280 + 7

287

3 \times 48

3 \times (40 + 8)

3 \times 40 + 3 \times 8

120 + 24

144

ⅰ

48 \times 7

(40 + 8) \times 7

40 \times 7 + 8 \times 7

280 + 56

336

24 + \frac{287 + 144}{336}

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

287 + 144

431

24 + \frac{431}{336}

▶Result:

25

\frac{95}{336}

ⓘ Since the fraction

\frac{431}{336}

exceeds 1, take

1

out of it and add it to the whole part:

24 + \frac{431}{336}

24 + \frac{336 + 95}{336}

24 + \frac{336}{336} + \frac{95}{336}

24 + 1 + \frac{95}{336}

25 + \frac{95}{336}

2) The numeric value of:

25 + \frac{95}{336}

is:

25 + \approx 0.2827

▷

\approx 25.2827

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