explain 12 2/3 + 7 3/16 + 5 3/7 — step-by-step solution

⚠ 12 2/3 is read as the mixed number 12 + 2/3

⚠ 7 3/16 is read as the mixed number 7 + 3/16

Let's evaluate:

12

+ \frac{2}{3}

+ 7

+ \frac{3}{16}

+ 5

+ \frac{3}{7}

ℹ

12 + 7

19

19

+ \frac{2}{3}

+ \frac{3}{16}

+ 5

+ \frac{3}{7}

ℹ

19 + 5

24

24

+ \frac{2}{3}

+ \frac{3}{16}

+ \frac{3}{7}

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

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

\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

(10 + 6) \times 2

10 \times 2 + 6 \times 2

20 + 12

32

‖

3 \times 16

(10 + 6) \times 3

10 \times 3 + 6 \times 3

30 + 18

48

ℹ

3 \times 3

9

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}

ℹ

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

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

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

ⓘ

41 \times 7

(40 + 1) \times 7

40 \times 7 + 7

280 + 7

287

‖

3 \times 48

(40 + 8) \times 3

40 \times 3 + 8 \times 3

120 + 24

144

‖

48 \times 7

(40 + 8) \times 7

40 \times 7 + 8 \times 7

280 + 56

336

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

ℹ

287 + 144

431

24 + \frac{431}{336}

ⓘThe fraction

\frac{431}{336}

is greater than 1: add its integer part

1

to the whole part:

\frac{431}{336} + 24

25 + \frac{95}{336}

▶Result:

25

\frac{95}{336}

The approximate value of:

25 + \frac{95}{336}

equals:

25 + \approx 0.2827

▷

\approx 25.2827