explain 6 3/7 + 6 13/16 + 6 5/9 — step-by-step solution

⚠ 6 3/7 is read as the mixed number 6 + 3/7

⚠ 6 13/16 is read as the mixed number 6 + 13/16

Let's evaluate:

6

+ \frac{3}{7}

+ 6

+ \frac{13}{16}

+ 6

+ \frac{5}{9}

ℹ

6 + 6

12

12

+ \frac{3}{7}

+ \frac{13}{16}

+ 6

+ \frac{5}{9}

ℹ

12 + 6

18

18

+ \frac{3}{7}

+ \frac{13}{16}

+ \frac{5}{9}

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

\frac{3}{7} + \frac{13}{16}

\frac{3 \times 16 + 13 \times 7}{7 \times 16}

18 + \frac{3 \times 16 + 13 \times 7}{7 \times 16} + \frac{5}{9}

ⓘMultiplications are done before additions and subtractions:

3 \times 16

(10 + 6) \times 3

10 \times 3 + 6 \times 3

30 + 18

48

‖

13 \times 7

(10 + 3) \times 7

10 \times 7 + 3 \times 7

70 + 21

91

‖

7 \times 16

(10 + 6) \times 7

10 \times 7 + 6 \times 7

70 + 42

112

18 + \frac{48 + 91}{112} + \frac{5}{9}

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

48 + 91

139

18 + \frac{139}{112} + \frac{5}{9}

ℹ

\frac{139}{112} + \frac{5}{9}

\frac{139 \times 9 + 5 \times 112}{112 \times 9}

18 + \frac{139 \times 9 + 5 \times 112}{112 \times 9}

ⓘ

139 \times 9

(100 + 30 + 9) \times 9

100 \times 9 + 30 \times 9 + 9 \times 9

900 + 270 + 81

1251

‖

5 \times 112

(100 + 10 + 2) \times 5

100 \times 5 + 10 \times 5 + 2 \times 5

500 + 50 + 10

560

‖

112 \times 9

(100 + 10 + 2) \times 9

100 \times 9 + 10 \times 9 + 2 \times 9

900 + 90 + 18

1008

18 + \frac{1251 + 560}{1008}

ℹ

1251 + 560

1811

18 + \frac{1811}{1008}

ⓘThe fraction

\frac{1811}{1008}

is greater than 1: add its integer part

1

to the whole part:

\frac{1811}{1008} + 18

19 + \frac{803}{1008}

▶Result:

19

\frac{803}{1008}

The approximate value of:

19 + \frac{803}{1008}

equals:

19 + \approx 0.7966

▷

\approx 19.7966