10 5/9 + 2 7/16 + 17 9/20

⚠ 10 5/9 is read as the mixed number 10 + 5/9■2 7/16 is read as the mixed number 2 + 7/16■17 9/20 is read as the mixed number 17 + 9/20

1) Let's calculate:

10

+ \frac{5}{9}

+ 2

+ \frac{7}{16}

+ 17

+ \frac{9}{20}

ⓘ Start from

10

and move forward

2

on the number line:

10 + 2

12

12

+ \frac{5}{9}

+ \frac{7}{16}

+ 17

+ \frac{9}{20}

ⓘ Start from

12

and move forward

17

on the number line:

12 + 17

29

29

+ \frac{5}{9}

+ \frac{7}{16}

+ \frac{9}{20}

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

144

, the least common multiple of

9

and

16

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

\frac{5}{9} + \frac{7}{16}

\frac{5 \times 16}{9 \times 16} + \frac{7 \times 9}{16 \times 9}

\frac{5 \times 16 + 7 \times 9}{9 \times 16}

29 + \frac{5 \times 16 + 7 \times 9}{9 \times 16} + \frac{9}{20}

ⓘ Multiplications are done before additions and subtractions:

5 \times 16

5 \times (10 + 6)

5 \times 10 + 5 \times 6

50 + 30

80

7 \times 9

63

ⅰ

9 \times 16

9 \times (10 + 6)

9 \times 10 + 9 \times 6

90 + 54

144

29 + \frac{80 + 63}{144} + \frac{9}{20}

ⓘ Calculate the numerator and denominator before dividing:

80 + 63

143

29 + \frac{143}{144} + \frac{9}{20}

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

720

, the least common multiple of

144

and

20

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

\frac{143}{144} + \frac{9}{20}

\frac{143 \times 5}{144 \times 5} + \frac{9 \times 36}{20 \times 36}

\frac{143 \times 5 + 9 \times 36}{144 \times 5}

29 + \frac{143 \times 5 + 9 \times 36}{144 \times 5}

ⓘ Multiplications are done before additions and subtractions:

143 \times 5

(100 + 40 + 3) \times 5

100 \times 5 + 40 \times 5 + 3 \times 5

500 + 200 + 15

715

9 \times 36

9 \times (30 + 6)

9 \times 30 + 9 \times 6

270 + 54

324

ⅰ

144 \times 5

(100 + 40 + 4) \times 5

100 \times 5 + 40 \times 5 + 4 \times 5

500 + 200 + 20

720

29 + \frac{715 + 324}{720}

ⓘ Calculate the numerator and denominator before dividing:

715 + 324

1039

29 + \frac{1039}{720}

▶Result:

30

\frac{319}{720}

ⓘ Since the fraction

\frac{1039}{720}

exceeds 1, take

1

out of it and add it to the whole part:

29 + \frac{1039}{720}

29 + \frac{720 + 319}{720}

29 + \frac{720}{720} + \frac{319}{720}

29 + 1 + \frac{319}{720}

30 + \frac{319}{720}

2) The numeric value of:

30 + \frac{319}{720}

equals:

30 + \approx 0.4431

▷

\approx 30.4431

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