17 13/20 + 24 1/9 + 24 11/16

⚠ 17 13/20 is read as the mixed number 17 + 13/20■24 1/9 is read as the mixed number 24 + 1/9■24 11/16 is read as the mixed number 24 + 11/16

1) Let's evaluate:

17

+ \frac{13}{20}

+ 24

+ \frac{1}{9}

+ 24

+ \frac{11}{16}

ⓘ Start from

17

and move forward

24

on the number line:

17 + 24

41

41

+ \frac{13}{20}

+ \frac{1}{9}

+ 24

+ \frac{11}{16}

ⓘ Start from

41

and move forward

24

on the number line:

41 + 24

65

65

+ \frac{13}{20}

+ \frac{1}{9}

+ \frac{11}{16}

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

180

, the least common multiple of

20

and

9

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

\frac{13}{20} + \frac{1}{9}

\frac{13 \times 9}{20 \times 9} + \frac{1 \times 20}{9 \times 20}

\frac{13 \times 9 + 1 \times 20}{20 \times 9}

\frac{13 \times 9 + 20}{20 \times 9}

65 + \frac{13 \times 9 + 20}{20 \times 9} + \frac{11}{16}

ⓘ Perform multiplications before additions and subtractions:

13 \times 9

(10 + 3) \times 9

10 \times 9 + 3 \times 9

90 + 27

117

ⅰ

20 \times 9

180

65 + \frac{117 + 20}{180} + \frac{11}{16}

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

117 + 20

137

65 + \frac{137}{180} + \frac{11}{16}

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

720

, the least common multiple of

180

and

16

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

\frac{137}{180} + \frac{11}{16}

\frac{137 \times 4}{180 \times 4} + \frac{11 \times 45}{16 \times 45}

\frac{137 \times 4 + 11 \times 45}{180 \times 4}

65 + \frac{137 \times 4 + 11 \times 45}{180 \times 4}

ⓘ Perform multiplications before additions and subtractions:

137 \times 4

(100 + 30 + 7) \times 4

100 \times 4 + 30 \times 4 + 7 \times 4

400 + 120 + 28

548

11 \times 45

(10 + 1) \times 45

10 \times 45 + 45

450 + 45

495

ⅰ

180 \times 4

(100 + 80) \times 4

100 \times 4 + 80 \times 4

400 + 320

720

65 + \frac{548 + 495}{720}

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

548 + 495

1043

65 + \frac{1043}{720}

▶Result:

66

\frac{323}{720}

ⓘ The fraction

\frac{1043}{720}

is greater than 1: extract

1

from it and add it to the whole part:

65 + \frac{1043}{720}

65 + \frac{720 + 323}{720}

65 + \frac{720}{720} + \frac{323}{720}

65 + 1 + \frac{323}{720}

66 + \frac{323}{720}

2) The numeric value of:

66 + \frac{323}{720}

is:

66 + \approx 0.4486

▷

\approx 66.4486

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