4 9/10 + 16 11/12 + 18 8/9

⚠ 4 9/10 is read as the mixed number 4 + 9/10■16 11/12 is read as the mixed number 16 + 11/12■18 8/9 is read as the mixed number 18 + 8/9

1) Let's evaluate:

4

+ \frac{9}{10}

+ 16

+ \frac{11}{12}

+ 18

+ \frac{8}{9}

ⓘ Start from

4

and move forward

16

on the number line:

4 + 16

20

20

+ \frac{9}{10}

+ \frac{11}{12}

+ 18

+ \frac{8}{9}

ⓘ Start from

20

and move forward

18

on the number line:

20 + 18

38

38

+ \frac{9}{10}

+ \frac{11}{12}

+ \frac{8}{9}

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

60

, the least common multiple of

10

and

12

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

\frac{9}{10} + \frac{11}{12}

\frac{9 \times 6}{10 \times 6} + \frac{11 \times 5}{12 \times 5}

\frac{9 \times 6 + 11 \times 5}{10 \times 6}

38 + \frac{9 \times 6 + 11 \times 5}{10 \times 6} + \frac{8}{9}

ⓘ Perform multiplications before additions and subtractions:

9 \times 6

54

11 \times 5

(10 + 1) \times 5

10 \times 5 + 5

50 + 5

55

ⅰ

10 \times 6

60

38 + \frac{54 + 55}{60} + \frac{8}{9}

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

54 + 55

109

38 + \frac{109}{60} + \frac{8}{9}

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

180

, the least common multiple of

60

and

9

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

\frac{109}{60} + \frac{8}{9}

\frac{109 \times 3}{60 \times 3} + \frac{8 \times 20}{9 \times 20}

\frac{109 \times 3 + 8 \times 20}{60 \times 3}

38 + \frac{109 \times 3 + 8 \times 20}{60 \times 3}

ⓘ Perform multiplications before additions and subtractions:

109 \times 3

(100 + 9) \times 3

100 \times 3 + 9 \times 3

300 + 27

327

8 \times 20

160

ⅰ

60 \times 3

180

38 + \frac{327 + 160}{180}

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

327 + 160

487

38 + \frac{487}{180}

▶Result:

40

\frac{127}{180}

ⓘ The fraction

\frac{487}{180}

is greater than 1: extract

2

from it and add it to the whole part:

38 + \frac{487}{180}

38 + \frac{360 + 127}{180}

38 + \frac{360}{180} + \frac{127}{180}

38 + 2 + \frac{127}{180}

40 + \frac{127}{180}

2) The numeric value of:

40 + \frac{127}{180}

is:

40 + \approx 0.7056

▷

\approx 40.7056

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