1 11/12 + 10 13/20 + 10 4/9

⚠ 1 11/12 is read as the mixed number 1 + 11/12■10 13/20 is read as the mixed number 10 + 13/20■10 4/9 is read as the mixed number 10 + 4/9

1) Let's calculate:

1

+ \frac{11}{12}

+ 10

+ \frac{13}{20}

+ 10

+ \frac{4}{9}

ⓘ Start from

1

and move forward

10

on the number line:

1 + 10

11

11

+ \frac{11}{12}

+ \frac{13}{20}

+ 10

+ \frac{4}{9}

ⓘ Start from

11

and move forward

10

on the number line:

11 + 10

21

21

+ \frac{11}{12}

+ \frac{13}{20}

+ \frac{4}{9}

ⓘ To add fractions, put them over the same denominator, then add the numerators. We choose

60

, the least common multiple of

12

and

20

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

\frac{11}{12} + \frac{13}{20}

\frac{11 \times 5}{12 \times 5} + \frac{13 \times 3}{20 \times 3}

\frac{11 \times 5 + 13 \times 3}{12 \times 5}

21 + \frac{11 \times 5 + 13 \times 3}{12 \times 5} + \frac{4}{9}

ⓘ Multiplications are done before additions and subtractions:

11 \times 5

(10 + 1) \times 5

10 \times 5 + 5

50 + 5

55

13 \times 3

(10 + 3) \times 3

10 \times 3 + 3 \times 3

30 + 9

39

ⅰ

12 \times 5

(10 + 2) \times 5

10 \times 5 + 2 \times 5

50 + 10

60

21 + \frac{55 + 39}{60} + \frac{4}{9}

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

55 + 39

94

21 + \frac{94}{60} + \frac{4}{9}

ⓘ To add fractions, put them over the same denominator, then add the 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{94}{60} + \frac{4}{9}

\frac{94 \times 3}{60 \times 3} + \frac{4 \times 20}{9 \times 20}

\frac{94 \times 3 + 4 \times 20}{60 \times 3}

21 + \frac{94 \times 3 + 4 \times 20}{60 \times 3}

ⓘ Multiplications are done before additions and subtractions:

94 \times 3

(90 + 4) \times 3

90 \times 3 + 4 \times 3

270 + 12

282

4 \times 20

80

ⅰ

60 \times 3

180

21 + \frac{282 + 80}{180}

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

282 + 80

362

21 + \frac{362}{180}

ⓘ We simplify the fraction by dividing the numerator and the denominator by

2

, their greatest common divisor:

\frac{362}{180}

\frac{181 \times 2}{90 \times 2}

\frac{181}{90}

21 + \frac{181}{90}

▶Result:

23

\frac{1}{90}

ⓘ The fraction

\frac{181}{90}

is greater than 1: extract

2

from it and add it to the whole part:

21 + \frac{181}{90}

21 + \frac{180 + 1}{90}

21 + \frac{180}{90} + \frac{1}{90}

21 + 2 + \frac{1}{90}

23 + \frac{1}{90}

2) The numeric value of:

23 + \frac{1}{90}

is:

23 + \approx 1.1111 \times 10^{- 2}

▷

\approx 23.0111

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