23 17/20 + 2 2/9 + 1 14/15

⚠ 23 17/20 is read as the mixed number 23 + 17/20■2 2/9 is read as the mixed number 2 + 2/9■1 14/15 is read as the mixed number 1 + 14/15

1) Let's evaluate:

23

+ \frac{17}{20}

+ 2

+ \frac{2}{9}

+ 1

+ \frac{14}{15}

ⓘ Start from

23

and move forward

2

on the number line:

23 + 2

25

25

+ \frac{17}{20}

+ \frac{2}{9}

+ 1

+ \frac{14}{15}

ⓘ Start from

25

and move forward

1

on the number line:

25 + 1

26

26

+ \frac{17}{20}

+ \frac{2}{9}

+ \frac{14}{15}

ⓘ To add fractions, put them over the same denominator, then add the 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{17}{20} + \frac{2}{9}

\frac{17 \times 9}{20 \times 9} + \frac{2 \times 20}{9 \times 20}

\frac{17 \times 9 + 2 \times 20}{20 \times 9}

26 + \frac{17 \times 9 + 2 \times 20}{20 \times 9} + \frac{14}{15}

ⓘ Multiplications are done before additions and subtractions:

17 \times 9

(10 + 7) \times 9

10 \times 9 + 7 \times 9

90 + 63

153

2 \times 20

40

ⅰ

20 \times 9

180

26 + \frac{153 + 40}{180} + \frac{14}{15}

ⓘ Calculate the numerator and denominator before dividing:

153 + 40

193

26 + \frac{193}{180} + \frac{14}{15}

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

180

, the least common multiple of

180

and

15

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

\frac{193}{180} + \frac{14}{15}

\frac{193}{180} + \frac{14 \times 12}{15 \times 12}

\frac{193 + 14 \times 12}{180}

26 + \frac{193 + 14 \times 12}{180}

ⓘ Multiplications are done before additions and subtractions:

14 \times 12

14 \times (10 + 2)

14 \times 10 + 14 \times 2

140 + 28

168

26 + \frac{193 + 168}{180}

ⓘ Calculate the numerator and denominator before dividing:

193 + 168

361

26 + \frac{361}{180}

▶Result:

28

\frac{1}{180}

ⓘ Since the fraction

\frac{361}{180}

exceeds 1, take

2

out of it and add it to the whole part:

26 + \frac{361}{180}

26 + \frac{360 + 1}{180}

26 + \frac{360}{180} + \frac{1}{180}

26 + 2 + \frac{1}{180}

28 + \frac{1}{180}

2) The numeric value of:

28 + \frac{1}{180}

equals:

28 + \approx 5.5556 \times 10^{- 3}

▷

\approx 28.0056

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