5 2/15 + 14 2/9 + 5 5/12

⚠ 5 2/15 is read as the mixed number 5 + 2/15■14 2/9 is read as the mixed number 14 + 2/9■5 5/12 is read as the mixed number 5 + 5/12

1) Let's evaluate:

5

+ \frac{2}{15}

+ 14

+ \frac{2}{9}

+ 5

+ \frac{5}{12}

ⓘ Start from

5

and move forward

14

on the number line:

5 + 14

19

19

+ \frac{2}{15}

+ \frac{2}{9}

+ 5

+ \frac{5}{12}

ⓘ Start from

19

and move forward

5

on the number line:

19 + 5

24

24

+ \frac{2}{15}

+ \frac{2}{9}

+ \frac{5}{12}

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

45

, the least common multiple of

15

and

9

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

\frac{2}{15} + \frac{2}{9}

\frac{2 \times 3}{15 \times 3} + \frac{2 \times 5}{9 \times 5}

\frac{2 \times 3 + 2 \times 5}{15 \times 3}

24 + \frac{2 \times 3 + 2 \times 5}{15 \times 3} + \frac{5}{12}

ⓘ Perform multiplications before additions and subtractions:

2 \times 3

6

2 \times 5

10

ⅰ

15 \times 3

(10 + 5) \times 3

10 \times 3 + 5 \times 3

30 + 15

45

24 + \frac{6 + 10}{45} + \frac{5}{12}

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

6 + 10

16

24 + \frac{16}{45} + \frac{5}{12}

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

180

, the least common multiple of

45

and

12

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

\frac{16}{45} + \frac{5}{12}

\frac{16 \times 4}{45 \times 4} + \frac{5 \times 15}{12 \times 15}

\frac{16 \times 4 + 5 \times 15}{45 \times 4}

24 + \frac{16 \times 4 + 5 \times 15}{45 \times 4}

ⓘ Perform multiplications before additions and subtractions:

16 \times 4

(10 + 6) \times 4

10 \times 4 + 6 \times 4

40 + 24

64

5 \times 15

5 \times (10 + 5)

5 \times 10 + 5 \times 5

50 + 25

75

ⅰ

45 \times 4

(40 + 5) \times 4

40 \times 4 + 5 \times 4

160 + 20

180

24 + \frac{64 + 75}{180}

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

64 + 75

139

24 + \frac{139}{180}

▶Result:

24

\frac{139}{180}

2) The numeric value of:

24 + \frac{139}{180}

is:

24 + \approx 0.7722

▷

\approx 24.7722

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