23 7/20 + 9 7/15 + 12 2/7

⚠ 23 7/20 is read as the mixed number 23 + 7/20■9 7/15 is read as the mixed number 9 + 7/15■12 2/7 is read as the mixed number 12 + 2/7

1) Let's evaluate:

23

+ \frac{7}{20}

+ 9

+ \frac{7}{15}

+ 12

+ \frac{2}{7}

ⓘ Start from

23

and move forward

9

on the number line:

23 + 9

32

32

+ \frac{7}{20}

+ \frac{7}{15}

+ 12

+ \frac{2}{7}

ⓘ Start from

32

and move forward

12

on the number line:

32 + 12

44

44

+ \frac{7}{20}

+ \frac{7}{15}

+ \frac{2}{7}

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

60

, the least common multiple of

20

and

15

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

\frac{7}{20} + \frac{7}{15}

\frac{7 \times 3}{20 \times 3} + \frac{7 \times 4}{15 \times 4}

\frac{7 \times 3 + 7 \times 4}{20 \times 3}

44 + \frac{7 \times 3 + 7 \times 4}{20 \times 3} + \frac{2}{7}

ⓘ Multiplications are done before additions and subtractions:

7 \times 3

21

7 \times 4

28

ⅰ

20 \times 3

60

44 + \frac{21 + 28}{60} + \frac{2}{7}

ⓘ Calculate the numerator and denominator before dividing:

21 + 28

49

44 + \frac{49}{60} + \frac{2}{7}

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

420

, the least common multiple of

60

and

7

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

\frac{49}{60} + \frac{2}{7}

\frac{49 \times 7}{60 \times 7} + \frac{2 \times 60}{7 \times 60}

\frac{49 \times 7 + 2 \times 60}{60 \times 7}

44 + \frac{49 \times 7 + 2 \times 60}{60 \times 7}

ⓘ Multiplications are done before additions and subtractions:

49 \times 7

(40 + 9) \times 7

40 \times 7 + 9 \times 7

280 + 63

343

2 \times 60

120

ⅰ

60 \times 7

420

44 + \frac{343 + 120}{420}

ⓘ Calculate the numerator and denominator before dividing:

343 + 120

463

44 + \frac{463}{420}

▶Result:

45

\frac{43}{420}

ⓘ The fraction

\frac{463}{420}

is greater than 1: extract

1

from it and add it to the whole part:

44 + \frac{463}{420}

44 + \frac{420 + 43}{420}

44 + \frac{420}{420} + \frac{43}{420}

44 + 1 + \frac{43}{420}

45 + \frac{43}{420}

2) The numeric value of:

45 + \frac{43}{420}

equals:

45 + \approx 0.1024

▷

\approx 45.1024

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