2 3/4 + 9 7/10 + 4 5/7

⚠ 2 3/4 is read as the mixed number 2 + 3/4■9 7/10 is read as the mixed number 9 + 7/10■4 5/7 is read as the mixed number 4 + 5/7

1) Let's evaluate:

2

+ \frac{3}{4}

+ 9

+ \frac{7}{10}

+ 4

+ \frac{5}{7}

ⓘ Start from

2

and move forward

9

on the number line:

2 + 9

11

11

+ \frac{3}{4}

+ \frac{7}{10}

+ 4

+ \frac{5}{7}

ⓘ Start from

11

and move forward

4

on the number line:

11 + 4

15

15

+ \frac{3}{4}

+ \frac{7}{10}

+ \frac{5}{7}

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

20

, the least common multiple of

4

and

10

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

\frac{3}{4} + \frac{7}{10}

\frac{3 \times 5}{4 \times 5} + \frac{7 \times 2}{10 \times 2}

\frac{3 \times 5 + 7 \times 2}{4 \times 5}

15 + \frac{3 \times 5 + 7 \times 2}{4 \times 5} + \frac{5}{7}

ⓘ Perform multiplications before additions and subtractions:

3 \times 5

15

7 \times 2

14

ⅰ

4 \times 5

20

15 + \frac{15 + 14}{20} + \frac{5}{7}

ⓘ Calculate the numerator and denominator before dividing:

15 + 14

29

15 + \frac{29}{20} + \frac{5}{7}

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

140

, the least common multiple of

20

and

7

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

\frac{29}{20} + \frac{5}{7}

\frac{29 \times 7}{20 \times 7} + \frac{5 \times 20}{7 \times 20}

\frac{29 \times 7 + 5 \times 20}{20 \times 7}

15 + \frac{29 \times 7 + 5 \times 20}{20 \times 7}

ⓘ Perform multiplications before additions and subtractions:

29 \times 7

(20 + 9) \times 7

20 \times 7 + 9 \times 7

140 + 63

203

5 \times 20

100

ⅰ

20 \times 7

140

15 + \frac{203 + 100}{140}

ⓘ Calculate the numerator and denominator before dividing:

203 + 100

303

15 + \frac{303}{140}

▶Result:

17

\frac{23}{140}

ⓘ Since the fraction

\frac{303}{140}

exceeds 1, take

2

out of it and add it to the whole part:

15 + \frac{303}{140}

15 + \frac{280 + 23}{140}

15 + \frac{280}{140} + \frac{23}{140}

15 + 2 + \frac{23}{140}

17 + \frac{23}{140}

2) The numeric value of:

17 + \frac{23}{140}

equals:

17 + \approx 0.1643

▷

\approx 17.1643

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