6 19/20 + 10 5/7 + 10 5/6

⚠ 6 19/20 is read as the mixed number 6 + 19/20■10 5/7 is read as the mixed number 10 + 5/7■10 5/6 is read as the mixed number 10 + 5/6

1) Let's calculate:

6

+ \frac{19}{20}

+ 10

+ \frac{5}{7}

+ 10

+ \frac{5}{6}

ⓘ Start from

6

and move forward

10

on the number line:

6 + 10

16

16

+ \frac{19}{20}

+ \frac{5}{7}

+ 10

+ \frac{5}{6}

ⓘ Start from

16

and move forward

10

on the number line:

16 + 10

26

26

+ \frac{19}{20}

+ \frac{5}{7}

+ \frac{5}{6}

ⓘ Add fractions by using a common denominator and then adding their 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{19}{20} + \frac{5}{7}

\frac{19 \times 7}{20 \times 7} + \frac{5 \times 20}{7 \times 20}

\frac{19 \times 7 + 5 \times 20}{20 \times 7}

26 + \frac{19 \times 7 + 5 \times 20}{20 \times 7} + \frac{5}{6}

ⓘ Perform multiplications before additions and subtractions:

19 \times 7

(10 + 9) \times 7

10 \times 7 + 9 \times 7

70 + 63

133

5 \times 20

100

ⅰ

20 \times 7

140

26 + \frac{133 + 100}{140} + \frac{5}{6}

ⓘ Calculate the numerator and denominator before dividing:

133 + 100

233

26 + \frac{233}{140} + \frac{5}{6}

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

420

, the least common multiple of

140

and

6

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

\frac{233}{140} + \frac{5}{6}

\frac{233 \times 3}{140 \times 3} + \frac{5 \times 70}{6 \times 70}

\frac{233 \times 3 + 5 \times 70}{140 \times 3}

26 + \frac{233 \times 3 + 5 \times 70}{140 \times 3}

ⓘ Perform multiplications before additions and subtractions:

233 \times 3

(200 + 30 + 3) \times 3

200 \times 3 + 30 \times 3 + 3 \times 3

600 + 90 + 9

699

5 \times 70

350

ⅰ

140 \times 3

(100 + 40) \times 3

100 \times 3 + 40 \times 3

300 + 120

420

26 + \frac{699 + 350}{420}

ⓘ Calculate the numerator and denominator before dividing:

699 + 350

1049

26 + \frac{1049}{420}

▶Result:

28

\frac{209}{420}

ⓘ The fraction

\frac{1049}{420}

is greater than 1: extract

2

from it and add it to the whole part:

26 + \frac{1049}{420}

26 + \frac{840 + 209}{420}

26 + \frac{840}{420} + \frac{209}{420}

26 + 2 + \frac{209}{420}

28 + \frac{209}{420}

2) The numeric value of:

28 + \frac{209}{420}

is:

28 + \approx 0.4976

▷

\approx 28.4976

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