What is (13-10 1/3)+2 2/3 ?

The solution to (13-10 1/3)+2 2/3 is 5 1/3

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Popular >

(13-10 1/3)+2 2/3

Solution

(13 - 10 \frac{1}{3}) + 2 \frac{2}{3}

Solution

5 \frac{1}{3}

Solution steps

(13 - 10 \frac{1}{3}) + 2 \frac{2}{3}

Convert mixed numbers to improper fractions:

2 \frac{2}{3} = \frac{8}{3}

2 \frac{2}{3}

Convert mixed numbers to improper fraction:

a \frac{b}{c} = \frac{a \cdot c + b}{c}

2 \frac{2}{3} = \frac{2 \cdot 3 + 2}{3}

= \frac{8}{3}

= (13 - 10 \frac{1}{3}) + \frac{8}{3}

Convert mixed numbers to improper fractions:

10 \frac{1}{3} = \frac{31}{3}

10 \frac{1}{3}

Convert mixed numbers to improper fraction:

a \frac{b}{c} = \frac{a \cdot c + b}{c}

10 \frac{1}{3} = \frac{10 \cdot 3 + 1}{3}

= \frac{31}{3}

= (13 - \frac{31}{3}) + \frac{8}{3}

Follow the PEMDAS order of operations

Calculate within parentheses

(13 - \frac{31}{3}) : \frac{8}{3}

13 - \frac{31}{3}

13 - \frac{31}{3} = \frac{8}{3}

13 - \frac{31}{3}

Convert element to fraction:

13 = \frac{13 \cdot 3}{3}

= \frac{13 \cdot 3}{3} - \frac{31}{3}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{13 \cdot 3 - 31}{3}

13 \cdot 3 - 31 = 8

13 \cdot 3 - 31

Multiply the numbers:

13 \cdot 3 = 39

= 39 - 31

Subtract the numbers:

39 - 31 = 8

= 8

= \frac{8}{3}

= \frac{8}{3}

= \frac{8}{3} + \frac{8}{3}

Add and subtract (left to right)

\frac{8}{3} + \frac{8}{3} : \frac{16}{3}

\frac{8}{3} + \frac{8}{3}

\frac{8}{3} + \frac{8}{3} = \frac{16}{3}

\frac{8}{3} + \frac{8}{3}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{8 + 8}{3}

Add the numbers:

8 + 8 = 16

= \frac{16}{3}

= \frac{16}{3}

= \frac{16}{3}

Convert improper fractions to mixed numbers:

\frac{16}{3} = 5 \frac{1}{3}

\frac{16}{3} = 5

Remainder

1

\frac{16}{3}

Write the problem in long division format

3 \overline{∣ 16}

Divide

16

3

to get

5

Divide

16

3

to get

5

5 3 \overline{∣ 16}

Multiply the quotient digit

(5)

by the divisor

3

5 3 \overline{∣ 16} \underline{15}

Subtract

15

from

16

5 3 \overline{∣ 16} \underline{15} 1

5 3 \overline{∣ 16} \underline{15} 1

The solution for Long Division of

\frac{16}{3}

5

with remainder of

1

5 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{16}{3} = 5 \frac{1}{3}

= 5 \frac{1}{3}

= 5 \frac{1}{3}

Popular Examples

3\div 16+5\div 2

3 \div 16 + 5 \div 2

6+8\times 3-7

6 + 8 \times 3 - 7

3-1 11/12 \div 2 4/21

3 - 1 \frac{11}{12} \div 2 \frac{4}{21}

(4^2-2^2\times 3)^2-7

(4^{2} - 2^{2} \times 3)^{2} - 7

5(8)+3

5 (8) + 3

Frequently Asked Questions (FAQ)

What is (13-10 1/3)+2 2/3 ?
The solution to (13-10 1/3)+2 2/3 is 5 1/3