What is (1/5+2/3)\div 3/5 ?

The solution to (1/5+2/3)\div 3/5 is 1 4/9

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Popular >

(1/5+2/3)\div 3/5

Solution

(\frac{1}{5} + \frac{2}{3}) \div \frac{3}{5}

Solution

1 \frac{4}{9}

Solution steps

(\frac{1}{5} + \frac{2}{3}) \div \frac{3}{5}

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{1}{5} + \frac{2}{3}) : \frac{13}{15}

\frac{1}{5} + \frac{2}{3}

\frac{1}{5} + \frac{2}{3} = \frac{13}{15}

\frac{1}{5} + \frac{2}{3}

Least Common Multiplier of

5, 3 : 15

5, 3

Least Common Multiplier (LCM)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Multiply each factor the greatest number of times it occurs in either

5

3

= 5 \cdot 3

Multiply the numbers:

5 \cdot 3 = 15

= 15

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

15

For

\frac{1}{5} :

multiply the denominator and numerator by

3

\frac{1}{5} = \frac{1 \cdot 3}{5 \cdot 3} = \frac{3}{15}

For

\frac{2}{3} :

multiply the denominator and numerator by

5

\frac{2}{3} = \frac{2 \cdot 5}{3 \cdot 5} = \frac{10}{15}

= \frac{3}{15} + \frac{10}{15}

Since the denominators are equal, combine the fractions:

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

= \frac{3 + 10}{15}

Add the numbers:

3 + 10 = 13

= \frac{13}{15}

= \frac{13}{15}

= \frac{13}{15} \div \frac{3}{5}

Multiply and divide (left to right)

\frac{13}{15} \div \frac{3}{5} : \frac{13}{9}

\frac{13}{15} \div \frac{3}{5}

Apply the fraction rule:

\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}

= \frac{13}{15} \cdot \frac{5}{3}

Cross-cancel common factor:

5

5, 15

Greatest Common Divisor (GCD)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

Prime factorization of

15 : 3 \cdot 5

15

15

divides by

315 = 5 \cdot 3

= 3 \cdot 5

3, 5

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 5

The prime factors common to

5, 15

are

= 5

= \frac{13}{3} \cdot \frac{1}{3}

Multiply fractions:

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

= \frac{13 \cdot 1}{3 \cdot 3}

Multiply the numbers:

13 \cdot 1 = 13

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

Multiply the numbers:

3 \cdot 3 = 9

= \frac{13}{9}

= \frac{13}{9}

Convert improper fractions to mixed numbers:

\frac{13}{9} = 1 \frac{4}{9}

\frac{13}{9} = 1

Remainder

4

\frac{13}{9}

Write the problem in long division format

9 \overline{∣ 13}

Divide

13

9

to get

1

Divide

13

9

to get

1

1 9 \overline{∣ 13}

Multiply the quotient digit

(1)

by the divisor

9

1 9 \overline{∣ 13} \underline{9}

Subtract

9

from

13

1 9 \overline{∣ 13} \underline{9} 4

1 9 \overline{∣ 13} \underline{9} 4

The solution for Long Division of

\frac{13}{9}

1

with remainder of

4

1 Remainder 4

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{13}{9} = 1 \frac{4}{9}

= 1 \frac{4}{9}

= 1 \frac{4}{9}

Popular Examples

8^2-8^3

8^{2} - 8^{3}

-2*1-5

- 2 \cdot 1 - 5

6(6*6)+6(4*4)-2(4*4)

6 (6 \cdot 6) + 6 (4 \cdot 4) - 2 (4 \cdot 4)

4*3^5+3*3^5+11*3^5

4 \cdot 3^{5} + 3 \cdot 3^{5} + 11 \cdot 3^{5}

(4+5+3)+8

(4 + 5 + 3) + 8

Frequently Asked Questions (FAQ)

What is (1/5+2/3)\div 3/5 ?
The solution to (1/5+2/3)\div 3/5 is 1 4/9