What is (3/4-2/5)\div 2/3 ?

The solution to (3/4-2/5)\div 2/3 is 21/40

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Popular >

(3/4-2/5)\div 2/3

Solution

(\frac{3}{4} - \frac{2}{5}) \div \frac{2}{3}

Solution

\frac{21}{40}

Solution steps

(\frac{3}{4} - \frac{2}{5}) \div \frac{2}{3}

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{3}{4} - \frac{2}{5}) : \frac{7}{20}

\frac{3}{4} - \frac{2}{5}

\frac{3}{4} - \frac{2}{5} = \frac{7}{20}

\frac{3}{4} - \frac{2}{5}

Least Common Multiplier of

4, 5 : 20

4, 5

Least Common Multiplier (LCM)

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

4

5

= 2 \cdot 2 \cdot 5

Multiply the numbers:

2 \cdot 2 \cdot 5 = 20

= 20

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

20

For

\frac{3}{4} :

multiply the denominator and numerator by

5

\frac{3}{4} = \frac{3 \cdot 5}{4 \cdot 5} = \frac{15}{20}

For

\frac{2}{5} :

multiply the denominator and numerator by

4

\frac{2}{5} = \frac{2 \cdot 4}{5 \cdot 4} = \frac{8}{20}

= \frac{15}{20} - \frac{8}{20}

Since the denominators are equal, combine the fractions:

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

= \frac{15 - 8}{20}

Subtract the numbers:

15 - 8 = 7

= \frac{7}{20}

= \frac{7}{20}

= \frac{7}{20} \div \frac{2}{3}

Multiply and divide (left to right)

\frac{7}{20} \div \frac{2}{3} : \frac{21}{40}

\frac{7}{20} \div \frac{2}{3}

Apply the fraction rule:

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

= \frac{7}{20} \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{7 \cdot 3}{20 \cdot 2}

Multiply the numbers:

7 \cdot 3 = 21

= \frac{21}{20 \cdot 2}

Multiply the numbers:

20 \cdot 2 = 40

= \frac{21}{40}

= \frac{21}{40}

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(22-18)(18\div 3)-2\times 8

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Frequently Asked Questions (FAQ)

What is (3/4-2/5)\div 2/3 ?
The solution to (3/4-2/5)\div 2/3 is 21/40