What is (13/15)/(7/10) ?

The solution to (13/15)/(7/10) is 1 5/21

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Popular >

Evaluate (13/15)÷(7/10)

Solution

(13/15) / (7/10)

Solution

1 \frac{5}{21}

Solution steps

(13/15) / (7/10)

Follow the PEMDAS order of operations

Calculate within parentheses

(13/15) : \frac{13}{15}

13/15

13/15 = \frac{13}{15}

= \frac{13}{15}

= \frac{13}{15} / (7/10)

Calculate within parentheses

(7/10) : \frac{7}{10}

7/10

7/10 = \frac{7}{10}

= \frac{7}{10}

= \frac{13}{15} / \frac{7}{10}

Multiply and divide (left to right)

\frac{13}{15} / \frac{7}{10} : \frac{26}{21}

\frac{13}{15} / \frac{7}{10}

Apply the fraction rule:

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

= \frac{13}{15} \cdot \frac{10}{7}

Cross-cancel common factor:

5

10, 15

Greatest Common Divisor (GCD)

Prime factorization of

10 : 2 \cdot 5

10

10

divides by

210 = 5 \cdot 2

= 2 \cdot 5

2, 5

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 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

10, 15

are

= 5

= \frac{13}{3} \cdot \frac{2}{7}

Multiply fractions:

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

= \frac{13 \cdot 2}{3 \cdot 7}

Multiply the numbers:

13 \cdot 2 = 26

= \frac{26}{3 \cdot 7}

Multiply the numbers:

3 \cdot 7 = 21

= \frac{26}{21}

= \frac{26}{21}

Convert improper fractions to mixed numbers:

\frac{26}{21} = 1 \frac{5}{21}

\frac{26}{21} = 1

Remainder

5

\frac{26}{21}

Write the problem in long division format

21 \overline{∣ 26}

Divide

26

21

to get

1

Divide

26

21

to get

1

1 21 \overline{∣ 26}

Multiply the quotient digit

(1)

by the divisor

21

1 21 \overline{∣ 26} \underline{21}

Subtract

21

from

26

1 21 \overline{∣ 26} \underline{21} 5

1 21 \overline{∣ 26} \underline{21} 5

The solution for Long Division of

\frac{26}{21}

1

with remainder of

5

1 Remainder 5

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{26}{21} = 1 \frac{5}{21}

= 1 \frac{5}{21}

= 1 \frac{5}{21}

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Frequently Asked Questions (FAQ)

What is (13/15)/(7/10) ?
The solution to (13/15)/(7/10) is 1 5/21