What is (10/13)/(4/9) ?

The solution to (10/13)/(4/9) is 1 19/26

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Popular >

Evaluate (10/13)÷(4/9)

Solution

(10/13) / (4/9)

Solution

1 \frac{19}{26}

Solution steps

(10/13) / (4/9)

Follow the PEMDAS order of operations

Calculate within parentheses

(10/13) : \frac{10}{13}

10/13

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

= \frac{10}{13}

= \frac{10}{13} / (4/9)

Calculate within parentheses

(4/9) : \frac{4}{9}

4/9

4/9 = \frac{4}{9}

= \frac{4}{9}

= \frac{10}{13} / \frac{4}{9}

Multiply and divide (left to right)

\frac{10}{13} / \frac{4}{9} : \frac{45}{26}

\frac{10}{13} / \frac{4}{9}

Apply the fraction rule:

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

= \frac{10}{13} \cdot \frac{9}{4}

Cross-cancel common factor:

2

10, 4

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

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

The prime factors common to

10, 4

are

= 2

= \frac{5}{13} \cdot \frac{9}{2}

Multiply fractions:

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

= \frac{5 \cdot 9}{13 \cdot 2}

Multiply the numbers:

5 \cdot 9 = 45

= \frac{45}{13 \cdot 2}

Multiply the numbers:

13 \cdot 2 = 26

= \frac{45}{26}

= \frac{45}{26}

Convert improper fractions to mixed numbers:

\frac{45}{26} = 1 \frac{19}{26}

\frac{45}{26} = 1

Remainder

19

\frac{45}{26}

Write the problem in long division format

26 \overline{∣ 45}

Divide

45

26

to get

1

Divide

45

26

to get

1

1 26 \overline{∣ 45}

Multiply the quotient digit

(1)

by the divisor

26

1 26 \overline{∣ 45} \underline{26}

Subtract

26

from

45

1 26 \overline{∣ 45} \underline{26} 19

1 26 \overline{∣ 45} \underline{26} 19

The solution for Long Division of

\frac{45}{26}

1

with remainder of

19

1 Remainder 19

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{45}{26} = 1 \frac{19}{26}

= 1 \frac{19}{26}

= 1 \frac{19}{26}

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Frequently Asked Questions (FAQ)

What is (10/13)/(4/9) ?
The solution to (10/13)/(4/9) is 1 19/26