What is (8+2/5)\div (6-9/4) ?

The solution to (8+2/5)\div (6-9/4) is 2 6/25

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(8+2/5)\div (6-9/4)

Solution

(8 + \frac{2}{5}) \div (6 - \frac{9}{4})

Solution

2 \frac{6}{25}

Solution steps

(8 + \frac{2}{5}) \div (6 - \frac{9}{4})

Follow the PEMDAS order of operations

Calculate within parentheses

(8 + \frac{2}{5}) : \frac{42}{5}

8 + \frac{2}{5}

8 + \frac{2}{5} = \frac{42}{5}

8 + \frac{2}{5}

Convert element to fraction:

8 = \frac{8 \cdot 5}{5}

= \frac{8 \cdot 5}{5} + \frac{2}{5}

Since the denominators are equal, combine the fractions:

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

= \frac{8 \cdot 5 + 2}{5}

8 \cdot 5 + 2 = 42

8 \cdot 5 + 2

Multiply the numbers:

8 \cdot 5 = 40

= 40 + 2

Add the numbers:

40 + 2 = 42

= 42

= \frac{42}{5}

= \frac{42}{5}

= \frac{42}{5} \div (6 - \frac{9}{4})

Calculate within parentheses

(6 - \frac{9}{4}) : \frac{15}{4}

6 - \frac{9}{4}

6 - \frac{9}{4} = \frac{15}{4}

6 - \frac{9}{4}

Convert element to fraction:

6 = \frac{6 \cdot 4}{4}

= \frac{6 \cdot 4}{4} - \frac{9}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{6 \cdot 4 - 9}{4}

6 \cdot 4 - 9 = 15

6 \cdot 4 - 9

Multiply the numbers:

6 \cdot 4 = 24

= 24 - 9

Subtract the numbers:

24 - 9 = 15

= 15

= \frac{15}{4}

= \frac{15}{4}

= \frac{42}{5} \div \frac{15}{4}

Multiply and divide (left to right)

\frac{42}{5} \div \frac{15}{4} : \frac{56}{25}

\frac{42}{5} \div \frac{15}{4}

Apply the fraction rule:

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

= \frac{42}{5} \cdot \frac{4}{15}

Cross-cancel common factor:

3

42, 15

Greatest Common Divisor (GCD)

Prime factorization of

42 : 2 \cdot 3 \cdot 7

42

42

divides by

242 = 21 \cdot 2

= 2 \cdot 21

21

divides by

321 = 7 \cdot 3

= 2 \cdot 3 \cdot 7

2, 3, 7

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 7

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

42, 15

are

= 3

= \frac{14}{5} \cdot \frac{4}{5}

Multiply fractions:

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

= \frac{14 \cdot 4}{5 \cdot 5}

Multiply the numbers:

14 \cdot 4 = 56

= \frac{56}{5 \cdot 5}

Multiply the numbers:

5 \cdot 5 = 25

= \frac{56}{25}

= \frac{56}{25}

Convert improper fractions to mixed numbers:

\frac{56}{25} = 2 \frac{6}{25}

\frac{56}{25} = 2

Remainder

6

\frac{56}{25}

Write the problem in long division format

25 \overline{∣ 56}

Divide

56

25

to get

2

Divide

56

25

to get

2

2 25 \overline{∣ 56}

Multiply the quotient digit

(2)

by the divisor

25

2 25 \overline{∣ 56} \underline{50}

Subtract

50

from

56

2 25 \overline{∣ 56} \underline{50} 6

2 25 \overline{∣ 56} \underline{50} 6

The solution for Long Division of

\frac{56}{25}

2

with remainder of

6

2 Remainder 6

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{56}{25} = 2 \frac{6}{25}

= 2 \frac{6}{25}

= 2 \frac{6}{25}

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Frequently Asked Questions (FAQ)

What is (8+2/5)\div (6-9/4) ?
The solution to (8+2/5)\div (6-9/4) is 2 6/25