What is (8+3/4)\div 4 1/5 ?

The solution to (8+3/4)\div 4 1/5 is 2 1/12

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Popular >

(8+3/4)\div 4 1/5

Solution

(8 + \frac{3}{4}) \div 4 \frac{1}{5}

Solution

2 \frac{1}{12}

Solution steps

(8 + \frac{3}{4}) \div 4 \frac{1}{5}

Convert mixed numbers to improper fractions:

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

4 \frac{1}{5}

Convert mixed numbers to improper fraction:

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

4 \frac{1}{5} = \frac{4 \cdot 5 + 1}{5}

= \frac{21}{5}

= (8 + \frac{3}{4}) \div \frac{21}{5}

Follow the PEMDAS order of operations

Calculate within parentheses

(8 + \frac{3}{4}) : \frac{35}{4}

8 + \frac{3}{4}

8 + \frac{3}{4} = \frac{35}{4}

8 + \frac{3}{4}

Convert element to fraction:

8 = \frac{8 \cdot 4}{4}

= \frac{8 \cdot 4}{4} + \frac{3}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{8 \cdot 4 + 3}{4}

8 \cdot 4 + 3 = 35

8 \cdot 4 + 3

Multiply the numbers:

8 \cdot 4 = 32

= 32 + 3

Add the numbers:

32 + 3 = 35

= 35

= \frac{35}{4}

= \frac{35}{4}

= \frac{35}{4} \div \frac{21}{5}

Multiply and divide (left to right)

\frac{35}{4} \div \frac{21}{5} : \frac{25}{12}

\frac{35}{4} \div \frac{21}{5}

Apply the fraction rule:

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

= \frac{35}{4} \cdot \frac{5}{21}

Cross-cancel common factor:

7

35, 21

Greatest Common Divisor (GCD)

Prime factorization of

35 : 5 \cdot 7

35

35

divides by

535 = 7 \cdot 5

= 5 \cdot 7

5, 7

are all prime numbers, therefore no further factorization is possible

= 5 \cdot 7

Prime factorization of

21 : 3 \cdot 7

21

21

divides by

321 = 7 \cdot 3

= 3 \cdot 7

3, 7

are all prime numbers, therefore no further factorization is possible

= 3 \cdot 7

The prime factors common to

35, 21

are

= 7

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

Multiply fractions:

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

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

Multiply the numbers:

5 \cdot 5 = 25

= \frac{25}{4 \cdot 3}

Multiply the numbers:

4 \cdot 3 = 12

= \frac{25}{12}

= \frac{25}{12}

Convert improper fractions to mixed numbers:

\frac{25}{12} = 2 \frac{1}{12}

\frac{25}{12} = 2

Remainder

1

\frac{25}{12}

Write the problem in long division format

12 \overline{∣ 25}

Divide

25

12

to get

2

Divide

25

12

to get

2

2 12 \overline{∣ 25}

Multiply the quotient digit

(2)

by the divisor

12

2 12 \overline{∣ 25} \underline{24}

Subtract

24

from

25

2 12 \overline{∣ 25} \underline{24} 1

2 12 \overline{∣ 25} \underline{24} 1

The solution for Long Division of

\frac{25}{12}

2

with remainder of

1

2 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{25}{12} = 2 \frac{1}{12}

= 2 \frac{1}{12}

= 2 \frac{1}{12}

Popular Examples

13(1-1)15+(2)

13 (1 - 1) 15 + (2)

8^2+4^2

8^{2} + 4^{2}

2^7-2

2^{7} - 2

5^2+13^2

5^{2} + 1 3^{2}

3(1)+1

3 (1) + 1

Frequently Asked Questions (FAQ)

What is (8+3/4)\div 4 1/5 ?
The solution to (8+3/4)\div 4 1/5 is 2 1/12