What is (4-1/4)\div 11/6 ?

The solution to (4-1/4)\div 11/6 is 2 1/22

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(4-1/4)\div 11/6

Solution

(4 - \frac{1}{4}) \div \frac{11}{6}

Solution

2 \frac{1}{22}

Solution steps

(4 - \frac{1}{4}) \div \frac{11}{6}

Follow the PEMDAS order of operations

Calculate within parentheses

(4 - \frac{1}{4}) : \frac{15}{4}

4 - \frac{1}{4}

4 - \frac{1}{4} = \frac{15}{4}

4 - \frac{1}{4}

Convert element to fraction:

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

= \frac{4 \cdot 4}{4} - \frac{1}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{4 \cdot 4 - 1}{4}

4 \cdot 4 - 1 = 15

4 \cdot 4 - 1

Multiply the numbers:

4 \cdot 4 = 16

= 16 - 1

Subtract the numbers:

16 - 1 = 15

= 15

= \frac{15}{4}

= \frac{15}{4}

= \frac{15}{4} \div \frac{11}{6}

Multiply and divide (left to right)

\frac{15}{4} \div \frac{11}{6} : \frac{45}{22}

\frac{15}{4} \div \frac{11}{6}

Apply the fraction rule:

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

= \frac{15}{4} \cdot \frac{6}{11}

Cross-cancel common factor:

2

6, 4

Greatest Common Divisor (GCD)

Prime factorization of

6 : 2 \cdot 3

6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

The prime factors common to

6, 4

are

= 2

= \frac{15}{2} \cdot \frac{3}{11}

Multiply fractions:

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

= \frac{15 \cdot 3}{2 \cdot 11}

Multiply the numbers:

15 \cdot 3 = 45

= \frac{45}{2 \cdot 11}

Multiply the numbers:

2 \cdot 11 = 22

= \frac{45}{22}

= \frac{45}{22}

Convert improper fractions to mixed numbers:

\frac{45}{22} = 2 \frac{1}{22}

\frac{45}{22} = 2

Remainder

1

\frac{45}{22}

Write the problem in long division format

22 \overline{∣ 45}

Divide

45

22

to get

2

Divide

45

22

to get

2

2 22 \overline{∣ 45}

Multiply the quotient digit

(2)

by the divisor

22

2 22 \overline{∣ 45} \underline{44}

Subtract

44

from

45

2 22 \overline{∣ 45} \underline{44} 1

2 22 \overline{∣ 45} \underline{44} 1

The solution for Long Division of

\frac{45}{22}

2

with remainder of

1

2 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{45}{22} = 2 \frac{1}{22}

= 2 \frac{1}{22}

= 2 \frac{1}{22}

Popular Examples

2\times 3/4+3/8

2 \times \frac{3}{4} + \frac{3}{8}

(2+7 1/3)+(2/3-4)+3

(2 + 7 \frac{1}{3}) + (\frac{2}{3} - 4) + 3

2(-3)^1+5^1

2 (- 3)^{1} + 5^{1}

-77+[-56-65-54+(-8)]

- 77 + [- 56 - 65 - 54 + (- 8)]

21-[-(3-4)-3]-5

21 - [- (3 - 4) - 3] - 5

Frequently Asked Questions (FAQ)

What is (4-1/4)\div 11/6 ?
The solution to (4-1/4)\div 11/6 is 2 1/22