What is (5 1/4-4)\div 1 1/2 ?

The solution to (5 1/4-4)\div 1 1/2 is 5/6

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Popular >

(5 1/4-4)\div 1 1/2

Solution

(5 \frac{1}{4} - 4) \div 1 \frac{1}{2}

Solution

\frac{5}{6}

Solution steps

(5 \frac{1}{4} - 4) \div 1 \frac{1}{2}

Convert mixed numbers to improper fractions:

1 \frac{1}{2} = \frac{3}{2}

1 \frac{1}{2}

Convert mixed numbers to improper fraction:

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

1 \frac{1}{2} = \frac{1 \cdot 2 + 1}{2}

= \frac{3}{2}

= (5 \frac{1}{4} - 4) \div \frac{3}{2}

Convert mixed numbers to improper fractions:

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

5 \frac{1}{4}

Convert mixed numbers to improper fraction:

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

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

= \frac{21}{4}

= (\frac{21}{4} - 4) \div \frac{3}{2}

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{21}{4} - 4) : \frac{5}{4}

\frac{21}{4} - 4

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

\frac{21}{4} - 4

Convert element to fraction:

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

= - \frac{4 \cdot 4}{4} + \frac{21}{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 + 21}{4}

- 4 \cdot 4 + 21 = 5

- 4 \cdot 4 + 21

Multiply the numbers:

4 \cdot 4 = 16

= - 16 + 21

Add/Subtract the numbers:

- 16 + 21 = 5

= 5

= \frac{5}{4}

= \frac{5}{4}

= \frac{5}{4} \div \frac{3}{2}

Multiply and divide (left to right)

\frac{5}{4} \div \frac{3}{2} : \frac{5}{6}

\frac{5}{4} \div \frac{3}{2}

Apply the fraction rule:

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

= \frac{5}{4} \cdot \frac{2}{3}

Cross-cancel common factor:

2

2, 4

Greatest Common Divisor (GCD)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

The prime factors common to

2, 4

are

= 2

= \frac{5}{2} \cdot \frac{1}{3}

Multiply fractions:

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

= \frac{5 \cdot 1}{2 \cdot 3}

Multiply the numbers:

5 \cdot 1 = 5

= \frac{5}{2 \cdot 3}

Multiply the numbers:

2 \cdot 3 = 6

= \frac{5}{6}

= \frac{5}{6}

Popular Examples

2(0)^2+4(0)

2 (0)^{2} + 4 (0)

[11(12-8)*6-8]\div 4

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(4\times 3)^2

(4 \times 3)^{2}

0-9+(-16)+25-(-4)

0 - 9 + (- 16) + 25 - (- 4)

Frequently Asked Questions (FAQ)

What is (5 1/4-4)\div 1 1/2 ?
The solution to (5 1/4-4)\div 1 1/2 is 5/6