What is 7 1/2 \div (3*5/9) ?

The solution to 7 1/2 \div (3*5/9) is 4 1/2

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7 1/2 \div (3*5/9)

Solution

7 \frac{1}{2} \div (3 \cdot \frac{5}{9})

Solution

4 \frac{1}{2}

Solution steps

7 \frac{1}{2} \div (3 \cdot \frac{5}{9})

Convert mixed numbers to improper fractions:

7 \frac{1}{2} = \frac{15}{2}

7 \frac{1}{2}

Convert mixed numbers to improper fraction:

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

7 \frac{1}{2} = \frac{7 \cdot 2 + 1}{2}

= \frac{15}{2}

= \frac{15}{2} \div (3 \cdot \frac{5}{9})

Follow the PEMDAS order of operations

Calculate within parentheses

(3 \cdot \frac{5}{9}) : \frac{5}{3}

3 \cdot \frac{5}{9}

3 \cdot \frac{5}{9} = \frac{5}{3}

3 \cdot \frac{5}{9}

Convert element to fraction:

3 = \frac{3}{1}

= \frac{3}{1} \cdot \frac{5}{9}

Cross-cancel common factor:

3

3, 9

Greatest Common Divisor (GCD)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

9 : 3 \cdot 3

9

9

divides by

39 = 3 \cdot 3

= 3 \cdot 3

The prime factors common to

3, 9

are

= 3

= \frac{5}{3}

= \frac{5}{3}

= \frac{15}{2} \div \frac{5}{3}

Multiply and divide (left to right)

\frac{15}{2} \div \frac{5}{3} : \frac{9}{2}

\frac{15}{2} \div \frac{5}{3}

Apply the fraction rule:

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

= \frac{15}{2} \cdot \frac{3}{5}

Cross-cancel common factor:

5

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

Multiply fractions:

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

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

Multiply the numbers:

3 \cdot 3 = 9

= \frac{9}{2 \cdot 1}

Multiply the numbers:

2 \cdot 1 = 2

= \frac{9}{2}

= \frac{9}{2}

Convert improper fractions to mixed numbers:

\frac{9}{2} = 4 \frac{1}{2}

\frac{9}{2} = 4

Remainder

1

\frac{9}{2}

Write the problem in long division format

2 \overline{∣ 9}

Divide

9

2

to get

4

Divide

9

2

to get

4

4 2 \overline{∣ 9}

Multiply the quotient digit

(4)

by the divisor

2

4 2 \overline{∣ 9} \underline{8}

Subtract

8

from

9

4 2 \overline{∣ 9} \underline{8} 1

4 2 \overline{∣ 9} \underline{8} 1

The solution for Long Division of

\frac{9}{2}

4

with remainder of

1

4 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{9}{2} = 4 \frac{1}{2}

= 4 \frac{1}{2}

= 4 \frac{1}{2}

Popular Examples

2*2^2-5^3-(-3)^3-(-1)^5

2 \cdot 2^{2} - 5^{3} - (- 3)^{3} - (- 1)^{5}

simplify (-3^0)/(-3^2)simplify

\frac{- 3 ^{0}}{- 3 ^{2}}

2(-3-5)^2+7

2 (- 3 - 5)^{2} + 7

(4+8)^2

(4 + 8)^{2}

0+1(1/2)

0 + 1 (\frac{1}{2})

Frequently Asked Questions (FAQ)

What is 7 1/2 \div (3*5/9) ?
The solution to 7 1/2 \div (3*5/9) is 4 1/2