What is (4/3-1/2)\div 6/9 ?

The solution to (4/3-1/2)\div 6/9 is 1 1/4

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Popular Pre Algebra >

(4/3-1/2)\div 6/9

Solution

(\frac{4}{3} - \frac{1}{2}) \div \frac{6}{9}

Solution

1 \frac{1}{4}

Decimal

1.25

Solution steps

(\frac{4}{3} - \frac{1}{2}) \div \frac{6}{9}

\frac{6}{9} = \frac{2}{3}

Cancel the common factor:

3

\frac{2}{3}

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

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{4}{3} - \frac{1}{2}) : \frac{5}{6}

\frac{4}{3} - \frac{1}{2}

\frac{4}{3} - \frac{1}{2} = \frac{5}{6}

\frac{4}{3} - \frac{1}{2}

Least Common Multiplier of

3, 2 : 6

3, 2

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Multiply each factor the greatest number of times it occurs in either

3

2

= 3 \cdot 2

Multiply the numbers:

3 \cdot 2 = 6

= 6

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

6

For

\frac{4}{3} :

multiply the denominator and numerator by

2

\frac{4}{3} = \frac{4 \cdot 2}{3 \cdot 2} = \frac{8}{6}

For

\frac{1}{2} :

multiply the denominator and numerator by

3

\frac{1}{2} = \frac{1 \cdot 3}{2 \cdot 3} = \frac{3}{6}

= \frac{8}{6} - \frac{3}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{8 - 3}{6}

Subtract the numbers:

8 - 3 = 5

= \frac{5}{6}

= \frac{5}{6}

= \frac{5}{6} \div \frac{2}{3}

Multiply and divide (left to right)

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

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

Apply the fraction rule:

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

= \frac{5}{6} \cdot \frac{3}{2}

Cross-cancel common factor:

3

3, 6

Greatest Common Divisor (GCD)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

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

The prime factors common to

3, 6

are

= 3

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

Multiply fractions:

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

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

Multiply the numbers:

5 \cdot 1 = 5

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{5}{4}

= \frac{5}{4}

Convert improper fractions to mixed numbers:

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

\frac{5}{4} = 1

Remainder

1

\frac{5}{4}

Write the problem in long division format

4 \overline{∣ 5}

Divide

5

4

to get

1

Divide

5

4

to get

1

1 4 \overline{∣ 5}

Multiply the quotient digit

(1)

by the divisor

4

1 4 \overline{∣ 5} \underline{4}

Subtract

4

from

5

1 4 \overline{∣ 5} \underline{4} 1

1 4 \overline{∣ 5} \underline{4} 1

The solution for Long Division of

\frac{5}{4}

1

with remainder of

1

1 Remainder 1

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

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

= 1 \frac{1}{4}

= 1 \frac{1}{4}

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Frequently Asked Questions (FAQ)

What is (4/3-1/2)\div 6/9 ?
The solution to (4/3-1/2)\div 6/9 is 1 1/4

(4/3-1/2)\div 6/9

Solution

Solution

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Frequently Asked Questions (FAQ)

What is (4/3-1/2)\div 6/9 ?

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