What is (2+1/3)/(2-1/3) ?

The solution to (2+1/3)/(2-1/3) is 1 2/5

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Popular >

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

Solution

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

Solution

1 \frac{2}{5}

Solution steps

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

Follow the PEMDAS order of operations

Calculate within parentheses

(2 + 1/3) : \frac{7}{3}

2 + 1/3

Multiply and divide (left to right)

1/3 : \frac{1}{3}

1/3

1/3 = \frac{1}{3}

= \frac{1}{3}

= 2 + \frac{1}{3}

Add and subtract (left to right)

2 + \frac{1}{3} : \frac{7}{3}

2 + \frac{1}{3}

2 + \frac{1}{3} = \frac{7}{3}

2 + \frac{1}{3}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

2 \cdot 3 + 1 = 7

2 \cdot 3 + 1

Multiply the numbers:

2 \cdot 3 = 6

= 6 + 1

Add the numbers:

6 + 1 = 7

= 7

= \frac{7}{3}

= \frac{7}{3}

= \frac{7}{3}

= \frac{7}{3} / (2 - 1/3)

Calculate within parentheses

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

2 - 1/3

Multiply and divide (left to right)

1/3 : \frac{1}{3}

1/3

1/3 = \frac{1}{3}

= \frac{1}{3}

= 2 - \frac{1}{3}

Add and subtract (left to right)

2 - \frac{1}{3} : \frac{5}{3}

2 - \frac{1}{3}

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

2 - \frac{1}{3}

Convert element to fraction:

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

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

Since the denominators are equal, combine the fractions:

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

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

2 \cdot 3 - 1 = 5

2 \cdot 3 - 1

Multiply the numbers:

2 \cdot 3 = 6

= 6 - 1

Subtract the numbers:

6 - 1 = 5

= 5

= \frac{5}{3}

= \frac{5}{3}

= \frac{5}{3}

= \frac{7}{3} / \frac{5}{3}

Multiply and divide (left to right)

\frac{7}{3} / \frac{5}{3} : \frac{7}{5}

\frac{7}{3} / \frac{5}{3}

Apply the fraction rule:

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

= \frac{7}{3} \cdot \frac{3}{5}

Cross-cancel:

3

= \frac{7}{5}

= \frac{7}{5}

Convert improper fractions to mixed numbers:

\frac{7}{5} = 1 \frac{2}{5}

\frac{7}{5} = 1

Remainder

2

\frac{7}{5}

Write the problem in long division format

5 \overline{∣ 7}

Divide

7

5

to get

1

Divide

7

5

to get

1

1 5 \overline{∣ 7}

Multiply the quotient digit

(1)

by the divisor

5

1 5 \overline{∣ 7} \underline{5}

Subtract

5

from

7

1 5 \overline{∣ 7} \underline{5} 2

1 5 \overline{∣ 7} \underline{5} 2

The solution for Long Division of

\frac{7}{5}

1

with remainder of

2

1 Remainder 2

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{7}{5} = 1 \frac{2}{5}

= 1 \frac{2}{5}

= 1 \frac{2}{5}

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64 \div 2^{4}

Frequently Asked Questions (FAQ)

What is (2+1/3)/(2-1/3) ?
The solution to (2+1/3)/(2-1/3) is 1 2/5