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

The solution to 1-3/5 (2/3+1/2) is 3/10

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1-3/5 (2/3+1/2)

Solution

1 - \frac{3}{5} (\frac{2}{3} + \frac{1}{2})

Solution

\frac{3}{10}

Solution steps

1 - \frac{3}{5} (\frac{2}{3} + \frac{1}{2})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{2}{3} + \frac{1}{2}) : \frac{7}{6}

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

\frac{2}{3} + \frac{1}{2} = \frac{7}{6}

\frac{2}{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{2}{3} :

multiply the denominator and numerator by

2

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

Add the numbers:

4 + 3 = 7

= \frac{7}{6}

= \frac{7}{6}

= 1 - \frac{3}{5} \cdot \frac{7}{6}

Multiply and divide (left to right)

\frac{3}{5} \cdot \frac{7}{6} : \frac{7}{10}

\frac{3}{5} \cdot \frac{7}{6}

Apply the fraction rule:

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

= \frac{3 \cdot 7}{5 \cdot 6}

Cancel

\frac{3 \cdot 7}{5 \cdot 6} : \frac{7}{10}

\frac{3 \cdot 7}{5 \cdot 6}

Factor the number:

6 = 3 \cdot 2

= \frac{3 \cdot 7}{5 \cdot 3 \cdot 2}

Cancel the common factor:

3

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

Multiply the numbers:

5 \cdot 2 = 10

= \frac{7}{10}

= \frac{7}{10}

= 1 - \frac{7}{10}

Add and subtract (left to right)

1 - \frac{7}{10} : \frac{3}{10}

1 - \frac{7}{10}

1 - \frac{7}{10} = \frac{3}{10}

1 - \frac{7}{10}

Convert element to fraction:

1 = \frac{1 \cdot 10}{10}

= \frac{1 \cdot 10}{10} - \frac{7}{10}

Since the denominators are equal, combine the fractions:

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

= \frac{1 \cdot 10 - 7}{10}

1 \cdot 10 - 7 = 3

1 \cdot 10 - 7

Multiply the numbers:

1 \cdot 10 = 10

= 10 - 7

Subtract the numbers:

10 - 7 = 3

= 3

= \frac{3}{10}

= \frac{3}{10}

= \frac{3}{10}

Popular Examples

-3(-4)+2

- 3 (- 4) + 2

-3(-4)+5

- 3 (- 4) + 5

(4+8-3+9)-4-(4+7-3-2)+(12+5-2)

(4 + 8 - 3 + 9) - 4 - (4 + 7 - 3 - 2) + (12 + 5 - 2)

476+97-564\times 9

476 + 97 - 564 \times 9

12-3^2

12 - 3^{2}

Frequently Asked Questions (FAQ)

What is 1-3/5 (2/3+1/2) ?
The solution to 1-3/5 (2/3+1/2) is 3/10