What is (5/22)(3/5+1/2) ?

The solution to (5/22)(3/5+1/2) is 1/4

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Popular >

(5/22)(3/5+1/2)

Solution

(\frac{5}{22}) (\frac{3}{5} + \frac{1}{2})

Solution

\frac{1}{4}

Solution steps

(\frac{5}{22}) (\frac{3}{5} + \frac{1}{2})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{3}{5} + \frac{1}{2}) : \frac{11}{10}

\frac{3}{5} + \frac{1}{2}

\frac{3}{5} + \frac{1}{2} = \frac{11}{10}

\frac{3}{5} + \frac{1}{2}

Least Common Multiplier of

5, 2 : 10

5, 2

Least Common Multiplier (LCM)

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

5

2

= 5 \cdot 2

Multiply the numbers:

5 \cdot 2 = 10

= 10

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

10

For

\frac{3}{5} :

multiply the denominator and numerator by

2

\frac{3}{5} = \frac{3 \cdot 2}{5 \cdot 2} = \frac{6}{10}

For

\frac{1}{2} :

multiply the denominator and numerator by

5

\frac{1}{2} = \frac{1 \cdot 5}{2 \cdot 5} = \frac{5}{10}

= \frac{6}{10} + \frac{5}{10}

Since the denominators are equal, combine the fractions:

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

= \frac{6 + 5}{10}

Add the numbers:

6 + 5 = 11

= \frac{11}{10}

= \frac{11}{10}

= (\frac{5}{22}) \frac{11}{10}

Multiply and divide (left to right)

(\frac{5}{22}) \frac{11}{10} : \frac{1}{4}

(\frac{5}{22}) \frac{11}{10}

Apply rule:

(a) = a

(\frac{5}{22}) = \frac{5}{22}

= \frac{5}{22} \cdot \frac{11}{10}

\frac{5}{22} \cdot \frac{11}{10} = \frac{1}{4}

\frac{5}{22} \cdot \frac{11}{10}

Apply the fraction rule:

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

= \frac{5 \cdot 11}{22 \cdot 10}

Cancel

\frac{5 \cdot 11}{22 \cdot 10} : \frac{1}{4}

\frac{5 \cdot 11}{22 \cdot 10}

Factor the number:

10 = 5 \cdot 2

= \frac{5 \cdot 11}{22 \cdot 5 \cdot 2}

Cancel the common factor:

5

= \frac{11}{22 \cdot 2}

Cancel the numbers:

\frac{11}{22} = \frac{1}{2}

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{1}{4}

= \frac{1}{4}

= \frac{1}{4}

= \frac{1}{4}

Popular Examples

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4 \div 6 + 3 \div 12

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2 - 3 (8)

5(-9)^2

5 (- 9)^{2}

-3*(-2)^2

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

-2^5\div 2^3

- 2^{5} \div 2^{3}

Frequently Asked Questions (FAQ)

What is (5/22)(3/5+1/2) ?
The solution to (5/22)(3/5+1/2) is 1/4