What is (4 3/5-4 1/2)\times 5 ?

The solution to (4 3/5-4 1/2)\times 5 is 1/2

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Popular >

(4 3/5-4 1/2)\times 5

Solution

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

Solution

\frac{1}{2}

Solution steps

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

Convert mixed numbers to improper fractions:

4 \frac{3}{5} = \frac{23}{5}

4 \frac{3}{5}

Convert mixed numbers to improper fraction:

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

4 \frac{3}{5} = \frac{4 \cdot 5 + 3}{5}

= \frac{23}{5}

= (\frac{23}{5} - 4 \frac{1}{2}) \cdot 5

Convert mixed numbers to improper fractions:

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

4 \frac{1}{2}

Convert mixed numbers to improper fraction:

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

4 \frac{1}{2} = \frac{4 \cdot 2 + 1}{2}

= \frac{9}{2}

= (\frac{23}{5} - \frac{9}{2}) \cdot 5

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{23}{5} - \frac{9}{2}) : \frac{1}{10}

\frac{23}{5} - \frac{9}{2}

\frac{23}{5} - \frac{9}{2} = \frac{1}{10}

\frac{23}{5} - \frac{9}{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{23}{5} :

multiply the denominator and numerator by

2

\frac{23}{5} = \frac{23 \cdot 2}{5 \cdot 2} = \frac{46}{10}

For

\frac{9}{2} :

multiply the denominator and numerator by

5

\frac{9}{2} = \frac{9 \cdot 5}{2 \cdot 5} = \frac{45}{10}

= \frac{46}{10} - \frac{45}{10}

Since the denominators are equal, combine the fractions:

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

= \frac{46 - 45}{10}

Subtract the numbers:

46 - 45 = 1

= \frac{1}{10}

= \frac{1}{10}

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

Multiply and divide (left to right)

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

\frac{1}{10} \cdot 5

Convert element to fraction:

5 = \frac{5}{1}

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

Apply the fraction rule:

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

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

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

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

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

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

Multiply the numbers:

1 \cdot 5 = 5

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

Multiply the numbers:

10 \cdot 1 = 10

= \frac{5}{10}

= \frac{5}{10}

Cancel the numbers:

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

= \frac{1}{2}

= \frac{1}{2}

= \frac{1}{2}

Popular Examples

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

-7-1+6-2

- 7 - 1 + 6 - 2

60^2-110+4

6 0^{2} - 110 + 4

(6*5)^2

(6 \cdot 5)^{2}

6^2\div 4(2^2)-2^3+7

6^{2} \div 4 (2^{2}) - 2^{3} + 7

Frequently Asked Questions (FAQ)

What is (4 3/5-4 1/2)\times 5 ?
The solution to (4 3/5-4 1/2)\times 5 is 1/2