What is 1500-(1/3+1/5) ?

The solution to 1500-(1/3+1/5) is 1499 7/15

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Popular Pre Algebra >

1500-(1/3+1/5)

Solution

1500 - (\frac{1}{3} + \frac{1}{5})

Solution

1499 \frac{7}{15}

Decimal

1499.46666 \dots

Solution steps

1500 - (\frac{1}{3} + \frac{1}{5})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{1}{3} + \frac{1}{5}) : \frac{8}{15}

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

\frac{1}{3} + \frac{1}{5} = \frac{8}{15}

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

Least Common Multiplier of

3, 5 : 15

3, 5

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

5 : 5

5

5

is a prime number, therefore no factorization is possible

= 5

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

3

5

= 3 \cdot 5

Multiply the numbers:

3 \cdot 5 = 15

= 15

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

15

For

\frac{1}{3} :

multiply the denominator and numerator by

5

\frac{1}{3} = \frac{1 \cdot 5}{3 \cdot 5} = \frac{5}{15}

For

\frac{1}{5} :

multiply the denominator and numerator by

3

\frac{1}{5} = \frac{1 \cdot 3}{5 \cdot 3} = \frac{3}{15}

= \frac{5}{15} + \frac{3}{15}

Since the denominators are equal, combine the fractions:

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

= \frac{5 + 3}{15}

Add the numbers:

5 + 3 = 8

= \frac{8}{15}

= \frac{8}{15}

= 1500 - \frac{8}{15}

Add and subtract (left to right)

1500 - \frac{8}{15} : \frac{22492}{15}

1500 - \frac{8}{15}

1500 - \frac{8}{15} = \frac{22492}{15}

1500 - \frac{8}{15}

Convert element to fraction:

1500 = \frac{1500 \cdot 15}{15}

= \frac{1500 \cdot 15}{15} - \frac{8}{15}

Since the denominators are equal, combine the fractions:

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

= \frac{1500 \cdot 15 - 8}{15}

1500 \cdot 15 - 8 = 22492

1500 \cdot 15 - 8

Multiply the numbers:

1500 \cdot 15 = 22500

= 22500 - 8

Subtract the numbers:

22500 - 8 = 22492

= 22492

= \frac{22492}{15}

= \frac{22492}{15}

= \frac{22492}{15}

Convert improper fractions to mixed numbers:

\frac{22492}{15} = 1499 \frac{7}{15}

\frac{22492}{15} = 1499

Remainder

7

\frac{22492}{15}

Write the problem in long division format

15 \overline{∣ 22492}

Divide

22

15

to get

1

Divide

22

15

to get

1

1 15 \overline{∣ 22492}

Multiply the quotient digit

(1)

by the divisor

15

1 15 \overline{∣ 22492} \underline{15}

Subtract

15

from

22

1 15 \overline{∣ 22492} \underline{15} 7

Bring down the next number of the dividend

1 15 \overline{∣ 22492} \underline{15} 74

1 15 \overline{∣ 22492} \underline{15} 74

Divide

74

15

to get

4

Divide

74

15

to get

4

14 15 \overline{∣ 22492} \underline{15} 74

Multiply the quotient digit

(4)

by the divisor

15

14 15 \overline{∣ 22492} \underline{15} 74 \underline{60}

Subtract

60

from

74

14 15 \overline{∣ 22492} \underline{15} 74 \underline{60} 14

Bring down the next number of the dividend

14 15 \overline{∣ 22492} \underline{15} 74 \underline{60} 149

14 15 \overline{∣ 22492} \underline{15} 74 \underline{60} 149

Divide

149

15

to get

9

Divide

149

15

to get

9

149 15 \overline{∣ 22492} \underline{15} 74 \underline{60} 149

Multiply the quotient digit

(9)

by the divisor

15

149 15 \overline{∣ 22492} \underline{15} 74 \underline{60} 149 \underline{135}

Subtract

135

from

149

149 15 \overline{∣ 22492} \underline{15} 74 \underline{60} 149 \underline{135} 14

Bring down the next number of the dividend

149 15 \overline{∣ 22492} \underline{15} 74 \underline{60} 149 \underline{135} 142

149 15 \overline{∣ 22492} \underline{15} 74 \underline{60} 149 \underline{135} 142

Divide

142

15

to get

9

Divide

142

15

to get

9

1499 15 \overline{∣ 22492} \underline{15} 74 \underline{60} 149 \underline{135} 142

Multiply the quotient digit

(9)

by the divisor

15

1499 15 \overline{∣ 22492} \underline{15} 74 \underline{60} 149 \underline{135} 142 \underline{135}

Subtract

135

from

142

1499 15 \overline{∣ 22492} \underline{15} 74 \underline{60} 149 \underline{135} 142 \underline{135} 7

1499 15 \overline{∣ 22492} \underline{15} 74 \underline{60} 149 \underline{135} 142 \underline{135} 7

The solution for Long Division of

\frac{22492}{15}

1499

with remainder of

7

1499 Remainder 7

Convert to mixed number: Quotient

\frac{Remainder}{Divisor}

\frac{22492}{15} = 1499 \frac{7}{15}

= 1499 \frac{7}{15}

= 1499 \frac{7}{15}

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What is 1500-(1/3+1/5) ?
The solution to 1500-(1/3+1/5) is 1499 7/15

1500-(1/3+1/5)

Solution

Solution

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What is 1500-(1/3+1/5) ?

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