What is 23(1/46-9/15) ?

The solution to 23(1/46-9/15) is -133/10

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23(1/46-9/15)

Solution

23 (\frac{1}{46} - \frac{9}{15})

Solution

- \frac{133}{10}

Solution steps

23 (\frac{1}{46} - \frac{9}{15})

\frac{9}{15} = \frac{3}{5}

Cancel the common factor:

3

\frac{3}{5}

= 23 (\frac{1}{46} - \frac{3}{5})

Follow the PEMDAS order of operations

Calculate within parentheses

(\frac{1}{46} - \frac{3}{5}) : - \frac{133}{230}

\frac{1}{46} - \frac{3}{5}

\frac{1}{46} - \frac{3}{5} = - \frac{133}{230}

\frac{1}{46} - \frac{3}{5}

Least Common Multiplier of

46, 5 : 230

46, 5

Least Common Multiplier (LCM)

Prime factorization of

46 : 2 \cdot 23

46

46

divides by

246 = 23 \cdot 2

= 2 \cdot 23

2, 23

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 23

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

46

5

= 2 \cdot 23 \cdot 5

Multiply the numbers:

2 \cdot 23 \cdot 5 = 230

= 230

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

230

For

\frac{1}{46} :

multiply the denominator and numerator by

5

\frac{1}{46} = \frac{1 \cdot 5}{46 \cdot 5} = \frac{5}{230}

For

\frac{3}{5} :

multiply the denominator and numerator by

46

\frac{3}{5} = \frac{3 \cdot 46}{5 \cdot 46} = \frac{138}{230}

= \frac{5}{230} - \frac{138}{230}

Since the denominators are equal, combine the fractions:

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

= \frac{5 - 138}{230}

Subtract the numbers:

5 - 138 = - 133

= \frac{- 133}{230}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{133}{230}

= - \frac{133}{230}

= 23 (- \frac{133}{230})

Multiply and divide (left to right)

23 (- \frac{133}{230}) : - \frac{133}{10}

23 (- \frac{133}{230})

Apply rule

a \cdot (- b) = - a \cdot b

23 (- \frac{133}{230}) = - 23 \cdot \frac{133}{230}

Convert element to fraction:

23 = \frac{23}{1}

= - \frac{23}{1} \cdot \frac{133}{230}

Apply the fraction rule:

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

\frac{23}{1} \cdot \frac{133}{230} = \frac{23 \cdot 133}{1 \cdot 230}

= - \frac{23 \cdot 133}{1 \cdot 230}

\frac{23 \cdot 133}{1 \cdot 230} = \frac{133}{10}

\frac{23 \cdot 133}{1 \cdot 230}

Multiply the numbers:

1 \cdot 230 = 230

= \frac{23 \cdot 133}{230}

Factor the number:

230 = 23 \cdot 10

= \frac{23 \cdot 133}{23 \cdot 10}

Cancel the common factor:

23

= \frac{133}{10}

= - \frac{133}{10}

= - \frac{133}{10}

Popular Examples

1-9^2

1 - 9^{2}

(12-2^4)^3

(12 - 2^{4})^{3}

16(1)^2

16 (1)^{2}

75^2+105+3

7 5^{2} + 105 + 3

5+3\times 2\div 6-4

5 + 3 \times 2 \div 6 - 4

Frequently Asked Questions (FAQ)

What is 23(1/46-9/15) ?
The solution to 23(1/46-9/15) is -133/10