What is 7/18-(19/32)/((2/9-17/48)) ?

The solution to 7/18-(19/32)/((2/9-17/48)) is 44/9

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Popular >

simplify 7/18-(19/32)/((2/9-17/48))

Solution

simplify

\frac{7}{18} - \frac{\frac{19}{32}}{( \frac{2}{9} - \frac{17}{48} )}

Solution

\frac{44}{9}

Decimal Notation

4.88888 \dots

Solution steps

\frac{7}{18} - \frac{\frac{19}{32}}{\frac{2}{9} - \frac{17}{48}}

\frac{\frac{19}{32}}{\frac{2}{9} - \frac{17}{48}} = - \frac{171}{38}

\frac{\frac{19}{32}}{\frac{2}{9} - \frac{17}{48}}

Apply the fraction rule:

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

= \frac{19}{32 ( \frac{2}{9} - \frac{17}{48} )}

Simplify

32 (\frac{2}{9} - \frac{17}{48}) : - \frac{38}{9}

32 (\frac{2}{9} - \frac{17}{48})

\frac{2}{9} - \frac{17}{48} = - \frac{19}{144}

\frac{2}{9} - \frac{17}{48}

Least Common Multiplier of

9, 48 : 144

9, 48

Least Common Multiplier (LCM)

Prime factorization of

9 : 3 \cdot 3

9

9

divides by

39 = 3 \cdot 3

= 3 \cdot 3

Prime factorization of

48 : 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3

48

48

divides by

248 = 24 \cdot 2

= 2 \cdot 24

24

divides by

224 = 12 \cdot 2

= 2 \cdot 2 \cdot 12

12

divides by

212 = 6 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 6

6

divides by

26 = 3 \cdot 2

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3

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

9

48

= 3 \cdot 3 \cdot 2 \cdot 2 \cdot 2 \cdot 2

Multiply the numbers:

3 \cdot 3 \cdot 2 \cdot 2 \cdot 2 \cdot 2 = 144

= 144

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

144

For

\frac{2}{9} :

multiply the denominator and numerator by

16

\frac{2}{9} = \frac{2 \cdot 16}{9 \cdot 16} = \frac{32}{144}

For

\frac{17}{48} :

multiply the denominator and numerator by

3

\frac{17}{48} = \frac{17 \cdot 3}{48 \cdot 3} = \frac{51}{144}

= \frac{32}{144} - \frac{51}{144}

Apply the fraction rule:

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

= \frac{32 - 51}{144}

32 - 51 = - 19

32 - 51

To subtract a larger number from a smaller one switch the order of the numbers. Negate the result by attaching a minus sign

51 - 32 = 19

51 - 32

Line up the numbers

- 5312

Subtract each column of digits, starting from the right and working left

If the digit being subtracted is larger than the digit above it, 'borrow' a digit from the next column to the left.

In the bolded column, subtract the second digit from the first

- 5312

The bottom number is larger than the upper number. Try to'borrow' a digit from the left.

Borrow

1

from

5

. The remainder is

4

- 4531012

Add

1

ten to

1

10 + 1 = 11

- 4531112

In the bolded column, subtract the second digit from the first:

11 - 2 = 9

\frac{- 4 5 3 11 1 2}{9}

In the bolded column, subtract the second digit from the first:

4 - 3 = 1

\frac{- 4 5 3 11 1 2}{1 9}

= 19

Place a minus sign in front of the answer

- 19

= \frac{- 19}{144}

Apply the fraction rule:

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

= - \frac{19}{144}

= 32 (- \frac{19}{144})

Apply rule:

a (- b) = - ab

32 (- \frac{19}{144}) = - 32 \cdot \frac{19}{144}

= - 32 \cdot \frac{19}{144}

- 32 \cdot \frac{19}{144} = - \frac{38}{9}

- 32 \cdot \frac{19}{144}

- 32 \cdot \frac{19}{144} = - \frac{608}{144}

- 32 \cdot \frac{19}{144}

Convert element to fraction:

32 = \frac{32}{1}

= - \frac{32}{1} \cdot \frac{19}{144}

Apply the fraction rule:

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

\frac{32}{1} \cdot \frac{19}{144} = \frac{32 \cdot 19}{1 \cdot 144}

= - \frac{32 \cdot 19}{1 \cdot 144}

Multiply the numbers:

32 \cdot 19 = 608

= - \frac{608}{1 \cdot 144}

Multiply the numbers:

1 \cdot 144 = 144

= - \frac{608}{144}

= - \frac{608}{144}

Factor the number:

608 = 16 \cdot 38

= - \frac{16 \cdot 38}{144}

Factor the number:

144 = 16 \cdot 9

= - \frac{16 \cdot 38}{16 \cdot 9}

Cancel the common factor:

16

= - \frac{38}{9}

= - \frac{38}{9}

= \frac{19}{- \frac{38}{9}}

Apply the fraction rule:

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

= - \frac{19}{\frac{38}{9}}

Apply the fraction rule:

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

\frac{19}{\frac{38}{9}} = \frac{19 \cdot 9}{38}

= - \frac{19 \cdot 9}{38}

Multiply the numbers:

19 \cdot 9 = 171

= - \frac{171}{38}

= \frac{7}{18} - (- \frac{171}{38})

\frac{7}{18} - (- \frac{171}{38}) = \frac{44}{9}

\frac{7}{18} - (- \frac{171}{38})

Apply rule:

a - (- b) = a + b

\frac{7}{18} - (- \frac{171}{38}) = \frac{7}{18} + \frac{171}{38}

= \frac{7}{18} + \frac{171}{38}

Cancel

\frac{171}{38} : \frac{9}{2}

\frac{171}{38}

Factor the number:

171 = 19 \cdot 9

= \frac{19 \cdot 9}{38}

Factor the number:

38 = 19 \cdot 2

= \frac{19 \cdot 9}{19 \cdot 2}

Cancel the common factor:

19

= \frac{9}{2}

= \frac{7}{18} + \frac{9}{2}

\frac{7}{18} + \frac{9}{2} = \frac{88}{18}

\frac{7}{18} + \frac{9}{2}

Least Common Multiplier of

18, 2 : 18

18, 2

Least Common Multiplier (LCM)

Prime factorization of

18 : 2 \cdot 3 \cdot 3

18

18

divides by

218 = 9 \cdot 2

= 2 \cdot 9

9

divides by

39 = 3 \cdot 3

= 2 \cdot 3 \cdot 3

2, 3

are all prime numbers, therefore no further factorization is possible

= 2 \cdot 3 \cdot 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

18

2

= 2 \cdot 3 \cdot 3

Multiply the numbers:

2 \cdot 3 \cdot 3 = 18

= 18

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

18

For

\frac{9}{2} :

multiply the denominator and numerator by

9

\frac{9}{2} = \frac{9 \cdot 9}{2 \cdot 9} = \frac{81}{18}

= \frac{7}{18} + \frac{81}{18}

Apply the fraction rule:

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

= \frac{7 + 81}{18}

Add the numbers:

7 + 81 = 88

= \frac{88}{18}

= \frac{88}{18}

Cancel

\frac{88}{18} : \frac{44}{9}

\frac{88}{18}

Factor the number:

88 = 2 \cdot 44

= \frac{2 \cdot 44}{18}

Factor the number:

18 = 2 \cdot 9

= \frac{2 \cdot 44}{2 \cdot 9}

Cancel the common factor:

2

= \frac{44}{9}

= \frac{44}{9}

= \frac{44}{9}

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4^{2} - 7

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2^2*2

2^{2} \cdot 2

2^4+2^4

2^{4} + 2^{4}

(2^4*3^4)/(6^2)

\frac{2 ^{4} \cdot 3 ^{4}}{6 ^{2}}

Frequently Asked Questions (FAQ)

What is 7/18-(19/32)/((2/9-17/48)) ?
The solution to 7/18-(19/32)/((2/9-17/48)) is 44/9