Question

(3 1/6 - 1 5/8) divided by (8 3/4 - 1.35)

Answer 1

let's firstly convert the mixed fractions to improper fractions, and the decimal amount to a fraction by dividing it by a power of 10, 1.35 has 2 decimals, so we'll divide it by 10 with 2 zeros, 100 and lose the dot.

`\bf \stackrel{mixed}{3(1)/(6)}\implies \cfrac{3\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{19}{6}}~\hfill \stackrel{mixed}{1(5)/(8)}\implies \cfrac{1\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{13}{8}} \\\\\\ \stackrel{mixed}{8(3)/(4)}\implies \cfrac{8\cdot 4+3}{4}\implies \stackrel{improper}{\cfrac{37}{4}}~\hfill 1.\underline{35}\implies \cfrac{135}{1\underline{00}}\implies \cfrac{27}{20} \\\\[-0.35em] ~\dotfill`

`\bf \left( \cfrac{19}{6}-\cfrac{13}{8} \right)/ \left(\cfrac{37}{4}-\cfrac{27}{20} \right)\implies \left(\stackrel{\textit{using an LCD of 24}}{\cfrac{(4)19-(3)13}{24}} \right)/\left( \stackrel{\textit{using an LCD of 20}}{\cfrac{(5)37-(1)27}{20}} \right) \\\\\\ \left( \cfrac{76-39}{24} \right)/ \left( \cfrac{185-27}{20} \right)\implies \cfrac{37}{24}/ \cfrac{158}{20}\implies \cfrac{37}{24}/ \cfrac{79}{10}`

`\bf \cfrac{37}{\underset{12}{~~\begin{matrix} 24 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\cdot \cfrac{\stackrel{5}{~~\begin{matrix} 10 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{79}\implies \cfrac{185}{948}`

Answer 2

The answer to the given expression when [3(1/6) - 1(5/8)] divided by [8{3/4} - 1.35) will be equal to 0.00896.

Convert mixed numbers to fractions:

`3((1)/(6)) = ((3 * 6 + 1) )/(6) = (19 )/( 6)\\\\8((3)/(4)) = ((8 * 4 + 3) )/( 4) = (35 )/( 4)`

Substitute the fractions into the expression:

`([ ((19)/(6)) - 1((5)/(8)) ] )/( [ ((35)/(4)) - 1.35 ])`

Simplify the expression:

Numerator:

Common denominator for (19/6) and (5/8) is 24

19/6 - 1(5/8) = (19/6) - (15/8) = (19*4 - 6*15)/24 = 1/24

Denominator:

Convert 1.35 to fraction: 1.35 = 135/100 = 27/20

Common denominator for (35/4) and (27/20) is 20

(35/4) - 1.35 = (35/4) - (27/20) = (35 * 5 - 27 * 1) / 20 = 123/20

Divide the numerator and denominator by their greatest common divisor (GCD):

GCD(1, 24) = 1

GCD(123, 20) = 1

Simplify the expression:

`(((1 )/( 24)) )/( ((123 )/( 20)))\\\\ = (1 )/( (24 * 123 )/( 20))\\\\ = (1 )/( 111.6)`

1 / 111.6 ≈ 0.00896