137k views
2 votes
(3 1/6 - 1 5/8) divided by (8 3/4 - 1.35)

(3 1/6 - 1 5/8) divided by (8 3/4 - 1.35)-example-1
User Leninhasda
by
8.3k points

2 Answers

5 votes

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}

User EastSw
by
8.5k points
4 votes

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

User London Student
by
8.0k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories