Chapter 1: Q. 228 (page 54)

Simplify $(\frac{3}{4} + \frac{1}{6}) \div (\frac{5}{8} - \frac{1}{3})$

Short Answer

Expert verified

The result of simplifying the expression is

$(\frac{3}{4} + \frac{1}{6}) \div (\frac{5}{8} - \frac{1}{3}) = \frac{22}{7}$

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegivenexpressionis \\ (\frac{3}{4} + \frac{1}{6}) \div (\frac{5}{8} - \frac{1}{3}) \\ Wehavetosimplifythegivenexpression. \end{array}$

Step 2. Solve the bracket

$\begin{array}{l} \Rightarrow (\frac{3}{4} + \frac{1}{6}) \div (\frac{5}{8} - \frac{1}{3}) = (\frac{3 \times 3 + 1 \times 2}{12}) \div (\frac{5 \times 3 - 1 \times 8}{24}) [TaketheLCMofdenominatorinbrackets] \\ \Rightarrow (\frac{3}{4} + \frac{1}{6}) \div (\frac{5}{8} - \frac{1}{3}) = (\frac{9 + 2}{12}) \div (\frac{15 - 8}{24}) \\ \Rightarrow (\frac{3}{4} + \frac{1}{6}) \div (\frac{5}{8} - \frac{1}{3}) = (\frac{11}{12}) \div (\frac{7}{24}) \end{array}$

Step 3. Divide the fractions

$\begin{array}{l} \Rightarrow (\frac{3}{4} + \frac{1}{6}) \div (\frac{5}{8} - \frac{1}{3}) = (\frac{11}{12}) \div (\frac{7}{24}) \\ Todivide,multiplythefirstfractionbythereciprocalofthesecond \\ \Rightarrow (\frac{3}{4} + \frac{1}{6}) \div (\frac{5}{8} - \frac{1}{3}) = (\frac{11}{12}) \times (\frac{24}{7}) \\ \Rightarrow (\frac{3}{4} + \frac{1}{6}) \div (\frac{5}{8} - \frac{1}{3}) = \frac{11}{12} \times \frac{2 \times 12}{7} \\ \Rightarrow (\frac{3}{4} + \frac{1}{6}) \div (\frac{5}{8} - \frac{1}{3}) = \frac{11}{7} \end{array}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Simplify $(\frac{3}{4} + \frac{1}{6}) \div (\frac{5}{8} - \frac{1}{3})$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve the bracket

Step 3. Divide the fractions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Discrete Mathematics

Decision Maths

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Simplify34+16÷58-13

Short Answer

Step by step solution

Step 1. Given information

Step 2. Solve the bracket

Step 3. Divide the fractions

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Discrete Mathematics

Decision Maths

Logic and Functions

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Simplify $(\frac{3}{4} + \frac{1}{6}) \div (\frac{5}{8} - \frac{1}{3})$