Chapter 1: Q 181. (page 53)

Add or Subtract Fraction.
$- \frac{2}{3} - (- \frac{3}{4})$

Short Answer

Expert verified

The value of the given fraction is $\frac{1}{12}$ .

Step by step solution

Step 1. Given information

Consider the expression.

$- \frac{2}{3} - (- \frac{3}{4})$

Apply the rule:a-(-b)=a+b, where a and b are any real numbers.

$- \frac{2}{3} - (- \frac{3}{4}) = - \frac{2}{3} + \frac{3}{4}$

Step 3. Determine the whether the given fraction has the same denominator.

The given fraction does not have the same denominator.

So, find the least common denominator of $3$ and role="math" localid="1644387616775" $4$ .

$\begin{array}{rcl} 3 & = & 3 \cdot 1 \\ 4 & = & 4 \cdot 1 \\ \Rightarrow & L C M = 3 \cdot 4 \\ \Rightarrow & L C M = 12 \end{array}$

Step 4. Multiply the numerator and denominator of each fraction by a factor to get the denominator 12.

$\begin{array}{rcl} - \frac{2}{3} - (- \frac{3}{4}) & = & - \frac{2 \cdot 4}{3 \cdot 4} + \frac{3 \cdot 3}{4 \cdot 3} \\ = & - \frac{8}{12} + \frac{9}{12} \end{array}$

Step 5. Apply the Fraction Addition rule:ac+bc=a+bc, where c≠0.

$\begin{array}{rcl} - \frac{2}{3} - (- \frac{3}{4}) & = & \frac{- 8 + 9}{12} \\ = & \frac{1}{12} \end{array}$

Hence, the value is $\frac{1}{12}$ .

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Add or Subtract Fraction.
$- \frac{2}{3} - (- \frac{3}{4})$

Short Answer

Step by step solution

Step 1. Given information

Apply the rule:a-(-b)=a+b, where a and b are any real numbers.

Step 3. Determine the whether the given fraction has the same denominator.

Step 4. Multiply the numerator and denominator of each fraction by a factor to get the denominator 12.

Step 5. Apply the Fraction Addition rule:ac+bc=a+bc, where c≠0.

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Add or Subtract Fraction.-23--34

Short Answer

Step by step solution

Step 1. Given information

Apply the rule:a-(-b)=a+b, where a and b are any real numbers.

Step 3. Determine the whether the given fraction has the same denominator.

Step 4. Multiply the numerator and denominator of each fraction by a factor to get the denominator 12.

Step 5. Apply the Fraction Addition rule:ac+bc=a+bc, where c≠0.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

Logic and Functions

Probability and Statistics

Theoretical and Mathematical Physics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Add or Subtract Fraction.
$- \frac{2}{3} - (- \frac{3}{4})$