Chapter 1: Q 188. (page 53)

Add or Subtract Fraction.
$a \frac{3 a}{8} \div \frac{7}{12} b \frac{3 a}{8} - \frac{7}{12}$

Short Answer

Expert verified

Part (a) The value of $\frac{3 a}{8} \div \frac{7}{12}$ is $\begin{array}{rcl} \frac{9 a}{14} \end{array}$ .

Part (b) The value of localid="1645593218325" $\frac{3 a}{8} - \frac{7}{12}$ is $\frac{9 a - 14}{24}$ .

Step by step solution

Part (a) Step 1. Given information

Consider the expression.

$a \frac{3 a}{8} \div \frac{7}{12}$

Part (a) Step 2. Determine the operation.

The operation is division.

Part (a) Step 3. Apply the Fraction Division Formula:ab÷cd=ab·dc, where b≠0, c≠0, and d≠0.

$\begin{array}{rcl} \frac{3 a}{8} \div \frac{7}{12} & = & \frac{3 a}{8} \cdot \frac{12}{7} \\ = & \frac{3 a}{4 \cdot 2} \cdot \frac{4 \cdot 3}{7} \\ = & \frac{9 a}{14} \end{array}$

Thus, the value is $\begin{array}{rcl} \frac{9 a}{14} \end{array}$ .

Part (b) Step 1. Now, consider the expression.b3a8-712Determine the operation.

The operation is subtraction.

Part (b) Step 2. 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 $8$ and $12$ .

$\begin{array}{rcl} 8 & = & 2 \cdot 4 \\ 12 & = & 3 \cdot 4 \\ \Rightarrow & L C M = 2 \cdot 3 \cdot 4 \\ \Rightarrow & L C M = 24 \end{array}$

Part (b) Step 3. Multiply the numerator and denominator of each fraction by a factor to get the denominator 24.

$\begin{array}{rcl} \frac{3 a}{8} - \frac{7}{12} & = & \frac{3 a \cdot 3}{8 \cdot 3} - \frac{7 \cdot 2}{12 \cdot 2} \\ = & \frac{9 a}{24} - \frac{14}{24} \end{array}$

Part (b) Step 4. Apply the Fraction Subtraction rule:ac-bc=a-bc, where c≠0.

$\frac{3 a}{8} - \frac{7}{12} = \frac{9 a - 14}{24}$

Hence, the value is $\frac{9 a - 14}{24}$ .

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Add or Subtract Fraction.
$a \frac{3 a}{8} \div \frac{7}{12} b \frac{3 a}{8} - \frac{7}{12}$

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Determine the operation.

Part (a) Step 3. Apply the Fraction Division Formula:ab÷cd=ab·dc, where b≠0, c≠0, and d≠0.

Part (b) Step 1. Now, consider the expression.b3a8-712Determine the operation.

Part (b) Step 2. Determine the whether the given fraction has the same denominator.

Part (b) Step 3. Multiply the numerator and denominator of each fraction by a factor to get the denominator 24.

Part (b) Step 4. Apply the Fraction Subtraction rule:ac-bc=a-bc, where c≠0.

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Add or Subtract Fraction.a3a8÷712b3a8-712

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Determine the operation.

Part (a) Step 3. Apply the Fraction Division Formula:ab÷cd=ab·dc, where b≠0, c≠0, and d≠0.

Part (b) Step 1. Now, consider the expression.b3a8-712Determine the operation.

Part (b) Step 2. Determine the whether the given fraction has the same denominator.

Part (b) Step 3. Multiply the numerator and denominator of each fraction by a factor to get the denominator 24.

Part (b) Step 4. Apply the Fraction Subtraction 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

Probability and Statistics

Decision Maths

Pure Maths

Discrete Mathematics

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Calculus

Study anywhere. Anytime. Across all devices.

Add or Subtract Fraction.
$a \frac{3 a}{8} \div \frac{7}{12} b \frac{3 a}{8} - \frac{7}{12}$