Chapter 1: Q 191. (page 53)

Add or Subtract Fraction.
$a - \frac{5 a}{3} + (- \frac{10}{6}) b - \frac{5 a}{3} \div (- \frac{10}{6})$

Short Answer

Expert verified

Part (a) The value of $- \frac{5 a}{3} + (- \frac{10}{6})$ is $\begin{array}{rcl} \frac{- 5 a - 5}{3} \end{array}$ .

Part (b) The value of $- \frac{5 a}{3} \div (- \frac{10}{6})$ is $a$ .

Step by step solution

Part (a) Step 1. Given information

Consider the expression.

$a - \frac{5 a}{3} + (- \frac{10}{6})$

Part (a) Step 2. Determine the operation.

The operation is subtraction.

Part (a) 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 $6$ .

$\begin{array}{rcl} 3 & = & 3 \cdot 1 \\ 6 & = & 2 \cdot 3 \\ \Rightarrow & L C M = 3 \cdot 2 \\ \Rightarrow & L C M = 6 \end{array}$

Part (a) Step 4. Multiply the numerator and denominator of each fraction by a factor to get the denominator 6.

$\begin{array}{rcl} - \frac{5 a}{3} + (- \frac{10}{6}) & = & - \frac{5 a}{3} - \frac{10}{6} \\ = & - \frac{5 a \cdot 2}{3 \cdot 2} - \frac{10}{6} \\ = & - \frac{10 a}{6} - \frac{10}{6} \end{array}$

Part (a) Step 5. Apply the Fraction Subtraction rule:ac-bc=a-bc, where c≠0.

$\begin{array}{rcl} - \frac{5 a}{3} + (- \frac{10}{6}) & = & \frac{- 10 a - 10}{6} \\ = & \frac{- 2 \cdot 5 a - 2 \cdot 5}{2 \cdot 3} \\ = & \frac{2 (- 5 a - 5)}{2 \cdot 3} \\ = & \frac{- 5 a - 5}{3} \end{array}$

Thus, the value is $\begin{array}{rcl} \frac{- 5 a - 5}{3} \end{array}$ .

Part (b) Step 1. Now, consider the fraction.b-5a3÷-106Determine the operation.

The operation is division.

Part (b) Step 2. Apply the Fraction Division Formula:ab÷cd=ab·dc, where b≠0, c≠0, and d≠0.

$- \frac{5 a}{3} \div (- \frac{10}{6}) = - \frac{5 a}{3} \cdot (- \frac{6}{10})$

Since the signs are the same, the product will be positive.

$\begin{array}{rcl} - \frac{5 a}{3} \div (- \frac{10}{6}) & = & \frac{5 a}{3} \cdot \frac{6}{10} \\ = & \frac{5 a}{3} \cdot \frac{3 \cdot 2}{5 \cdot 2} \\ = & a \end{array}$

Hence, the value is $a$ .

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Add or Subtract Fraction.
$a - \frac{5 a}{3} + (- \frac{10}{6}) b - \frac{5 a}{3} \div (- \frac{10}{6})$

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Determine the operation.

Part (a) Step 3. Determine the whether the given fraction has the same denominator.

Part (a) Step 4. Multiply the numerator and denominator of each fraction by a factor to get the denominator 6.

Part (a) Step 5. Apply the Fraction Subtraction rule:ac-bc=a-bc, where c≠0.

Part (b) Step 1. Now, consider the fraction.b-5a3÷-106Determine the operation.

Part (b) Step 2. Apply the Fraction Division Formula:ab÷cd=ab·dc, where b≠0, c≠0, and d≠0.

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Add or Subtract Fraction.a-5a3+-106b-5a3÷-106

Short Answer

Step by step solution

Part (a) Step 1. Given information

Part (a) Step 2. Determine the operation.

Part (a) Step 3. Determine the whether the given fraction has the same denominator.

Part (a) Step 4. Multiply the numerator and denominator of each fraction by a factor to get the denominator 6.

Part (a) Step 5. Apply the Fraction Subtraction rule:ac-bc=a-bc, where c≠0.

Part (b) Step 1. Now, consider the fraction.b-5a3÷-106Determine the operation.

Part (b) Step 2. Apply the Fraction Division Formula:ab÷cd=ab·dc, where b≠0, c≠0, and d≠0.

One App. One Place for Learning.

Most popular questions from this chapter

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Mechanics Maths

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Study anywhere. Anytime. Across all devices.

Add or Subtract Fraction.
$a - \frac{5 a}{3} + (- \frac{10}{6}) b - \frac{5 a}{3} \div (- \frac{10}{6})$