Chapter 1: Q 1.57. (page 48)

Simplify:
(a) $\frac{3 a}{4} - \frac{8}{9}$
(b) $\frac{3 a}{4} \cdot \frac{8}{9}$

Short Answer

Expert verified

Part (a) The obtained result is $\frac{27 a - 32}{36}$ .

Part (b) The obtained result isrole="math" localid="1644493880508" $\frac{2 a}{3}$ .

Step by step solution

Part (a) Step 1. Find the LCD of the denominator.

Consider the given expression.

\frac{3 a}{4} - \frac{8}{9}

Find the factor of 4 and 9.

$9 = 3 \times 3 4 = 2 \times 2 \bar{LCD = 2 \times 2 \times 3 \times 3} = 36$

Part (a) Step 2. Rewrite the expression.

Write the fraction as an equivalent fraction LCD.

$\begin{array}{rcl} \frac{3 a}{4} - \frac{8}{9} & = & \frac{3 a \cdot 9}{4 \cdot 9} - \frac{8 \cdot 4}{9 \cdot 4} \\ = & \frac{27 a}{36} - \frac{32}{36} \end{array}$

Subtract the numerators and place the difference over the common denominators.

$\begin{array}{rcl} \frac{27 a}{36} - \frac{32}{36} & = & \frac{27 a - 32}{36} \end{array}$

Part (b) Step 1. Multiply the fractions.

Since the given operation is multiplication. Thus,

$\begin{array}{rcl} \frac{3 a}{4} \end{array} \cdot \begin{array}{rcl} \frac{8}{9} \end{array} = \frac{3 a \cdot 8}{4 \cdot 9}$

Part (b) Step 2. Cancel the common factors.

Factor the number and cancel the common factor from numerators and denominators.

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

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Simplify:
(a) $\frac{3 a}{4} - \frac{8}{9}$
(b) $\frac{3 a}{4} \cdot \frac{8}{9}$

Short Answer

Step by step solution

Part (a) Step 1. Find the LCD of the denominator.

Part (a) Step 2. Rewrite the expression.

Part (b) Step 1. Multiply the fractions.

Part (b) Step 2. Cancel the common factors.

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Simplify:(a) 3a4−89(b)3a4⋅89

Short Answer

Step by step solution

Part (a) Step 1. Find the LCD of the denominator.

Part (a) Step 2. Rewrite the expression.

Part (b) Step 1. Multiply the fractions.

Part (b) Step 2. Cancel the common factors.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

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Study anywhere. Anytime. Across all devices.

Simplify:
(a) $\frac{3 a}{4} - \frac{8}{9}$
(b) $\frac{3 a}{4} \cdot \frac{8}{9}$