Question

practice 7

1. if the value of a, b and c in the following fraction are all doubled, how does the value of the fraction change?

\\(\frac{a \cdot d}{c \cdot b}\\)
a. doubles
b. increases by half
c. stays the same
d. decreases by half
e. quadruples

1. which of the following fractions is the equivalent of 0.2%?

a. \\(\frac{1}{5}\\)
b. \\(\frac{1}{50}\\)
c. \\(\frac{1}{500}\\)
d. \\(\frac{1}{1000}\\)
e. \\(\frac{1}{20}\\)

1. \\(\frac{2}{3} - \frac{3}{4} =?\\)

a. \\(-\frac{1}{12}\\)
b. \\(\frac{1}{12}\\)
c. 1
d. \\(-\frac{9}{8}\\)
e. \\(-\frac{8}{9}\\)

Explanation:

Step1: Substitute doubled A,B,C

Original fraction: $\frac{A \cdot D}{C \cdot B}$
New fraction: $\frac{(2A) \cdot D}{(2C) \cdot (2B)} = \frac{2A \cdot D}{4C \cdot B}$

Step2: Simplify the new fraction

$\frac{2A \cdot D}{4C \cdot B} = \frac{1}{2} \cdot \frac{A \cdot D}{C \cdot B}$

Step3: Convert 0.2% to fraction

$0.2\% = \frac{0.2}{100} = \frac{2}{1000} = \frac{1}{500}$

Step4: Find common denominator for subtraction

Common denominator of 3 and 4 is 12:
$\frac{2}{3} = \frac{8}{12}$, $\frac{3}{4} = \frac{9}{12}$

Step5: Perform the subtraction

$\frac{8}{12} - \frac{9}{12} = -\frac{1}{12}$

Answer:

1. D. decreases by half
2. C. $\frac{1}{500}$
3. A. $-\frac{1}{12}$