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ACT Math : Compound Fractions

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Example Question #1 : Compound Fractions

John's shadow is six feet long, and Mary's shadow is five feet long. If John is four feet tall, which of the following is closest to Mary's height in inches?

Possible Answers:

$40\ inches$ $\displaystyle 40\ inches$

$48\ inches$ $\displaystyle 48\ inches$

$60\ inches$ $\displaystyle 60\ inches$

$12\ inches$ $\displaystyle 12\ inches$

$33\ inches$ $\displaystyle 33\ inches$

Correct answer:

$40\ inches$ $\displaystyle 40\ inches$

Explanation:

First we set up a proportion. Mary's shadow (5 feet) to John's shadow (6 feet) is equal to Mary's height (x feet) to John's height (4 feet), i.e. 5 / 6 = x / 4.

Solve for x by first cross-mulitplying: 20 = 6x.

Divide both sides by 6: x = 20 / 6 feet

Multiply by 12 to find this height in inches: 20 * 12 / 6 = 20 * 2 = 40 inches

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Example Question #2 : Compound Fractions

When two resistors ( $R_{1}$ $\displaystyle R_{1}$ and $R_{2}$ $\displaystyle R_{2}$) are added together in a parallel circuit to create an equivalent single resistor, the equivalent resistor ( $R_{eq}$ $\displaystyle R_{eq}$) has a resistance defined by the following equation:

$\frac{1}{R_{eq}}= \frac{1}{R_{1}}+\frac{1}{R_{2}}$ $\displaystyle \frac{1}{R_{eq}}= \frac{1}{R_{1}}+\frac{1}{R_{2}}$

If $R_{1}=10$ $\displaystyle R_{1}=10$ and $R_{2}=20$ $\displaystyle R_{2}=20$, what does $R_{eq}$ $\displaystyle R_{eq}$ equal?

Possible Answers:

$\displaystyle 60$

$\frac{20}{3}$ $\displaystyle \frac{20}{3}$

$\displaystyle 30$

None of the other answers

$\frac{3}{20}$ $\displaystyle \frac{3}{20}$

Correct answer:

$\frac{20}{3}$ $\displaystyle \frac{20}{3}$

Explanation:

Plugging $R_{1}=10$ $\displaystyle R_{1}=10$ and R_2=20 $\displaystyle R_2=20$ into the equation gives:

$\frac{1}{R_{eq}}=\frac{1}{10}+\frac{1}{20}$ $\displaystyle \frac{1}{R_{eq}}=\frac{1}{10}+\frac{1}{20}$

Create a common denominator by multiplying $\frac{1}{10}$ $\displaystyle \frac{1}{10}$ by $\displaystyle 2$ in the numerator and denominator:

$\frac{1}{R_{eq}}=\frac{2}{20}+\frac{1}{20}$ $\displaystyle \frac{1}{R_{eq}}=\frac{2}{20}+\frac{1}{20}$

$\frac{1}{R_{eq}}=\frac{3}{20}$ $\displaystyle \frac{1}{R_{eq}}=\frac{3}{20}$

Finally:

$R_{eq} = \frac{20}{3}$ $\displaystyle R_{eq} = \frac{20}{3}$

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Example Question #453 : Arithmetic

What does $\small \frac{\frac{2}{3}\times \frac{1}{4}}{\frac{2}{9}+\frac{1}{3}}$ $\displaystyle \small \frac{\frac{2}{3}\times \frac{1}{4}}{\frac{2}{9}+\frac{1}{3}}$ equal?

Possible Answers:

$\frac{3}{10}$ $\displaystyle \frac{3}{10}$

$\frac{5}{54}$ $\displaystyle \frac{5}{54}$

$\frac{11}{17}$ $\displaystyle \frac{11}{17}$

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{18}{35}$ $\displaystyle \frac{18}{35}$

Correct answer:

$\frac{3}{10}$ $\displaystyle \frac{3}{10}$

Explanation:

Simplify the numerator first: $\small \frac{2}{3}\times \frac{1}{4}=\frac{2}{12}=\frac{1}{6}$ $\displaystyle \small \frac{2}{3}\times \frac{1}{4}=\frac{2}{12}=\frac{1}{6}$.

Then, simplify the denominator: $\frac{2}{9}+\frac{1}{3}=\frac{2}{9}+\frac{3}{9}=\frac{5}{9}$ $\displaystyle \frac{2}{9}+\frac{1}{3}=\frac{2}{9}+\frac{3}{9}=\frac{5}{9}$.

Next, you have to do $\frac{1}{6}\div \frac{5}{9}$ $\displaystyle \frac{1}{6}\div \frac{5}{9}$, which is the same as $\small \small \frac{1}{6}\times \frac{9}{5}=\frac{9}{30}=\frac{3}{10}$ $\displaystyle \small \small \frac{1}{6}\times \frac{9}{5}=\frac{9}{30}=\frac{3}{10}$, when solved for and simplified.

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ACT Math : Compound Fractions

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Compound Fractions

Example Question #2 : Compound Fractions

Example Question #453 : Arithmetic

All ACT Math Resources

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