How to find a solution to a compound fraction - ACT Math

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Question

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?

Answer

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

Compare your answer with the correct one above

Question

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

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

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

Answer

Plugging $R_{1}=10$ and into the equation gives:

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

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

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

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

Finally:

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

Compare your answer with the correct one above

Question

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

Answer

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

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

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

Compare your answer with the correct one above

Question

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?

Answer

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

Compare your answer with the correct one above

Question

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

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

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

Answer

Plugging $R_{1}=10$ and into the equation gives:

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

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

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

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

Finally:

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

Compare your answer with the correct one above

Question

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

Answer

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

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

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

Compare your answer with the correct one above

Question

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?

Answer

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

Compare your answer with the correct one above

Question

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

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

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

Answer

Plugging $R_{1}=10$ and into the equation gives:

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

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

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

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

Finally:

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

Compare your answer with the correct one above

Question

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

Answer

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

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

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

Compare your answer with the correct one above

Question

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?

Answer

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

Compare your answer with the correct one above

Question

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

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

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

Answer

Plugging $R_{1}=10$ and into the equation gives:

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

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

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

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

Finally:

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

Compare your answer with the correct one above

Question

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

Answer

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

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

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

Compare your answer with the correct one above

Question

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?

Answer

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

Compare your answer with the correct one above

Question

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

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

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

Answer

Plugging $R_{1}=10$ and into the equation gives:

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

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

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

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

Finally:

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

Compare your answer with the correct one above

Question

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

Answer

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

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

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

Compare your answer with the correct one above

Question

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?

Answer

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

Compare your answer with the correct one above

Question

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

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

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

Answer

Plugging $R_{1}=10$ and into the equation gives:

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

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

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

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

Finally:

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

Compare your answer with the correct one above

Question

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

Answer

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

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

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

Compare your answer with the correct one above

Question

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?

Answer

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

Compare your answer with the correct one above

Question

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

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

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

Answer

Plugging $R_{1}=10$ and into the equation gives:

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

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

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

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

Finally:

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

Compare your answer with the correct one above

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How to find a solution to a compound fraction - ACT Math

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?

When two resistors ( and ) are added together in a parallel circuit to create an equivalent single resistor, the equivalent resistor () has a resistance defined by the following equation: If and , what does equal?

Plugging and into the equation gives: Create a common denominator by multiplying by in the numerator and denominator: Finally:

What does equal?

Simplify the numerator first: . Then, simplify the denominator: . Next, you have to do , which is the same as , when solved for and simplified.

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?

When two resistors ( and ) are added together in a parallel circuit to create an equivalent single resistor, the equivalent resistor () has a resistance defined by the following equation: If and , what does equal?

Plugging and into the equation gives: Create a common denominator by multiplying by in the numerator and denominator: Finally:

What does equal?

Simplify the numerator first: . Then, simplify the denominator: . Next, you have to do , which is the same as , when solved for and simplified.

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?

When two resistors ( and ) are added together in a parallel circuit to create an equivalent single resistor, the equivalent resistor () has a resistance defined by the following equation: If and , what does equal?

Plugging and into the equation gives: Create a common denominator by multiplying by in the numerator and denominator: Finally:

What does equal?

Simplify the numerator first: . Then, simplify the denominator: . Next, you have to do , which is the same as , when solved for and simplified.

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?

When two resistors ( and ) are added together in a parallel circuit to create an equivalent single resistor, the equivalent resistor () has a resistance defined by the following equation: If and , what does equal?

Plugging and into the equation gives: Create a common denominator by multiplying by in the numerator and denominator: Finally:

What does equal?

Simplify the numerator first: . Then, simplify the denominator: . Next, you have to do , which is the same as , when solved for and simplified.

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?

When two resistors ( and ) are added together in a parallel circuit to create an equivalent single resistor, the equivalent resistor () has a resistance defined by the following equation: If and , what does equal?

Plugging and into the equation gives: Create a common denominator by multiplying by in the numerator and denominator: Finally:

What does equal?

Simplify the numerator first: . Then, simplify the denominator: . Next, you have to do , which is the same as , when solved for and simplified.

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?

When two resistors ( and ) are added together in a parallel circuit to create an equivalent single resistor, the equivalent resistor () has a resistance defined by the following equation: If and , what does equal?

Plugging and into the equation gives: Create a common denominator by multiplying by in the numerator and denominator: Finally:

What does equal?

Simplify the numerator first: . Then, simplify the denominator: . Next, you have to do , which is the same as , when solved for and simplified.

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?

When two resistors ( and ) are added together in a parallel circuit to create an equivalent single resistor, the equivalent resistor () has a resistance defined by the following equation: If and , what does equal?

Plugging and into the equation gives: Create a common denominator by multiplying by in the numerator and denominator: Finally:

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

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

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

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

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

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