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TACHS Math : Fractions

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Example Questions

Example Question #1 : Fractions

What is the value of $\frac{3}{4 }+\frac{1}{2}-\frac{2}{3}$ ?

Possible Answers:

$\frac{5}{12}$

$\frac{3}{4}$

$\frac{7}{12}$

$\frac{1}{3}$

Correct answer:

$\frac{7}{12}$

Explanation:

Start with finding the value of $\frac{3}{4 }+\frac{1}{2}$ .

In order to add fractions with different denominators, we will need to change one or both denominators first. Notice that is a factor of , which means we can multiply the numerator and the denominator of $\frac{1}{2}$ by to get $\frac{2}{4}$ .

Now, add the two fractions together as they have the same denominator.

$\frac{3}{4}+\frac{1}{2}=\frac{3}{4}+\frac{2}{4}=\frac{5}{4}$

Next, solve $\frac{5}{4}-\frac{2}{3}$ .

The least common multiple of and is .

Thus, $\frac{5}{4}-\frac{2}{3}=\frac{15}{12}-\frac{8}{12}=\frac{7}{12}$

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Example Question #1 : Operations

Janice's car can travel miles on one gallon of gas. Her car can normally hold gallons of gas, but it is only $\frac{2}{3}$ full. How many miles can Janice travel before the tank is empty?

Possible Answers:

360

270

300

450

Correct answer:

300

Explanation:

Start by finding out how many gallons is currently in Janice's tank.

Since it is only $\frac{2}{3}$ full,

$\frac{2}{3}\times 15=10$ .

The tank only has gallons in it right now. Multiply this by the number of miles traveled per gallon to find how far Janice can travel before the tank is empty.

$10 \times 30 = 300$

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Example Question #14 : Tachs: Math And Ability

What is the product of $\frac{5}{6}$ and $\frac{3}{8}$ ?

Possible Answers:

$\frac{1}{8}$

$\frac{7}{16}$

$\frac{3}{8}$

$\frac{5}{16}$

Correct answer:

$\frac{5}{16}$

Explanation:

Since the question asks for the product, you will need to multiply the two fractions. Recall that in multiplying two fractions, you will multiply the numerators together and then multiply the denominators together.

$\frac{5}{6}\times \frac{3}{8}=\frac{15}{48}$

Next, reduce the fraction.

$\frac{15}{48}=\frac{5}{16}$

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Example Question #2 : Operations

What is the difference between $\frac{11}{12}$ and $\frac{3}{4}$ ?

Possible Answers:

$\frac{1}{4}$

$\frac{1}{5}$

$\frac{1}{8}$

$\frac{1}{6}$

Correct answer:

$\frac{1}{6}$

Explanation:

Since the question asks you to find the difference, you will need to subtract the two fractions:

$\frac{11}{12}-\frac{3}{4}$

Start by making both denominators the same. Multiply the numerator and denominator of $\frac{3}{4}$ by to get $\frac{9}{12}$ .

Now, subtract.

$\frac{11}{12}-\frac{3}{4}=\frac{11}{12}-\frac{9}{12}=\frac{2}{12}$

Make sure to simplify the answer.

$\frac{2}{12}=\frac{1}{6}$

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Example Question #2 : Fractions

Paul can type words per minute. If Josie can type $15\%$ faster than Paul can, how many words can Josie type in minutes?

Possible Answers:

Cannot be determined

1035

1173

897

Correct answer:

1035

Explanation:

Start by finding out Josie's typing rate.

Since she types $15\%$ faster, we can find her rate with the following equation:

60+0.15(60)=69

Since Josie types at words per minute, we can multiply by the total number of given minutes to find out how many words she can type in the given time frame.

$69 \times 15=1035$

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TACHS Math : Fractions

Study concepts, example questions & explanations for TACHS Math

All TACHS Math Resources

Example Questions

Example Question #1 : Fractions

Example Question #1 : Operations

Example Question #14 : Tachs: Math And Ability

Example Question #2 : Operations

Example Question #2 : Fractions

All TACHS Math Resources

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