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SAT Math : Fractions

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Example Question #6 : Operations With Fractions

If $\dpi{100} \small x=\frac{2}{3}$ and $\dpi{100} \small y= \frac {3}{4}$ , then what is the value of $\dpi{100} \small \frac {x}{y}$ ?

Possible Answers:

$\dpi{100} \small \frac{8}{9}$

$\dpi{100} \small \frac{1}{2}$

$\dpi{100} \small \frac{5}{7}$

$\dpi{100} \small \frac{9}{8}$

$\dpi{100} \small 2$

Correct answer:

$\dpi{100} \small \frac{8}{9}$

Explanation:

Dividing by a number (in this case $\dpi{100} \small \frac {3}{4}$ ) is equivalent to multiplying by its reciprocal (in this case $\dpi{100} \small \frac {4}{3}$ ). Therefore:

$\dpi{100} \small \frac {2}{3}\div \frac{3}{4} = \frac{2}{3}\times \frac{4}{3} = \frac{8}{9}$

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Example Question #1 : Operations With Fractions

Evaluate the following:

$\left ( \frac{5}{6}\times \frac{12}{13} \right )^{2}\div \frac{3}{4}$

Possible Answers:

$\frac{507}{400}$

$\frac{4}{5}$

$\frac{25}{507}$

None of the available answers

$\frac{400}{507}$

Correct answer:

$\frac{400}{507}$

Explanation:

$\left ( \frac{5}{6}\times \frac{12}{13} \right )^{2}\div \frac{3}{4}$

First we will evaluate the terms in the parentheses:

$\left ( \frac{5}{6}\times \frac{2\times 6}{13} \right )^{2}\div \frac{3}{4}$

$\left ( \frac{5}{1}\times \frac{2}{13} \right )^{2}\div \frac{3}{4}$

$\left ( \frac{10}{13} \right )^{2}\div \frac{3}{4}$

Next, we will square the first fraction:

$\left ( \frac{10^{2}}{13^{2}} \right )\div \frac{3}{4}$

$\frac{100}{169}\div \frac{3}{4}$

We can evaluate the division as such:

$\frac{100}{169}\times\frac{4}{3}=\frac{400}{507}$

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Example Question #1 : How To Divide Fractions

Evaluate the expression:

$\frac{3}{9}\div \frac{4}{15}$

Possible Answers:

$\frac{4}{45}$

$\frac{5}{2}$

$1\frac{1}{4}$

$1\frac{2}{7}$

$\frac{3}{5}$

Correct answer:

$1\frac{1}{4}$

Explanation:

When dividing fractions, you invert the second term and multiply the numbers.

$\frac{3}{9}\times\frac{15}{4}$

You can reduce the numbers that are diagonal from each other to make the numbers smaller and easier to multiply.

$\frac{3}{3}\times\frac{5}{4}=\frac{5}{4}=1\frac{1}{4}$

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Example Question #11 : Operations With Fractions

Simplify $\frac{\frac{13x}{5y}}{\frac{3x}{8y}}$

Possible Answers:

Fractions with variables cannot be divided

$\frac{39}{40}$

$\frac{16}{13}$

$\frac{18}{8}$

$\frac{104}{15}$

Correct answer:

$\frac{104}{15}$

Explanation:

When you dividing fractions, multiply by the reciprocal of the denominator.

$\frac{\frac{13x}{5y}}{\frac{3x}{8y}}=\frac{13x}{5y}*\frac{8y}{3x}=\frac{13*x*8*y}{5*y*3*x}=\frac{13*8}{5*3}=\frac{104}{15}$

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Example Question #11 : Operations With Fractions

Which fraction has a value greater than that of X?

$x = \frac{4}{3}-\frac{7}{12}$

Possible Answers:

$\frac{3}{5}$

$\frac{2}{3}$

$\frac{3}{4}$

$\frac{5}{7}$

$\frac{7}{8}$

Correct answer:

$\frac{7}{8}$

Explanation:

First, start by putting changing the fractions in the equation so that they have the same denominator.

$x=\frac{4}{3}-\frac{7}{12}$

$x=\frac{16}{12}-\frac{7}{12}$

Then, you can easily subtract the numerators. The denominator stays the same at this point:

$x=\frac{9}{12}$

At this point, you can reduce the fraction by dividing the numerator and the denominator by :

$x=\frac{3}{4}$

Then, to easily compare the fraction to the answer choices, you can change the fraction to a decimal:

$\frac{3}{4}=0.75$

By changing the answer choices to decimals as well, you can easily figure out which value is greater than 0.75 :

$\frac{3}{5}=0.6<0.75$

$\frac{5}{7}=0.71<0.75$

$\frac{2}{3}=0.667<0.75$

$\frac{3}{4}=0.75=0.75$

$\frac{7}{8}=0.875>0.75$ , so $\frac{7}{8}$ is the correct answer.

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Example Question #1 : How To Add Fractions

Jesse has a large movie collection containing X movies. 1/3 of his movies are action movies, 3/5 of the remainder are comedies, and the rest are historical movies. How many historical movies does Jesse own?

Possible Answers:

(3/9)*X

(7/12)*X

(2/5)*X

(11/15)*X

(4/15)*X

Correct answer:

(4/15)*X

Explanation:

1/3 of the movies are action movies. 3/5 of 2/3 of the movies are comedies, or (3/5)*(2/3), or 6/15. Combining the comedies and the action movies (1/3 or 5/15), we get 11/15 of the movies being either action or comedy. Thus, 4/15 of the movies remain and all of them have to be historical.

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Example Question #1 : How To Add Fractions

If x = 1/3 and y = 1/2, find the value of 2x + 3y.

Possible Answers:

5/6

6/5

13/6

Correct answer:

13/6

Explanation:

Substitute the values of x and y into the given expression:

2(1/3) + 3(1/2)

= 2/3 + 3/2

= 4/6 + 9/6

= 13/6

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Example Question #2 : How To Add Fractions

Alternating1

Possible Answers:

$\dpi{100} \frac{17}{60}$

$\dpi{100} \frac{47}{60}$

$\dpi{100} \frac{43}{60}$

$\dpi{100} -\frac{43}{60}$

$\dpi{100} -\frac{47}{60}$

Correct answer:

$\dpi{100} \frac{47}{60}$

Explanation:

Alternating2

Alternating3

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Example Question #13 : Operations With Fractions

What is the solution, reduced to its simplest form, for $x = \frac{7}{9}+\frac{3}{5}+\frac{2}{15}+\frac{7}{45}}$ ?

Possible Answers:

$x = \frac{115}{45}$

$x = \frac{7}{15}$

$x = \frac{75}{45}$

$x = \frac{5}{3}$

$x =2$

Correct answer:

$x = \frac{5}{3}$

Explanation:

$x=\frac{7}{9}+\frac{3}{5}+\frac{2}{15}+\frac{7}{45}=\frac{35}{45}+\frac{27}{45}+\frac{6}{45}+\frac{7}{45}=\frac{75}{45}=\frac{5}{3}$

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Example Question #1 : Operations

What is the result of adding $20\%$ of $\frac{2}{7}$ to $\frac{1}{4}$ ?

Possible Answers:

$\frac{23}{11}$

$\frac{43}{140}$

$\frac{47}{140}$

$\frac{3}{28}$

$\frac{3}{39}$

Correct answer:

$\frac{43}{140}$

Explanation:

Let us first get our value for the percentage of the first fraction. 20% of 2/7 is found by multiplying 2/7 by 2/10 (or, simplified, 1/5): (2/7) * (1/5) = (2/35)

Our addition is therefore (2/35) + (1/4). There are no common factors, so the least common denominator will be 35 * 4 or 140. Multiply the numerator and denominator of 2/35 by 4/4 and the numerator of 1/4 by 35/35.

This yields:

(8/140) + (35/140) = 43/140, which cannot be reduced.

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SAT Math : Fractions

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #6 : Operations With Fractions

Example Question #1 : Operations With Fractions

Example Question #1 : How To Divide Fractions

Example Question #11 : Operations With Fractions

Example Question #11 : Operations With Fractions

Example Question #1 : How To Add Fractions

Example Question #1 : How To Add Fractions

Example Question #2 : How To Add Fractions

Example Question #13 : Operations With Fractions

Example Question #1 : Operations

All SAT Math Resources

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