Fractions - SAT Math

Card 0 of 20

Question

Add: $\frac{\frac{9}{8}}{7}+\frac{7}{\frac{1}{7}}$

Answer

To add $\frac{\frac{9}{8}}{7}+\frac{7}{\frac{1}{7}}$ , first simply each term by rewriting the terms using a division sign.

$\frac{9}{8}\div7 + 7 \div \frac{1}{7}$

Take the reciprocal of the terms after the division sign, and change the division sign to a multiplication sign. Simplify.

$\frac{9}{8}\times \frac{1}{7}+ 7 \times 7 = \frac{9}{56} + 49= 49\frac{9}{56}$

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Question

Add: $\frac{1}{\frac{3}{2}}+ \frac{\frac{4}{1}}{\frac{1}{5}}$

Answer

The terms shown are complex fractions. We first need to simplify each and find the least common denominator before solving.

Rewrite the complex fraction using a division sign.

$\frac{1}{\frac{3}{2}} = 1\div\frac{3}{2}$

Change the division sign to a multiplication sign, and take the reciprocal of the second term.

$1\div\frac{3}{2} = 1\times \frac{2}{3} = \frac{2}{3}$

Repeat this step for the second term.

$\frac{\frac{4}{1}}{\frac{1}{5}} = \frac{4}{1} \div \frac{1}{5} = \frac{4}{1} \times \frac{5}{1}=20$

Add the two terms together.

The answer is: $20\frac{2}{3}$

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Question

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?

Answer

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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Question

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

Answer

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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Question

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

Answer

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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Question

Answer

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Question

Solve $\frac{3}{7}+\frac{5}{8}-\frac{1}{2}$ .

Answer

Finding the common denominator yields $\frac{24}{56}+\frac{35}{56}-\frac{28}{56}$ . We can then evaluate leaving $\frac{31}{56}$ .

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Question

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

Answer

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

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Question

Add:

$\frac{2}{9x}+\frac{4}{27}$

Answer

Find the least common denominator to solve this problem

Multiply 27 with , and multiply with 3 to obtain common denominators.

Convert the fractions.

$\frac{2}{9x}+\frac{4}{27}=\frac{6}{27x}+\frac{4x}{27x}$

Combine the terms as one fraction.

The answer is: $\frac{4x+6}{27x}$

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Question

Simplify: $\frac{\frac{1}{2}}{\frac{3}{4}}$

Answer

Rewrite this complex fraction using a division sign.

$\frac{1}{2}\div\frac{3}{4}$

Take the reciprocal of the second term and change the division of the division sign. Simplify.

$\frac{1}{2}\times\frac{4}{3}=\frac{2}{3}$

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Question

Simplify:

Answer

Division is the same as multiplying by the reciprocal. Thus, a/b ÷ c/d = a/b x d/c = ad/bc

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Question

If p is a positive integer, and 4 is the remainder when p-8 is divided by 5, which of the following could be the value of p?

Answer

Remember that if x has a remainder of 4 when divided by 5, xminus 4 must be divisible by 5. We are therefore looking for a number p such that p - 8 - 4 is divisible by 5. The only answer choice that fits this description is 17.

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Question

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

Answer

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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Question

Evaluate the following:

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

Answer

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

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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Question

Evaluate the expression:

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

Answer

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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Question

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

Answer

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

$\frac{\frac{13x}{5y}}{\frac{3x}{8y}}=\frac{13x}{5y}\frac{8y}{3x}=\frac{13x8y}{5y3x}=\frac{138}{5*3}=\frac{104}{15}$

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Question

express 7/8 as a ratio

Answer

a ratio that comes from a fraction is the numerator: denominator

7/8 = 7:8

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Question

1 meter contains 100 centimeters.

Find the ratio of 1 meter and 40 centimeters to 1 meter:

Answer

1m 40cm = 140cm. 1m = 100cm. So the ratio is 140cm:100cm. This can be put as a fraction 140/100 and then reduced to 14/10 and further to 7/5. This, in turn, can be rewritten as a ratio as 7:5.

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Question

When television remotes are shipped from a certain factory, 1 out of every 200 is defective. What is the ratio of defective to nondefective remotes?

Answer

One remote is defective for every 199 non-defective remotes.

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Question

On a desk, there are papers for every paper clips and papers for every greeting card. What is the ratio of paper clips to total items on the desk?

Answer

Begin by making your life easier: presume that there are papers on the desk. Immediately, we know that there are paper clips. Now, if there are papers, you know that there also must be greeting cards. Technically you figure this out by using the ratio:

$\frac{3}{1}=\frac{6}{x}$

By cross-multiplying you get:

Solving for , you clearly get .

(Many students will likely see this fact without doing the algebra, however. The numbers are rather simple.)

Now, this means that our desk has on it:

papers

paper clips

greeting cards

Therefore, you have total items. Based on this, your ratio of paper clips to total items is:

$\frac{2}{10}=\frac{1}{5}$ , which is the same as .

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