Ratios and Proportions - SAT Math

Card 0 of 48

Question

Convert $\small \frac{3}{8}$ into a percentage.

Answer

Set up a proportion:

$\frac{3}{8}=\frac{x}{100}$

Cross-multiply:

Isolate by dividing by 8:

$x=\frac{300}{8}$

Finally, simplify:

$\frac{300}{8}=\frac{75}{2}=37\frac{1}{2}=37.5$

The fraction is therefore equivalent to .

Compare your answer with the correct one above

Question

Convert the following fraction into a percent.

$\small \frac{7}{12}$

Answer

Set up a proportion:

$\small \frac{7}{12}=\frac{x}{100}$

Cross multiply:

$\small 12x=700$

Isolate $\small x$ by dividing both sides by 12:

$\small x = \frac{700}{12}$

Simplify:

$\small \frac{700}{12} = \frac{350}{6} = \frac{175}{3} = 58.33$

(Hint: If you are unable to use long division to solve the fraction $\small \frac{175}{3}$ , take a look at your answer choices and see if you can narrow down your choices. You know that value is going to be greater than one, since 175 is greater than 3. You also know that dividing any number by 3 is going to result in a decimal of .33, .66, or no decimal at all. With these two pieces of information, you should be able to isolate the correct answer without actually solving for it like I did in the last step.)

Compare your answer with the correct one above

Question

Solve for :

$\frac{8}{11} = \frac{11x}{8}$

Answer

To solve this proportion, cross multiply.

$\frac{8}{11} = \frac{11x}{8}$

From here to solve, divide both sides by 121.

$x=\frac{64}{121}$

Compare your answer with the correct one above

Question

If for every $\frac{1}{2}$ inch on a map it represents miles, how many inches will be needed for a distance of miles?

Answer

The ratio of inches to miles is

$\frac{0.5}{25}$

so you can set up a proportion of $\frac{0.5}{25}=\frac{x}{275}$ .

You then cross multiply to get

.

Then you solve for the variable by dividing by which gives us

.

Compare your answer with the correct one above

Question

In a geometric sequence the ratio of the first term to the third term is 9:1. What is the ratio of the second term to the fifth term?

Answer

Recall that in a geometric sequence there is a constant ratio between any pair of consecutive terms:

$r \cdot a_{n} =a_{n+1}$

If the ratio of the first term to the third term is 9:1 then the ratio of two consecutive terms is a number that when multiplied by itself is 9:

Therefore the common ratio for this sequence is 3.

There are three terms between term 2 and 5 so the common ratio will be applied to the second term three times to get the fifth term:

$r^3 \cdot a_{2} = a_{5}$

Since for this sequence

$3^{3} = 27$

Compare your answer with the correct one above

Question

Solve the proportion: $\frac{2x+3}{2} = \frac{1}{3}$

Answer

To solve the proportion, cross multiply the terms.

Subtract 9 on both sides.

Divide by 6 on both sides.

$\frac{6x}{6}=\frac{-7}{6}$

The answer is: $-\frac{7}{6}$

Compare your answer with the correct one above

Question

Solve the ratio: $\frac{5}{9} = \frac{x}{6}$

Answer

To solve the proportion, cross multiply.

Divide by 9 on both sides.

$\frac{30}{9}=\frac{9x}{9}$

Reduce the fractions.

The answer is: $\frac{10}{3}$

Compare your answer with the correct one above

Question

Determine the value of : $\frac{2x-2}{8} = \frac{8x-2}{3}$

Answer

Cross multiply the fractions.

Simplify both sides.

Subtract on both sides.

Add 16 on both sides.

Divide by 58 on both sides.

$\frac{10}{58}= \frac{58x}{58}$

Reduce both fractions.

The answer is: $x = \frac{5}{29}$

Compare your answer with the correct one above

Question

Solve the proportion: $\frac{x}{3} = \frac{2}{5}$

Answer

Cross multiply both sides.

Simplify and solve for x.

$\frac{5x}{5}=\frac{6}{5}$

The answer is: $\frac{6}{5}$

Compare your answer with the correct one above

Question

Solve the proportion: $\frac{3x}{5} = \frac{1}{3}$

Answer

Cross multiply both sides.

Divide by 9 on both sides.

$\frac{9x}{9}=\frac{5}{9}$

The answer is: $\frac{5}{9}$

Compare your answer with the correct one above

Question

Solve the proportion: $\frac{3x}{4} = \frac{8}{3}$

Answer

Cross multiply the two fractions.

Divide by nine on both sides.

$\frac{9x}{9}=\frac{32}{9}$

The answer is: $\frac{32}{9}$

Compare your answer with the correct one above

Question

Solve the proportion: $\frac{2x}{9} = \frac{7}{3}$

Answer

Cross multiply the two fractions.

Divide by six on both sides.

$\frac{6x }{6}= \frac{63}{6}$

The answer is: $\frac{21}{2}$

Compare your answer with the correct one above

Question

Convert $\small \frac{3}{8}$ into a percentage.

Answer

Set up a proportion:

$\frac{3}{8}=\frac{x}{100}$

Cross-multiply:

Isolate by dividing by 8:

$x=\frac{300}{8}$

Finally, simplify:

$\frac{300}{8}=\frac{75}{2}=37\frac{1}{2}=37.5$

The fraction is therefore equivalent to .

Compare your answer with the correct one above

Question

Convert the following fraction into a percent.

$\small \frac{7}{12}$

Answer

Set up a proportion:

$\small \frac{7}{12}=\frac{x}{100}$

Cross multiply:

$\small 12x=700$

Isolate $\small x$ by dividing both sides by 12:

$\small x = \frac{700}{12}$

Simplify:

$\small \frac{700}{12} = \frac{350}{6} = \frac{175}{3} = 58.33$

(Hint: If you are unable to use long division to solve the fraction $\small \frac{175}{3}$ , take a look at your answer choices and see if you can narrow down your choices. You know that value is going to be greater than one, since 175 is greater than 3. You also know that dividing any number by 3 is going to result in a decimal of .33, .66, or no decimal at all. With these two pieces of information, you should be able to isolate the correct answer without actually solving for it like I did in the last step.)

Compare your answer with the correct one above

Question

Solve for :

$\frac{8}{11} = \frac{11x}{8}$

Answer

To solve this proportion, cross multiply.

$\frac{8}{11} = \frac{11x}{8}$

From here to solve, divide both sides by 121.

$x=\frac{64}{121}$

Compare your answer with the correct one above

Question

If for every $\frac{1}{2}$ inch on a map it represents miles, how many inches will be needed for a distance of miles?

Answer

The ratio of inches to miles is

$\frac{0.5}{25}$

so you can set up a proportion of $\frac{0.5}{25}=\frac{x}{275}$ .

You then cross multiply to get

.

Then you solve for the variable by dividing by which gives us

.

Compare your answer with the correct one above

Question

In a geometric sequence the ratio of the first term to the third term is 9:1. What is the ratio of the second term to the fifth term?

Answer

Recall that in a geometric sequence there is a constant ratio between any pair of consecutive terms:

$r \cdot a_{n} =a_{n+1}$

If the ratio of the first term to the third term is 9:1 then the ratio of two consecutive terms is a number that when multiplied by itself is 9:

Therefore the common ratio for this sequence is 3.

There are three terms between term 2 and 5 so the common ratio will be applied to the second term three times to get the fifth term:

$r^3 \cdot a_{2} = a_{5}$

Since for this sequence

$3^{3} = 27$

Compare your answer with the correct one above

Question

Solve the proportion: $\frac{2x+3}{2} = \frac{1}{3}$

Answer

To solve the proportion, cross multiply the terms.

Subtract 9 on both sides.

Divide by 6 on both sides.

$\frac{6x}{6}=\frac{-7}{6}$

The answer is: $-\frac{7}{6}$

Compare your answer with the correct one above

Question

Solve the ratio: $\frac{5}{9} = \frac{x}{6}$

Answer

To solve the proportion, cross multiply.

Divide by 9 on both sides.

$\frac{30}{9}=\frac{9x}{9}$

Reduce the fractions.

The answer is: $\frac{10}{3}$

Compare your answer with the correct one above

Question

Determine the value of : $\frac{2x-2}{8} = \frac{8x-2}{3}$

Answer

Cross multiply the fractions.

Simplify both sides.

Subtract on both sides.

Add 16 on both sides.

Divide by 58 on both sides.

$\frac{10}{58}= \frac{58x}{58}$

Reduce both fractions.

The answer is: $x = \frac{5}{29}$

Compare your answer with the correct one above

Tap the card to reveal the answer