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ISEE Lower Level Math : Ratio and Proportion

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Example Question #31 : Ratio And Proportion

The scale on a map is 2cm : 12km . If and the actual distance between two lakes is 600 km, find the distance between the lakes as shown on a map.

Possible Answers:

400cm

300cm

100cm

1200cm

Correct answer:

100cm

Explanation:

To solve this problem, set up the proportion:

$\frac{2cm}{12km} = \frac{x}{600km}$

Cross multiply:

$12x\ km = 1200\ cm\ km$

Divide both sides by 12 to isolate x.

$\\ \frac{12x\ km}{12\ km} = \frac{1200\ cm\ km}{12\ km} \\ \\ x=\frac{12\cdot 100\ cm \ km}{12\ km} \\ \\x=100cm$

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Example Question #31 : How To Find A Ratio

You and a friend win a raffle of $\$2,000$ . You and him split it with a ratio of 2:3 since he paid more into the raffle. What is your share?

Possible Answers:

800

900

400

1,000

2,000

Correct answer:

800

Explanation:

Since there are a total of five shares in the ratio

(2+3=5)

and you get two shares, your share is $\frac{2}{5}$ of the total.

2,000*2=4,000

and

$\frac{4,000}{5}=800.$

Your share is $\$800$ .

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Example Question #31 : How To Find A Ratio

If three friends start a business and two invested equally while the third invested twice the amount each of them did, what is the ratio for their shares?

Possible Answers:

2:4

1:1:1

1:1:2

1:2

Correct answer:

1:1:2

Explanation:

Since the first two have to be equal, you can start by representing them by share apiece.

The third invested twice the amount that each of the others did so you double their share to get 1*2=2 .

So the first friend gets one share and so does the second.

The third friend gets two shares and the ratios looks like,

1:1:2 .

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Example Question #34 : How To Find A Ratio

Sharon has marbles, of which are blue and of which are white. Write the ratio of blue marbles to white marbles in simplest form.

Possible Answers:

$8 \textrm{ to }6$

$1 \textrm{ to }3$

$3 \textrm{ to }1$

$6 \textrm{ to }8$

$8 \textrm{ to }2$

Correct answer:

$3 \textrm{ to }1$

Explanation:

The ratio of blue marbles to white marbles is $60 \textrm{ to 20}$ , but this is not in simplest form. Rewrite this as a fraction for simplicity, then divide both numbers by GCF (60,20) = 20 :

$\frac{60}{20} = \frac{60\div 20}{20\div 20} = \frac{3}{1}$

In simplest form, the ratio is $3 \textrm{ to }1$

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Example Question #32 : Ratio And Proportion

A fruit punch recipe calls for 1 cup of orange juice, half a cup of pineapple juice, and 2 cups of soda. What is the ratio of orange juice to pineapple juice to soda water?

Possible Answers:

2:1:8

3:1:4

2:1:4

1:1:8

Correct answer:

2:1:4

Explanation:

If a fruit punch recipe calls for 1 cup or orange juice, half a cup of pineapple juice, and 2 cups of soda, the ratio would be:

$1:\frac{1}{2}:2$

Multiply all three numbers by 2:

2:1:4

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Example Question #521 : Numbers And Operations

A cookie recipe that bakes 12 cookies calls for 3 eggs. How many eggs would be needed to make 36 cookies?

Possible Answers:

$\dpi{100} 9$

$\dpi{100} 10$

$\dpi{100} 8$

$\dpi{100} 7$

Correct answer:

$\dpi{100} 9$

Explanation:

36 cookies is 3 times more than 12. Multiply the number of eggs by 3 to get 9.

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Example Question #2 : How To Find A Proportion

Give the value of that makes this proportion statement correct:

$\frac{49}{N} = \frac{14}{24}$

Possible Answers:

N= 72

N= 84

N= 91

N= 80

N= 77

Correct answer:

N= 84

Explanation:

Cross-multiply, then solve for :

$\frac{49}{N} = \frac{14}{24}$

$14 N = 49 \cdot 24$

$14 N \div 14= 49 \cdot 24\div 14$

N= 84

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Example Question #3 : How To Find A Proportion

Give the value of that makes this proportion statement correct:

$\frac{N}{60} = \frac{14}{24}$

Possible Answers:

N = 32

N = 42

N = 35

N = 40

N = 45

Correct answer:

N = 35

Explanation:

Solve for by multiplying both sides by 60:

$\frac{N}{60} = \frac{14}{24}$

$\frac{N}{60} \cdot 60= \frac{14}{24}\cdot 60$

$N = \frac{14}{24}\cdot \frac{60}{1} = \frac{840}{24} = 35$

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Example Question #522 : Numbers And Operations

If 1 inch on a map represents 5 miles, how far apart, in miles, are two cities that are 6.6 inches apart on the map?

Possible Answers:

36 miles

12 miles

33 miles

24 miles

6.6 miles

Correct answer:

33 miles

Explanation:

Set up a proportion with the inches on the map and physical miles:

$\frac{1}{5}=\frac{6.6}{x}$

Solve for x:

1*x=5*6.6

x = 33

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Example Question #5 : How To Find A Proportion

A group of 6th grade students at Manor Intermediate are going on a field trip to the local theme park.

There are 2 chaperones required for every 9 students on the field trip. How many chaperones will need to attend the field trip if there are 27 students going?

Possible Answers:

chaperones

None of the other answers

Correct answer:

chaperones

Explanation:

The best way to solve this problem is to set it up as two ratios that are equivalent to each other. This forms a proportion. Make sure to set up the ratios so that the relationships go together across the equal sign.

$\frac{2}{9}= \frac{\square }{27}$

Use cross products to then solve for the missing value.

$2\times 27= 54$

Therefore, mental math or division can be used to find

$9\times \square = 54$ .

Since $9\times 6= 54$ ,

there would need to be 6 chaperones attending the field trip.

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ISEE Lower Level Math : Ratio and Proportion

Study concepts, example questions & explanations for ISEE Lower Level Math

All ISEE Lower Level Math Resources

Example Questions

Example Question #31 : Ratio And Proportion

Example Question #31 : How To Find A Ratio

Example Question #31 : How To Find A Ratio

Example Question #34 : How To Find A Ratio

Example Question #32 : Ratio And Proportion

Example Question #521 : Numbers And Operations

Example Question #2 : How To Find A Proportion

Example Question #3 : How To Find A Proportion

Example Question #522 : Numbers And Operations

Example Question #5 : How To Find A Proportion

All ISEE Lower Level Math Resources

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