ISEE Middle Level Math : Numbers and Operations

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

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Example Questions

Example Question #11 : How To Find A Ratio

In March, there were 8 rainy days, 13 sunny days and 10 cloudy days. What is the ratio of sunny days to total days in March?

Possible Answers:

Correct answer:

Explanation:

Identify the number of sunny days in March:

Create a ratio showing sunny days in March to toal days in March (31 day month):

 

Example Question #12 : How To Find A Ratio

A 32-ounce bottle of Emerald Cola costs $1.39. What is the cost per ounce, taken to the nearest tenth of a cent?

Possible Answers:

Correct answer:

Explanation:

To find the cost per ounce, divide the total cost, $1.39, by the number of ounces, 32.

This rounds to 4.3 cents per ounce.

Example Question #13 : How To Find A Ratio

A batting average is defined as the ratio of hits to turns at bat. It is expressed as a decimal rounded to the nearest thousand.

In 2013, Carlos Beltran's batting average was 0.296. If he maintains this same batting average over the 2014 baseball season, how many turns at bat should he expect to need to achieve 40 hits? (Nearest whole number)

Possible Answers:

Correct answer:

Explanation:

Since a batting average is a ratio of hits to turns at bat,

Let  be the number of turns at bat Beltran needs to get 40 hits. Then solve for  in this equation:

Beltran should need 135 turns at bat.

Example Question #14 : Ratio And Proportion

A furlong is a unit of length used in horse racing. Eight furlongs are equal to one mile. How many feet are equal to twelve furlongs?

Possible Answers:

Correct answer:

Explanation:

Multiply 12 furlongs by  miles per furlong, and by 5,280 feet per mile:

 feet.

 

Example Question #11 : Numbers And Operations

A fathom is a unit of underwater depth equal to 6 feet. How many fathoms are equal to two miles?

Possible Answers:

Correct answer:

Explanation:

Multiply 2 miles by 5,280 feet per mile by  fathoms per foot:

 fathoms.

Example Question #11 : How To Find A Ratio

A class has  girls and  boys. What is the ratio of girls to boys?

Possible Answers:

Correct answer:

Explanation:

The question asks to compare the number of girls to the number of boys. The ratio is .

Example Question #12 : How To Find A Ratio

If the ratio of boys to girl in a class is 2:3 and there are 18 boys in the class, how many girls are there?

Possible Answers:

Correct answer:

Explanation:

Since you know the ratio and the number of boys, you can set up a proportion from that ratio: .

Since you can multiply the denominator by 9 as well. Therefore, and there are 27 girls in the class.

Example Question #901 : Isee Middle Level (Grades 7 8) Mathematics Achievement

In a pet shop, there are 21 animals. There are 7 hamsters and 2 dogs. There are also equal numbers of cats, rabbits, and guinea pigs. What is the ratio of hamsters to guinea pigs?

Possible Answers:

Correct answer:

Explanation:

In a pet shop, there are 21 animals. Since there are 7 hamsters and 2 dogs, this leaves 12 animals that are neither a hamster nor a dog.

Given that there are also equal numbers of cats, rabbits, and guinea pigs, this means that the remaining number of animals must be divided by 3 to find the number of each species.

There are 4 cats, 4 rabbits, and 4 guinea pigs.

The ratio of hamsters to guinea pigs is therefore 7:4 because there are 7 hamsters and 4 guinea pigs.

Example Question #902 : Isee Middle Level (Grades 7 8) Mathematics Achievement

Mike invited forty friends from his current school, fifteen of whom are girls, to his birthday party. He wants the ratio of girls to boys at the party to be three to two, so he decides to invite some girls from his old school. How many girls will he need to invite, assuming he does not invite anyone else?

Possible Answers:

Correct answer:

Explanation:

So far, there are 15 girls and, counting Mike himself,  boys. For the ratio of girls to boys to be 3 to 2, the number of girls must be  times the number of boys, or

 girls.

15 girls have been invited already, so Mike needs to invite  more girls.

Example Question #12 : Numbers And Operations

Sharon is having a birthday party. So far, she has invited twenty of her friends from school, nine of whom are girls. She wants to make the ratio of boys to girls at the party two to one. If she decides to add her two cousins, both boys, to the guest list, and no other girls, how many more boys does she need to invite?

Possible Answers:

Correct answer:

Explanation:

So far, Sharon has invited twenty friends from school - eleven boys and nine girls. Including Sharon's cousins and Sharon herself, there are thirteen boys and ten girls. 

For there to be a two-to-one boy-to-girl ratio, Sharon must have twice as many boys as girls. She will need  boys total, so she will need to invite  more boys.

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