ISEE Middle Level Math : ISEE Middle Level (grades 7-8) Mathematics Achievement

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

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Example Questions

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

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

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 #903 : Isee Middle Level (Grades 7 8) Mathematics Achievement

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 #17 : Ratio And Proportion

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 #18 : Ratio And Proportion

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 #904 : 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 #905 : Isee Middle Level (Grades 7 8) Mathematics Achievement

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.

Example Question #904 : Isee Middle Level (Grades 7 8) Mathematics Achievement

A boardgame has 22 pieces. Half of the pieces are blue and the other half are red. John has hidden 4 red pieces and 3 blue pieces. Of the remaining pieces, what is the ratio of red pieces to blue pieces?

Possible Answers:

Correct answer:

Explanation:

If there is a boardgame in which there are 22 pieces, half of which are blue and half of which are red, this means that there are 11 blue pieces and 11 red pieces. If John has hidden 4 red pieces and 3 blue pieces, there are therefore 7 red pieces remaining and 8 blue pieces remaining. 

Thus, the ratio of red pieces to blue pieces (of what remains) is .

Example Question #22 : Ratio And Proportion

The ratio of cats to dogs in the pet store is 2:3.  If there are 21 dogs, how many more dogs are there than cats? 

Possible Answers:

Correct answer:

Explanation:

Set up a proportion and cross multiply to determine the number of cats. 

Then find the difference between the number of dogs and cats by using subtraction.  

Example Question #910 : Isee Middle Level (Grades 7 8) Mathematics Achievement

If you want to share a pizza with your friend with a ratio of  with you getting  part and your friend getting  parts, how much pizza does your friend get if there are  slices of pizza?

Possible Answers:

Correct answer:

Explanation:

If the ratio is , there are  total parts.  

That means your friend get  out of  parts or .  

If a pizza has  slices, that means that your friend's number of slices is  of  or  slices.

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