ISEE Middle Level Math : Numbers and Operations
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Example Questions
Example Question #21 : How To Find A Ratio
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?
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 : How To Find A Ratio
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?
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 #23 : How To Find A Ratio
If you want to share a pizza with your friend with a ratio of 
If the ratio is 
That means your friend get 
If a pizza has 
Example Question #21 : How To Find A Ratio
A car travels 
Divide the number of miles by the number of hours to get the number of miles per hour.
Example Question #24 : How To Find A Ratio
Simplify the ratio: 8.5 to 2.5
19 to 5
18 to 5
16 to 5
17 to 5
17 to 5
8.5 to 2.5 can be rewritten and simplified as follows:
The simplified form of the ratio is 17 to 5.
Example Question #25 : How To Find A Ratio
Billy has six horses and Susie has fifteen horses. What is the appropriate ratio of Susie's horses to Billy's horses?
Use the colon symbol to represent the ratio. If we have a ratio of A to B, then this can be rewritten as 
Write the ratio of Susie's horses to Billy's horses.
We can reduce this like fractions.
This means that the ratio can also be:
The answer is:
Example Question #2 : How To Find A Proportion
For every $3 I earn at work, I donate $1 to charity. How much money will I donate if I make $27.00/week.
To find the amount of the donation, divide 27 by 3.
The answer is 9.
Example Question #1 : How To Find A Proportion
A Spanish class has 
A proportion is an amount that is part of a whole. There are 
Example Question #21 : Numbers And Operations
The distance between Youngston and Wynne is 240 miles in reality and three inches on a map. On the same map, Charlesville and Petersburg are one and three-fourths inches apart. How far apart are they in reality?
240 real miles is represented by 3 map inches, making this a ratio of 
Therefore, one and three-fourths inches represents
Example Question #4 : How To Find A Proportion
Read this problem, but do not solve it: Two inches on a map represent twenty-five miles of actual distance. If Pierce Springs and Buchanan Falls are eight inches apart on the map, how far apart are they in actuality?
If we let 
The ratios that are set equal to each other in a proportion must compare the same quantities in the same order.
In each ratio, we can put number of map inches in the numerator and the number of actual miles in the denominator.
One ratio is two map inches to twenty-five actual miles (the map scale); this ratio is 
The other ratio is eight map inches to 
The proportion statement that sets these equal to each other is 
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All ISEE Middle Level Math Resources
