# ISEE Middle Level Math : Numbers and Operations

## Example Questions

### Example Question #791 : Ssat Middle Level Quantitative (Math)

What is the value of x in

Explanation:

Since this is a proportion, you can cross-multiply. Once you do that, the left side is Your right side is . Set those equal to each other. Then, combine like terms. Subtract from both sides so that the equation is now . Divide both sides by Your answer is

### Example Question #6 : How To Find A Proportion

Michelle is having a party, and she is experimenting with different mixtures of soda, trying to come up with something original. In particular, she likes a drink she made when she mixed together three ounces of cola and five ounces of grape soda. She has two and a half liters of cola and wants to use it all to make some of this drink; how much grape soda does she need to mix it with?

None of the other responses gives the correct answer.

Explanation:

The ratio of ounces of cola to ounces of grape soda in the initial mixture can be expressed as . It must be equal to that of liters of cola to liters of grape soda in the mixture Michelle will make for the party, which, since the number of liters of grape soda is unknown, is . Set these equal and solve for :

Set the cross-products equal to each other:

Michelle will use  liters of grape soda in the final mixture.

### Example Question #11 : How To Find A Proportion

Robert, Jeff, and Paul are sharing a bag of chips that contains 20 chips. The three of them eat all of the chips. If Robert has eaten 8 chips, and Jeff eats twice as many chips as Paul, how many chips has Jeff eaten?

Explanation:

What do we know? We know that there are 20 chips in the bag, and we know that Robert has eaten 8 of them. Thus, we can calculate that there are  chips remaining. Of this remaining, Jeff has eaten 2 parts and Paul has eaten 1 part: that's 3 parts, so let's calculate how many chips constitute each part:

So, each part is equal to 4 chips.

Jeff has eaten 2 parts, so  gives us our answer.

### Example Question #1 : How To Find A Proportion

If one cupcake costs 75 cents, how much does a dozen cupcakes cost?

Explanation:

You can solve this problem using a proportion.

To solve for x, cross multiply.

9 dollars

### Example Question #9 : How To Find A Proportion

If you can purchase two pairs of jeans for 50 dollars, how many pairs of jeans can you purchase with 200 dollars?

Explanation:

You can use a proportion to solve this problem.

Cross multiply to solve for x.

### Example Question #1 : How To Find A Proportion

For every  he earns an hour, Phil gives  to his sister Lola. How much money will Lola have if Phil works  hours?

Explanation:

To Solve:

Multiply the  Lola receives by the  hours Phil worked:

Phil will give Lola  if he works  hours.

### Example Question #11 : How To Find A Proportion

If the ratio of boys to girls in a classroom is , and there are a total of of  students in the classroom, how many boys are in the classroom?

Explanation:

If the ratio of boys to girls in a classroom is , that means that there are  boys for every  girls. Thus, when there are  students in a classroom, the breakdown will be  boys and  girls. If there are  students in a classroom, the breakdown will be  boys and  girls, which translates to a ratio of , or

Thus, if there are  students,  will be boys.

### Example Question #11 : How To Find A Proportion

You survey  students about the plans for a new practice court for the basketball team and they must give a yes or no answer.  students are against the use of funds on this project.  What proportion of students said that they agreed with the plan?

Explanation:

If  disagreed with the plan, that means the rest agreed.

So to find that value, you must do the total minus the no's

.

To find the proportion you must divide the part by the whole giving us an answer of

.

### Example Question #12 : How To Find A Proportion

If Mike gets two times the amount of work done than Joe, what is a ratio representing the work that each get done?

Explanation:

Since Mike does twice the work that Joe does, his part of the ratio must be double the value of Joe's.  The only ratio given that has that is .

### Example Question #31 : Numbers And Operations

Which statement does not follow from the statement  ?

Explanation:

If , then:

The ratio of the numerators is equivalent to that of the denominators, in the same order. Hence,

and  are true.

The reciprocals of the ratios are equivalent, so

However, it does not hold that

.

This can be seen as follows:

.