# ISEE Middle Level Math : Numbers and Operations

## Example Questions

### Example Question #41 : How To Find The Part From The Whole With Percentage

If  is  of , what is the value of ?

Explanation:

If  is  of , that means that . When we plug 1 into , the result is .

### Example Question #45 : How To Find The Part From The Whole With Percentage

King Middle School has 320 students enrolled in the 7th grade.  Sixty percent of the 7th graders at King are girls.  How many 7th grade girls are enrolled at King Middle School?

Explanation:

When given the quantity of the whole, you can determine a part using a percentage by converting the percentage to a decimal and multiplying the whole by that decimal.

### Example Question #46 : How To Find The Part From The Whole With Percentage

What is 60% of 300?

Explanation:

Substitute in the proportion:

Cross multiply:

### Example Question #47 : How To Find The Part From The Whole With Percentage

What number is 85% of 560?

Explanation:

To determine the number that is 85% of 560, convert the percentage to a decimal:

Then multiply:

### Example Question #43 : How To Find The Part From The Whole With Percentage

What is  of  ?

Explanation:

To find a percentage of a whole, we will first write the percentage as a fraction.  We know that all percentages can be written as a number over 100.  So,

Now, we will multiply the fraction by the whole number.  We get

Now, we can simplify/multiply.

We write 150 as a fraction over 1.

We can cancel out the zero in 150 and the zero in 100.

We can cancel out the zero in 30 and the zero in 10.

Now, we can multiply.

Therefore,  of  is .

### Example Question #13 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

What is the sale price of a product that costs  if the sale is  off the original price?

Explanation:

First, find  of :

Then, subtract this value from the whole:

### Example Question #14 : Use Proportional Relationships To Solve Multistep Ratio And Percent Problems: Ccss.Math.Content.7.Rp.A.3

What is the sale price of a television if it is % off the original price of

Explanation:

First, multiply:

Then subtract that amount from the original price:

Answer: The sale price is .

### Example Question #51 : How To Find The Part From The Whole With Percentage

What is  of ?

Explanation:

To find a percentage of a whole, we will multiply the percentage by the whole number.  So,

of

can be written as

We know that a percentage can be written as a fraction over 100.  So,

Now, we can solve.

We can cancel out the zero in 30 and the zero in 100.

We can cancel out the zero in 10 and the zero in 270.

Now, we multiply.

Therefore,  of  is .

### Example Question #51 : How To Find The Part From The Whole With Percentage

What is  of 999?

Explanation:

of a number is equivalent to

times the number.

Therefore,   of 999 is equal to

.

### Example Question #901 : Numbers And Operations

What is  of ?

Explanation:

To find the percentage of a whole, we will multiply the percentage by the whole number.  So,

of

can be written as

Now, we know percentages can be written as a number of 100.  So,

Now, we can multiply.

We can cancel the zero in 40 and the zero in 100.  We get

We can cancel the zero in 10 and the zero in 240.  We get

Now, we multiply.