# ISEE Middle Level Math : Numbers and Operations

## Example Questions

### Example Question #91 : Numbers And Operations

What is  of  ?

Explanation:

To find a fraction of a whole number, we will multiply the fraction by the whole number.  So, in the problem

of

we can re-write it as

Now, we will write 36 as a fraction.  We know that whole numbers can be written as fractions over 1.  So, we get

Now, before we multiply, we will simplify to make things easier.  The 3 and the 36 can both be divided by 3.  So, we get

Now, we can multiply straight across.  We get

Therefore,  of  is .

### Example Question #91 : Numbers And Operations

What is two-thirds of 24 ?

Explanation:

To find a fraction of a whole number, we will multiply the fraction by the whole number. So, in the problem

two-thirds of 24

we will first write two-thirds as a fraction.  We know two-thirds can be written as .  So, we can write

of

Now, we can multiply them.  We get

Before we can multiply, we need to write 24 as a fraction.  We know whole numbers can be written as fractions over 1.  So, we get

Now, we can simplify before we multiply to make things easier.  The 3 and the 24 can both be divided by 3.  So, we get

Now, we can multiply straight across.  We get

Therefore, two-thirds of 24 is 16.

### Example Question #91 : Numbers And Operations

What is one-third of 27 ?

Explanation:

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

So, in the problem

one-third of 27

we will first write one-third as a fraction.  We know one-third can be written as .

So, we get

of

Now, we can multiply them together.  So,

Now, we will write 27 as a fraction.  We know that whole numbers can be written as fractions over 1.  So,

Now, we can multiply straight across.  We get

Therefore,  of  is .

### Example Question #52 : Whole And Part

What is  of  ?

Explanation:

To find a fraction of a whole number, we will multiply the fraction by the whole number. So, in the problem

of

we can write it like this:

Now, we will write  as a fraction.  We know that whole numbers can be written as fractions over 1.  So, we get

Now, we will simplify before we multiply to make things easier.  The 7 and the 63 can both be divided by 7.  So, we get

Now, we will multiply straight across.  We get

Therefore,   of  is .

### Example Question #201 : Whole And Part

Amanda has 3 more marbles than Jason and 5 fewer marbles than Kate. Together, they all have 17 marbles. How many marbles does Amanda have?

5 marbles

6 marbles

7 marbles

4 marbles

5 marbles

Explanation:

Amanda has 3 more marbles than Jason and 5 fewer marbles than Kate. Together, they all have 17 marbles.

To solve this problem, we should experiment by picking a number for Amanda. We can pick the number 4.

If Amanda has 4 marbles, this means that Jason has 1 marble, since Amanda has 3 more. If she has 5 fewer marbles than Kate, that means that Kate must have 9 marbles.

This leaves us with:

Amanda - 4 marbles

Jason - 1 marble

Kate - 9 marbles

This adds up to a total of 14 marbles. However, we know that there are a total of 17 marbles. Thus, each child must have 1 more marble than what is stated above. The correct information would be below:

Amanda - 5 marbles

Jason - 2 marble

Kate - 10 marbles

Here, the sum of the marbles is 17 and Amanda still has 3 more marbles that Jason and 5 fewer marbles that Kate.

Thus, the correct answer is that Amanda has 5 marbles.

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

What is a third of 42?

Explanation:

To find a fraction of a whole number, we will multiply the fraction by the whole number.  First, given the problem,

a third of 42

we know that a third can be written as .  So, we can re-write it as

of

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

Now, we need to write 42 as a fraction.  We know that whole numbers can be written as fractions over 1.  So,

Now, we can multiply straight across.  We get

Therefore, a third of 42 is 14.

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

What is a third of 336?

Explanation:

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

So, we know a third is the same as .  Now, we can multiply.

We will write 336 as a fraction.  We know whole numbers can be written as fractions over 1.  So, we get

Now, we can multiply straight across.  We get

Therefore, a third of 336 is 112.

### Example Question #92 : Numbers And Operations

What is  of ?

Explanation:

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

So, in the problem

of

We can re-write it as

Now, we will write 52 as a fraction.  We know that whole numbers can be written as fractions over 1.  So, we get

Now, we can simplify before we multiply.  The 4 and the 52 can both be divided by 4.  We get

Now, we multiply straight across.

Therefore,  of  is .

### Example Question #93 : Numbers And Operations

What is  of  ?

Explanation:

To find a fraction of a whole number, we will multiply the fraction by the whole number.  We get

Now, we can simplify.  The 4 and the 100 can both be divided by 4.  We get

Therefore,  of  is .

### Example Question #94 : Numbers And Operations

Find  of .

Explanation:

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

Therefore,  of  is .