# ISEE Middle Level Math : Numbers and Operations

## Example Questions

### Example Question #81 : Numbers And Operations

Find  of .

Explanation:

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

So,

of

can be written as

Now, we can write  so it is in fraction form. We get

Now, before we multiply, we can make things easier and simplify.  We can simplify the  and .  The number  can go into both numbers.  We get

Now, we can multiply straight across.

Therefore,  of  is .

### Example Question #82 : Numbers And Operations

Multiply in modulo 13 arithmetic:

Explanation:

To multiply two numbers in modulo 13 arithmetic, find the product, divide by 13, and note the remainder.

The remainder is 11, so

modulo 13.

### Example Question #83 : 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,

of

we can write it as

To multiply, we will write  in fraction form.  We get

Now, we multiply straight across.

### Example Question #84 : 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,

of

can be written as

Now, to multiply, we will write 91 in fraction form.  We get

Now, we can multiply straight across.  We get

Therefore,  of  is .

### Example Question #85 : 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,

of

can be written as

To multiply we will write 24 as a fraction.  We get

To make multiplication easier, we will simplify before we multiply.  We can simplify the 3 and the 24.  We get

Now, we can multiply straight across.

Therefore,  of  is .

### Example Question #86 : 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,

of

can be written as

Now, to multiply, we need to write  as a fraction.  We know that any whole number can be written as the number over 1.  So, we get

Now, we can simplify before we multiply to make things easier.  The 4 and 36 can simplify.  Each number can be divided by 4.  We get

Now, we can multiply straight across.  We get

Therefore,   of  is .

### Example Question #87 : 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, the problem

of

can be re-written as

To multiply, we will write 36 as a fraction.  We know that a whole number can be written as the number over 1.  So,

Now, we will multiply straight across.  We get

Therefore,  of  is .

### Example Question #88 : 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,

of

can be written as

Now, we will write 21 as a fraction.  We know that whole numbers can be written as a fraction over 1.  So,

Now, we can multiply.  We get

Therefore,  of  is .

### Example Question #89 : Numbers And Operations

What is a third of ?

Explanation:

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

So, given the problem

third of

we will first write third as a fraction.  We know that third is the same as . So, we can write

of

Now, we can multiply.

To multiply, we will write 33 as a fraction.  We know that we can write a whole number as a fraction over 1.  So, we get

Now, we multiply straight across.  We get

Therefore, a third of  is .

### Example Question #90 : Numbers And Operations

Find three-quarters of 24.

Explanation:

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

three-quarters of 24

we will first write three-quarters as a fraction.  We know that three-quarters can be written as .  So, we can re-write the problem as

of

Now, we will multiply them together.  We get

To multiply, we will write 24 as a fraction.  To write a whole number as a fraction, we can write it over 1.  So, we get

Now, before we multiply, we can simplify to make things easier.  The 4 in the denominator of the first fraction and the 24 in the numerator of the second fraction can both be divided by 4.  So, we get

Now, we can multiply.  We will multiply straight across.  We get

Therefore, three-quarters of 24 is 18.