# ISEE Middle Level Math : How to find the part from the whole

## Example Questions

### Example Question #71 : Numbers And Operations

You bought  pieces of fruit including  apples,  oranges, and  pineapples. How many pineapples did you buy?

Explanation:

You know that you bought  fruit and you have three kinds; apples, oranges, and pineapples.

If  are apples and  are oranges, the rest would be pineapples.

So you must subtract those values from the total and that will be the number of pineapples.

so you bought  pineapples.

### Example Question #31 : How To Find The Part From The Whole

You and you friends make  doing some yard work.  If you have four friends and you need to split the revenue evenly, how much do you make?

Explanation:

Since there are five of people to split it (you and four friends) you must divide the  by  which is,

.

### Example Question #71 : Numbers And Operations

Find  of .

Explanation:

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

Therefore,  of  is .

### Example Question #32 : How To Find The Part From The Whole

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 solve.

We can simplify this, and we get

Therefore,  of  is .

### Example Question #72 : Numbers And Operations

Which of the following numbers yields a remainder of 7 when divided by 9?

Explanation:

We can test each of the numbers in tun by dividing each by 9:

106 is the correct choice.

### Example Question #32 : How To Find The Part From The Whole

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 multiply.

### Example Question #78 : Numbers And Operations

Explanation:

To add numbers in modulo 13 arithmetic, we can add, divide by 13 and note the remainder:

The remainder is 4, so

modulo 13.

### Example Question #79 : Numbers And Operations

Subtract in modulo 13 arithmetic:

Explanation:

To subtract two numbers in modulo 13 arithmetic, we can simply subtract first:

Since the number is negative, add 13:

in modulo 13 arithmetic.

### 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: