# ISEE Middle Level Math : How to divide fractions

## Example Questions

### Example Question #31 : How To Divide Fractions

Simplify the following expression:

Explanation:

Simplify the following expression:

To divide fractions, we need to multiply by the reciprocal. This means that we flip the second fraction and then multiply:

Before multiplying, simplify the two fractions by factoring out a seven from the 42 and the 35. We can do this, because they are on opposite sides of the fraction.

So we get an answer of:

### Example Question #32 : How To Divide Fractions

Simplify the following:

Explanation:

To divide fractions, we will take the first fraction and multiply it by the reciprocal of the second fraction.

(Reciprocal simply means we will take the fraction and flip it.  The numerator will become the denominator and the denominator will become the numerator.)

So,

will become

Now, we multiply.

Now, we can simplify.  We can divide the numerator and the denominator by 3.  We get

### Example Question #33 : How To Divide Fractions

The reciprocal of  is . What is the reciprocal of  ?

Explanation:

The reciprocal of  is , so  is the reciprocal of , or

The reciprocal of this is 3.

### Example Question #34 : How To Divide Fractions

Divide the following:

Explanation:

To divide fractions, we will simply turn it into multiplication.  We will leave the first fraction alone.  We will take the second fraction, and write the reciprocal.  Then, we will multiply the two fractions together.  We have

we will leave  alone.  We will take  and write the reciprocal (flip the fraction, the numerator and denominator switch places).  The reciprocal is .  Now, we multiply.

### Example Question #401 : Fractions

The above parallelogram has been divided into triangles of equal size and shape. The total area of the shaded region is 2,400. Calculate the area of the entire parallelogram.

Explanation:

20 of 24 triangles have been shaded in; this is  of the parallelogram. I we let  stand for the total area of the parallelogram, then  is equal to the shaded area, or 2,400, so we solve:

### Example Question #402 : Fractions

Solve the following:

Explanation:

When dividing fractions, we will leave the first fraction as it is.  We will then take the reciprocal of the second fraction.  The reciprocal of a fraction is when the numerator becomes the denominator and the denominator becomes the numerator.  In other words, we flip the fraction.  Once we find the reciprocal, we will then multiply the fractions together.  That's right, we will NOT actually be dividing any numbers.

So,

we must take leave the first fraction alone.  For the second fraction, we will take the reciprocal.  We must first write the number in fraction form.  We get

Now, we will take the reciprocal and multiply.

We will multiply straight across.

### Example Question #403 : Fractions

Divide the following:

Explanation:

To divide fractions, we will follow these steps:

1. Leave the first fraction alone.
2. Change the division sign to a multiplication sign.
3. Write the reciprocal of the second fraction (i.e. the numerator becomes the denominator and the denominator becomes the numerator).
4. Multiply.

So to solve,

we will follow the steps.

1. Leave the first fraction alone.

2. Change the division sign to a multiplication sign.

3. Write the reciprocal of the second fraction.

4. Multiply

### Example Question #404 : Fractions

Divide the following:

Explanation:

To divide fractions, we will use the following steps:

1. Leave the first fraction alone
2. Change the division sign to a multiplication sign.
3. Write the reciprocal of the second fraction.a
4. Multiply.

So, let's follow the steps.

1.  Leave the first fraction alone.  So, we get

2.  Change the division sign to a multiplication sign.

3.  Write the reciprocal of the second fraction.  To do this, we will move the numerator to the denominator, and move the denominator to the numerator.  In other words, we will flip the fraction.

4.  Multiply.  We will multiply straight across.

### Example Question #405 : Fractions

Solve the following:

Explanation:

To divide, we will follow these steps:

1. Write any whole number as a fraction.
2. Keep the first fraction as is.
3. Change the division sign to a multiplication sign.
4. Replace the second fraction with it's reciprocal.
5. Multiply.

Now, we will follow those steps for the problem

1. We will write all whole numbers as fractions.  So the number 6 can be written as a fraction.  We know that any whole number can be written over 1.  So,

2. Now, we will keep the first fraction the way it is.  We get

3. Now, we will change the division sign to a multiplication sign. We get

4. Now, we will replace the second fraction with it's reciprocal.  To do that, the numerator will become the denominator, and the denominator will become the numerator.  In other words, we will flip the fraction.  We get

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

Therefore,

### Example Question #406 : Fractions

Divide the following:

Explanation:

To divide fractions, use the following steps:

1. Leave the first fraction alone.
2. Change the division sign to a multiplication sign.
3. Replace the second fraction with it's reciprocal.
4. Multiply.

So, given the problem

we will follow the steps.

1. Leave the first fraction alone.

2. Change the division sign to a multiplication sign.

3. Replace the second fraction with it's reciprocal.  To write the reciprocal of a fraction, the numerator will become the denominator, and the denominator will become the numerator.  In other words, we will flip the fraction.

4. Multiply. To multiply, we will multiply straight across.  We get