# SSAT Middle Level Math : How to add fractions

## Example Questions

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### Example Question #1 : How To Add Fractions

Explanation:

I think the easiest way to do this problem is to make a common denominator.  4 is the smallest common denominator.

is equivalent to .

When you add  and  you get .

reduces to and is equivalent to .

### Example Question #1 : Negative Numbers

Evaluate:

Explanation:

The sum of two numbers of unlike sign is the difference of their absolute values, with the sign of the "dominant" number (the positive number here) affixed:

Subtract vertically by aligning the decimal points, making sure you append the 3.2 with a placeholder zero:

This is the correct choice.

### Example Question #2 : How To Add Fractions

Evaluate:

Explanation:

Rewrite these numbers as improper fractions.

Now evaluate:

, so

### Example Question #181 : Fractions

Explanation:

Rewrite using the lowest comon denominator. Since :

### Example Question #182 : Fractions

Explanation:

When adding fractions, both denominators must be the same. A quick and easy way to do this is to multiply the numerator and the denominator of each fraction by the other fraction's denominator:

and

The  is multiplied by 6 on both ends because the denominator of  is 6. Likewise,  is multiplied by 3 on both ends because the denominator of  is 3. The problem should now look like this:

Remember to reduce. 15 and 18 are both divisible by 3.

### Example Question #1 : How To Add Fractions

Add the following fractions and simplify, if possible.

Explanation:

In order to add fractions with different denominators, first find a common denominator of the fractions by finding the least common multiple. The least common multiple of these denominators is:

and .

Because  already has the required denominator, nothing needs to be done to  .

Since the  in  needs to be multiplied by  in order to get  as the deonominator, multiply the numberator of    by .

The "new" addition problem is now: .

The answer to this question is therefore  .

Because  and  do not have a common factor, the answer cannot be simplified.

### Example Question #2 : How To Add Fractions

Explanation:

To add two fractions, first find the common denominator. We can convert  to , which reduces to .

### Example Question #2 : How To Add Fractions

Find .

Explanation:

To add two fractions, first find the common denominator, then add the two numerators.

### Example Question #3 : Commutative Property Of Addition

Which of the following statements demonstrates the commutative property of addition?

None of the examples in the other responses demonstrates the commutative property of addition.

Explanation:

The commutative property of addition states that two numbers can be added in either order to obtain the same sum. Of the given responses, only

demonstrates this property, so it is the correct choice.

### Example Question #6 : Associative Property Of Addition

Which of the following statements demonstrates the associative property of addition?