# ISEE Middle Level Quantitative : How to add fractions

## Example Questions

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

Express the sum as a fraction in lowest terms:

Explanation:

Rewrite the fractions in terms of their least common denominator, 12.

Add, then rewrite as a mixed fraction:

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

Explanation:

In order to add fractions we must find a common denominator.  Since is a multiple of both and , we must multiply the numerator and denominator of each fraction by a number to get a denomintor of

Since times is , we can multiply the numerator and denominator of the first fraction by .

Since times is , we can multiply the numerator and demonimator of the second fraction by .

Now we add together the numerators.

### Example Question #3 : How To Add Fractions

If a rectangle has a length of and a width of what is the perimeter of the rectangle, in simplest form?

Explanation:

In order to find the perimeter of a rectangle, you add together all the sides.  In this particular case, however, you must first find a common denominator for all of the fractions.  Luckily, is a multiple of , so we can multiply the numerator and denominator of  by to get a denominator of .

Now we simply add all four sides.

Since  can be reduced by dividing the numerator and denominator by , we must simplify.

The perimeter of the rectangle is .

### Example Question #4 : How To Add Fractions

Which is the greater quantity?

(a)

(b)

(a) is greater

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

(a) and (b) are equal

Explanation:

Add both sides of the two equations:

### Example Question #5 : How To Add Fractions

Which is the greater quantity?

(a)

(b)

(a) is greater

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

(b) is greater

Explanation:

(a)

(b)

### Example Question #6 : How To Add Fractions

Column A                             Column B

There is no way to determine the relationship between the quantities in the columns.

The quantity in Column A is greater.

The quantity in Column B is greater.

The quantities in each column are equal.

The quantity in Column B is greater.

Explanation:

First, you must add the fractions in each column. When adding fractions, find the common denominator. The common denominator for Column A is 10. Then, change the numerators to reflect changing the denominators to give you . Combie the numerators to give you Then, add the fractions in Column B. The common denominator for those fractions is 72. Therefore, you get . Combine the numerators to get . Compare those two fractions. Think of them as slices of pizza. There would be way more of Column B. Therefore, it is greater. Also, a little to trick to comparing fractions is cross-multiply. The side that has the biggest product is the greatest.

### Example Question #7 : How To Add Fractions

Which is the greater quantity?

(A)

(B)

(B) is greater

(A) and (B) are equal

It is impossible to determine which is greater from the information given

(A) is greater

(A) is greater

Explanation:

and , so

, the decimal equivalent of (A).

, the value of (B).

(A) is the greater.

### Example Question #8 : How To Add Fractions

Which is the greater quantity?

(A)

(B)

(A) and (B) are equal

(B) is greater

It is impossible to determine which is greater from the information given

(A) is greater

(A) and (B) are equal

Explanation:

The two quantities are equal.

### Example Question #22 : Numbers And Operations

Explanation:

When adding fractions with different denominators, you must first find a common denominator. Some multiples of 2 and 5 are:

2: 2, 4, 6, 8, 10...

5: 5, 10, 15, 20...

The first multiple 2 and 5 have in common is 10. Change each fraction accordingly so that the denominator of each is 10.

The problem now looks like this:

### Example Question #9 : How To Add Fractions

Explanation:

When adding fractions with different denominators, first change the fractions so that the denominators are equal. To do this, find the least common multiple of 5 and 10. Some multiples of 5 and 10 are:

5: 5, 10, 15, 20...

10: 10, 20, 30, 40...

Since the first multiple shared by 5 and 10 is 10, change the fractions so that their denominators equal 10.  already has a denominator of 10, so there is no need to change it.

The problem now looks like this:

Add the fractions by finding the sum of the numerators.

When possible, always reduce your fraction. In this case, both 5 and 10 are divisible by 5.