### All ISEE Middle Level Quantitative Resources

## Example Questions

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

Express the sum as a fraction in lowest terms:

**Possible Answers:**

**Correct answer:**

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

Add, then rewrite as a mixed fraction:

Add the integers:

Now add the sums:

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

**Possible Answers:**

**Correct answer:**

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.

The answer is .

### Example Question #1 : 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?

**Possible Answers:**

**Correct answer:**

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 #1 : How To Add Fractions

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(b) is greater

It is impossible to tell from the information given

(a) is greater

(a) and (b) are equal

**Correct answer:**

(a) and (b) are equal

Add both sides of the two equations:

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

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

It is impossible to tell from the information given

(a) is greater

(a) and (b) are equal

(b) is greater

**Correct answer:**

(b) is greater

(a)

(b)

### Example Question #11 : Numbers And Operations

Column A Column B

**Possible Answers:**

The quantities in each column are equal.

The quantity in Column B is greater.

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

The quantity in Column A is greater.

**Correct answer:**

The quantity in Column B is greater.

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 #1 : How To Add Fractions

Which is the greater quantity?

(A)

(B)

**Possible Answers:**

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

(B) is greater

(A) and (B) are equal

(A) is greater

**Correct answer:**

(A) is greater

and , so

, the decimal equivalent of (A).

, the value of (B).

(A) is the greater.

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

Which is the greater quantity?

(A)

(B)

**Possible Answers:**

(A) and (B) are equal

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

(B) is greater

(A) is greater

**Correct answer:**

(A) and (B) are equal

The two quantities are equal.

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

**Possible Answers:**

**Correct answer:**

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:

Add the numerators once the denominators are equal. The result is your answer.

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

**Possible Answers:**

**Correct answer:**

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.

The result is your answer.

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