### All ISEE Lower Level Quantitative Resources

## Example Questions

### Example Question #1 : How To Add

Add. Reduce to the lowest terms, if necessary.

**Possible Answers:**

**Correct answer:**

When adding fractions, you must first make sure that the denominators are equal. If they are not equal, then you must make them equal by finding the LCD (lowest common denominator). In this case the LCD is 28. Now set up the new equation:

Then add the numerators to get:

Since the factors cannot be reduced any further, the correct answer is .

### Example Question #2 : How To Add

Ms. Thompson and Mr. Bloomberg decided to throw a pizza party for their class. While taking orders, they found that of the students in Ms. Thompson's class, and of the students in Mr. Bloomberg's class wanted supreme pizza. What fraction of the two classes combined wanted supreme pizza?

**Possible Answers:**

**Correct answer:**

In order to find the fraction of students who wanted supreme pizza in the two classes combined, we must add the fractions. To add fractions, however, we must first find a common denominator. Since and share the least common multiple , each fraction can be written with a denominator of .

In order to convert into a fraction with a denominator of , we multply the top and bottom by .

In order to convert into a fraction with a denominator of 24, we multiply the top and bottom by .

Now we add the two fractions, but when we add fractions with the same denominator, we only add the numerators. The denominator will remain the same.

Next we simplify by dividing both the numerator and denominator by .

### Example Question #3 : How To Add

If and are negative numbers, which of the following statements is true?

**Possible Answers:**

**Correct answer:**

If two negative numbers are multiplied, the answer is always positive (greater than ).

### Example Question #1 : How To Add

Add to .

**Possible Answers:**

**Correct answer:**

The best way to solve this is to turn both mixed numbers into improper fractions. For , multiply the denominator of the fraction by the whole number, and then add the numerator to the answer. is , and . This gives us our new numerator, , which we put over the old denominator, :

.

Using the same process with , we get , or , as our new numerator:

.

To add , the denominators need to match. Find a common multiple of and . works! In order to get to equal , multiply both the numerator, , and denominator, , by :

For the second fraction, multiply both the numerator, , and denominator, , by :

Now we can add the two fractions together:

We need to convert this improper fraction back into a mixed number. To do this, divide by to get with a remainder of . The remainder becomes the numerator of the fraction. remains the denominator. Therefore the answer is .

### Example Question #5 : How To Add

Add:

**Possible Answers:**

**Correct answer:**

In order to add fractions, each fraction must have the same denominator. We must convert the fraction into a fraction that has a denominator of 10.

We multiply the numerator and denominator by 2.

So, now we have

Then we add the numerators together: .

We keep the same denominator (10), and the answer is .

### Example Question #1 : How To Add

Felicity has 4 jackets, 5 sweaters, and 10 t-shirts. How many pieces of clothing does she own?

**Possible Answers:**

**Correct answer:**

This problem requires adding up all of the different clothing items . The answer is 19.

### Example Question #7 : How To Add

Compare the fractions and fill in the box with the appropriate sign.

**Possible Answers:**

**Correct answer:**

This problem is asking you to determine the relationship between the two fractions. Think of the fractions as pieces of a pizza. Which fraction has more pieces? does, so that is your answer. Then, you have to pick the correct inequality sign. Since is greater, the point of the inequality sign must be pointing to the lower fraction. Therefore, is the correct sign.

### Example Question #1 : How To Add

Which of the following is the sum of eight-ninths and one-third?

**Possible Answers:**

**Correct answer:**

### Example Question #1 : How To Add

Add:

**Possible Answers:**

**Correct answer:**

First, add feet and inches separately.

Since 12 inches make one foot,we divide 23 by 12:

23 inches is equal to 1 foot 11 inches. Therefore,

, and:

+

### Example Question #1 : How To Add

In five years, Allen will be twice as old as his sister Elaine, who is nine years old now. How old is Allen now?

**Possible Answers:**

**Correct answer:**

Elaine is nine years old now, so in five years, she will be years old. Allen will be twice this, or , so now, he is years old.