### All ISEE Middle Level Quantitative Resources

## Example Questions

### Example Question #1 : Numbers And Operations

Which is the greater quantity?

(a) The reciprocal of

(b) The reciprocal of

**Possible Answers:**

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

(a) is greater

**Correct answer:**

(b) is greater

The reciprocal of any fraction can be found by switching numerator and denominator. Since both numbers are negative, both reciprocals will be negative.

(a) will have reciprocal

(b) will have reciprocal

We can compare these by writing them both with common denominator .

making (b) greater

### Example Question #2 : Numbers And Operations

Which is the greater quantity?

(a) The reciprocal of

(b) The reciprocal of

**Possible Answers:**

It cannot be determined from the information given

(a) is greater

(a) and (b) are equal

(b) is greater

**Correct answer:**

(b) is greater

The reciprocal of any fraction can be found by switching numerator and denominator.

(a) will have reciprocal

(b) and will have reciprocal

We can compare these by writing them both with common denominator :

making (b) greater

### Example Question #3 : Numbers And Operations

**Possible Answers:**

**Correct answer:**

When dealing with math problems that involve fractions and whole numbers or mixed numbers, you should first convert the non-fraction into a fraction:

The problem should look like this:

When dividing with fractions, you need to find the reciprocal of the second fraction before you can do anything else. In other words, flip the second number.

When you find the reciprocal of the second number, change the problem from division to multiplication. The new problem should look like this:

The answer is 6.

### Example Question #4 : Numbers And Operations

**Possible Answers:**

**Correct answer:**

When dividing fractions, you must first find the reciprocal of the second number in the operation. In other words, flip the second fraction.

When you do this, the operation also changes from division to multiplication. The problem should now look like this:

Then multiply both the numerators and denominators.

When possible, always reduce the fraction. In this case, both 2 and 8 are divisible by 2.

The result is your answer.

### Example Question #5 : Numbers And Operations

**Possible Answers:**

**Correct answer:**

When dividing fractions, you must first find the reciprocal of the second fraction. In other words, flip the second fraction.

When you do this, the operation also changes from division to multiplication. The problem should now look like this:

Multiply the numerators and denominators. The result is your answer.

### Example Question #6 : Numbers And Operations

**Possible Answers:**

**Correct answer:**

When dealing with fractions and whole numbers, first convert the whole number to a fraction. This is easily done by putting the whole number over 1.

When dividing fractions, you must first find the reciprocal of the second fraction in the operation. In other words, flip the second fraction.

When you do this, the operation changes from division to multiplication. The problem should now look like this:

Solve the multiplication by multiplying the numerators and the denominators.

Since the result is , it reduces to 16 as any fraction with a denominator of 1 is equal to the value of its numerator.

### Example Question #7 : Numbers And Operations

If Candy has a cup of trail mix and she wants to divide it evenly among herself and seven of her friends, how much does each person get?

**Possible Answers:**

**Correct answer:**

Candy has cups of trail mix. If she divides it amoung herself and seven of her friends, she is dividing it by . In order to solve this problem, we simply find the reciprocal of the second fraction and multiply.

To find the reciprical of a fraction, we switch the numerator and denominator.

becomes .

Now we multiply by .

Each person gets of the trail mix.

### Example Question #8 : Numbers And Operations

is a positive integer.

Which is the greater quantity?

(a)

(b)

**Possible Answers:**

(a) is the greater quantity

(b) is the greater quantity

(a) and (b) are equal

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

**Correct answer:**

(a) is the greater quantity

Division by a fraction is equivalent to multiplication by its reciprocal, so

can be rewritten as

, and is positive, so, by the multiplication property of inequality,

or

.

### Example Question #9 : Numbers And Operations

is the reciprocal of . Which of the following is the reciprocal of in terms of ?

**Possible Answers:**

**Correct answer:**

If is the reciprocal of , then

The reciprocal of is .

### Example Question #10 : Numbers And Operations

The reciprocal of is . Which is the greater quantity?

(a) The reciprocal of

(b)

**Possible Answers:**

(a) and (b) are equal

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

(a) is the greater quantity

(b) is the greater quantity

**Correct answer:**

(b) is the greater quantity

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

The reciprocal of is , which is less than 0.