Ch 5: Rational Numbers

Question 1

Adding Rational Numbers

Answer 1

Rational numbers are all the numbers that can be expressed as the ratio of two integers. Rational numbers include fractions, decimals, and integers. The form p/q, where p and q are integers, but q is not zero, is used to describe rational numbers. Because p and q are integers, rational numbers may be positive, negative, or zero.

The rules for adding rational numbers are like the rules for adding integers.

• To add two or more numbers that have the same sign, add their absolute values. The sum has the same sign as the addends.
• To add two numbers that have different signs, subtract their absolute values. The sum has the sign of the number with the greater absolute value.

To add rational numbers that have the same sign, add the absolute values. The sum has the same sign as the addends.
To add two rational numbers that have different signs, subtract the absolute values. The sum has the sign of the addend with the greater absolute value.

Question 2

Subtracting Rational Numbers

Answer 2

To subtract a number, you can add its opposite.
Subtract 30.5 from -150:
-150 - 30.5 = -150 + (-30.5) = -180.5
“To subtract a rational number, add its opposite.”

Question 3

Multiplying Rational Numbers

Answer 3

To multiply rational numbers, multiply as you did with positive numbers. But remember to follow the rules for multiplying signed numbers.

For example…
1/2 * 3/5 = 3/10 and 1/2 - (-3/5) = - 3/10
The signs of the factors are different, so the product is negative.

A negative fraction such as - 1/12 can be written three ways:
- 1/12 = -1/12 = 1/-12
for calculations, it is often best to use the form -1/12

Rules for Multiplication

• To multiply two rational numbers that have the same sign, multiply the absolute values. The product is positive.
• To multiply two rational numbers that have different signs, multiply the absolute values. The product is negative.
• The product of any number and zero is zero.

Question 4

Dividing Rational Numbers

Answer 4

To divide rational numbers, divide as you did with positive numbers, but remember to follow the rules for dividing signed numbers.

For example…
10 / 2.5 = 4 and 10 / (-2.5) = -4
If the numbers have different signs, the quotient is negative.

Rules for Division

• To divide rational numbers that have the same sign, divide the absolute values. The quotient is positive.
• To divide rational numbers that have different signs, divide the absolute values. The quotient is negative.
• Zero divided by any nonzero number is zero; division by zero is undefined.