Lesson 3: Subtracting Rational Numbers

Property

To subtract rational numbers with the same denominator, subtract the numerators and keep the common denominator: $\frac{a}{b} - \frac{c}{b} = \frac{a-c}{b}$.

Examples

Property

To subtract decimal numbers, align the decimal points vertically and subtract as you would with whole numbers. The decimal point in the answer goes directly below the aligned decimal points. If the numbers have different numbers of decimal places, add zeros to the right of the shorter decimal to make them equal in length.

Examples

Property

Understand subtraction of rational numbers as adding the additive inverse, $p - q = p + (-q)$. Show that the distance between two rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts. This means $a - b$ can be written as $a + (-b)$ and $a - (-b)$ can be written as $a + b$.

Examples

• The expression $15 - 8$ can be rewritten as adding the opposite: $15 + (-8)$, which equals 7.
• To calculate $11 - (-5)$, we change it to adding the opposite of $-5$, which is $11 + 5$, equaling 16.
• The problem $-10 - 4$ is equivalent to solving $-10 + (-4)$. The result is $-14$.

Explanation

Subtracting any number gives the same result as adding its opposite. This powerful rule transforms every subtraction problem into an addition problem, making calculations with negative numbers much simpler to solve.