Add and subtract rational numbers

Key Notes

Definition of Rational Numbers

• A rational number is any number that can be expressed as a fraction a/b​, where aaa and b are integers and b≠0.
• Examples: 3/4, − 5,0.75, − 2/3 ,1.25.

---

Addition of Rational Numbers

• Same Denominator: Add the numerators and keep the denominator the same.

Example: 3 / 8 + 5 / 8 = 3+5 / 8 = 8 / 8 = 1.

• Different Denominators: Find the Least Common Denominator (LCD), convert the fractions, and then add.

Example: 1/3 + 2/5​

LCD of 3 and 5 = 15

Convert: 1/3 = 5/15 , 2/5 = 6/156​

Add: 5/15 + 6/15 = 11/15​.

• Adding Decimals: Align decimal points and add normally.

---

Subtraction of Rational Numbers

• Same Denominator: Subtract the numerators and keep the denominator the same.

Example: 7/9 − 2/9 = 7−2 / 9 = 5/9​.

• Different Denominators: Find the LCD, convert the fractions, and subtract.

Example: 5 6 − 1 4​

LCD of 6 and 4 = 12

Convert: 5/6 = 10/12 , 1/4 = 3/12​

Subtract: 10/12 − 3/12 = 7/12​.

• Subtracting Decimals: Align decimal points and subtract normally.

---

Adding and Subtracting Negative Rational Numbers

• Adding a Negative Number: This is the same as subtraction.

Example: 4/5 + (−2/5) = 4/5 − 2/5 = 2/5​.

• Subtracting a Negative Number: This is the same as addition.

Example: 3/7 − (−2/7) = 3/7 + 2/7 = 5/7​.

---

Using a Number Line for Addition and Subtraction

• Start at the first number and move right for addition or left for subtraction.

---

Word Problems with Rational Numbers

• Identify key information and decide whether to add or subtract.
• Convert mixed numbers to improper fractions if necessary.

Learn with an example

Let’s practice!🖊️