Grade 7 Integers: Add/Subtract Rationals

Add and subtract rational numbers

What You'll Learn

Add positive and negative decimals
Subtract by adding the opposite

📖Same rules, new numbers

Rational numbers follow the same sign rules as integers. Same signs: add the sizes and keep the sign. Different signs: subtract the smaller size from the larger and keep the sign of the number farther from zero. Line up the decimal points before you add or subtract.

💡Subtracting a negative

Subtracting a number is the same as adding its opposite: 4.2 − (−1.5) = 4.2 + 1.5 = 5.7.

Worked examples

Real problems from the practice worksheets, solved one step at a time.

Example 1
4.9 − 14.84 = ?
1. Subtracting is adding the opposite: 4.9 − 14.84 = 4.9 + (−14.84).
2. The signs are different: subtract 14.84 − 4.9 = 9.94 and keep the sign of (−14.84), the number farther from zero.
3. 4.9 − 14.84 = −9.94
Answer: −9.94
Example 2
(−6.3) + (−0.2) = ?
1. Both numbers have the same sign: add 6.3 + 0.2 = 6.5 and keep the sign.
2. (−6.3) + (−0.2) = −6.5
Answer: −6.5
Example 3
12.72 − (−2.03) = ?
1. Subtracting is adding the opposite: 12.72 − (−2.03) = 12.72 + 2.03.
2. Both numbers have the same sign: add 12.72 + 2.03 = 14.75 and keep the sign.
3. 12.72 − (−2.03) = 14.75
Answer: 14.75