Adding and Subtracting Rational Numbers

Fractions, decimals, negatives — all at once now.

🧱 See It

"Rational numbers" just means every number type learned so far, combined: whole numbers, decimals, fractions, and negatives. Adding or subtracting them means using two rules already known, together: the same-sign/different-sign rule from integers, and the common-denominator (or lined-up decimal point) rule from fractions.

✏️ Draw It

Before combining −2.5 + 1/4, convert everything to the SAME form — here, turn the fraction into a decimal:

Before (mixed forms)After (same form)
−2.5 + 1/4−2.5 + 0.25

1/4 converts to 0.25 — now both numbers are decimals and can be combined.

🔢 Write It

Step 1 — convert everything to the same form (all decimals or all fractions):

−2.5 + 1/4 = −2.5 + 0.25

Step 2 — apply the integer sign rule: different signs, so subtract the smaller magnitude from the larger, and keep the sign of the larger:

−2.5 + 0.25 = −2.25

The number type never changes the sign logic. Convert first, THEN apply the exact same rules used for integers.

💡 Worked Examples

Example 1: −2.5 + 1/4

  1. Convert to the same form: 1/4 = 0.25
  2. Now it reads: −2.5 + 0.25
  3. Different signs → subtract magnitudes: 2.5 − 0.25 = 2.25, keep the sign of the larger magnitude (negative)
  4. Answer: −2.25

Example 2: −3/4 − (−1/2)

  1. Two signs together: subtracting a negative is the same as adding (from Level 2): −3/4 − (−1/2) = −3/4 + 1/2
  2. Convert to a common denominator: LCM(4, 2) = 4, so 1/2 = 2/4
  3. Now it reads: −3/4 + 2/4
  4. Different signs → subtract magnitudes: 3/4 − 2/4 = 1/4, keep the sign of the larger magnitude (negative)
  5. Answer: −1/4

🧠 Quick Reference

Convert to the SAME form first (all fractions or all decimals). THEN apply the same-sign/different-sign rules exactly like integers — the type of number never changes the sign logic.
👪 For Parents & Tutors

BC Curriculum (Level 4 / Grade 9, Number): "Operations with rational numbers: addition, subtraction, multiplication, division, and order of operations."

Watch for: trying to combine a fraction and a decimal without converting to a common form first (e.g. attempting −2.5 + 1/4 directly). Always convert to ONE consistent form — whichever is easier for the specific numbers involved — before applying any sign rule.

Why this isn't new: this page is a direct synthesis of two things already mastered — Level 2's integer sign rules and Level 3's fraction common-denominator rule. There is nothing conceptually new here, just the two combined in the same problem.