L2 · Adding and Subtracting Rational Numbers

Learning goal

“I can add and subtract any two rational numbers - fractions, mixed numbers, decimals, negatives - by choosing one shared form, and I can check the sign and size of my answer before I trust it.”

Additive inverse — the number that cancels a number to zero: the additive inverse of 3/4 is -3/4. Subtracting any number means adding its additive inverse.

Common denominator — a shared name for the size of the parts; adding fractions means counting parts of the SAME size (from Grade 6-7, now applied to signed rationals).

Difference — the result of a subtraction; for signed numbers it can be negative, and that is a real answer, not an error.

Worked example

-3/4 + 1/6. Step 1: Choose one form - fractions. The parts are different sizes (quarters, sixths), so rewrite with a common denominator: LCD 12. -3/4 = -9/12 and 1/6 = 2/12. Step 2: Count signed twelfths on the line: start at -9/12, move RIGHT 2/12 (adding a positive): land on -7/12. The bar model agrees: 9 negative twelfths with 2 cancelled by positives leaves 7 negative twelfths. Step 3: Predict-then-check: the negative addend has the bigger magnitude (9/12 > 2/12), so a negative answer near -3/4 is reasonable: -3/4 + 1/6 = -7/12. Say it plainly: Grade 7's rules did not change - common denominators for the parts, Grade 6's magnitude comparison for the sign. Rational addition is both skills at once.

Check yourself — explain it

In -3/4 + 1/6, why is the sum negative?

Paired problem — example still visible

5/8 + (-1/2) -> -1/2 = -4/8, so 5/8 - 4/8 = 1/8

Faded completion — last step is yours

"-2/5 + 3/10: in tenths, -2/5 = -4/10, so -4/10 + 3/10 = ___." -> -1/10

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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