L3 · Multiplying Integers and Rational Numbers

Learning goal

“I can multiply any two rational numbers - integers, decimals, fractions - predict the sign of the product before computing, and justify the sign rules with patterns and repeated addition instead of just memorizing them.”

Product — the result of a multiplication.

Factor — one of the numbers being multiplied: in -2.5 x 3/5, the factors are -2.5 and 3/5.

Magnitude — a number's distance from zero, ignoring sign (review from Grade 7). Multiplication splits into two jobs: multiply the magnitudes, then settle the sign.

Worked example

Build the pattern before using it. 3 x (-4) is repeated addition: (-4) + (-4) + (-4) = -12. So a positive x a negative is negative: 3 x (-4) = -12. On the line: three jumps of -4 land at -12. Now run the multiplier down for (-3) x n and watch the products climb by 3: (-3) x 2 = -6, (-3) x 1 = -3, (-3) x 0 = 0, (-3) x (-1) = 3, (-3) x (-2) = 6. Each step the product grows by +3, so the pattern FORCES (-3) x (-4) = 12 - a negative x a negative is positive, because anything else would break the pattern. Summary (now earned, not memorized): same signs -> positive product; different signs -> negative product; and the magnitude is always just the product of the magnitudes.

Check yourself — explain it

Why must (-3) x (-4) be positive?

Paired problem — example still visible

-6 x 7 -> different signs: -42

Faded completion — last step is yours

"-9 x (-5): same signs, so the sign is ___; magnitudes 9 x 5 = 45, so the product is ___." -> positive; 45

Ready to practise?

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

Start practice →Take the unit quiz