ACT Math: Cross Multiplication Solves Proportions in Seconds

Cross multiplication is a shortcut for solving proportions and rational equations. If a/b=c/d, then ad=bc. Instead of finding a common denominator or isolating variables traditionally, cross multiply and solve. Example: 3/x=12/20. Cross multiply: 3(20)=12(x) → 60=12x → x=5. This method works because multiplying both sides by bd (the product of denominators) clears fractions instantly. It is faster than traditional algebra on time-pressured tests.

Use it whenever you see fractions set equal to each other, or when a variable is in a denominator. This appears in 2-3 ACT Math questions per section.

Proportion 1: 5/8=x/32. Cross multiply: 5(32)=8(x) → 160=8x → x=20. Proportion 2: 2/(x+1)=6/15. Cross multiply: 2(15)=6(x+1) → 30=6x+6 → x=4. Proportion 3: (x-2)/3=10/15. Cross multiply: (x-2)(15)=3(10) → 15x-30=30 → x=4. Speed drill: complete three proportions daily until you solve each in under 30 seconds.

Verify your answer by substituting back into the original proportion to confirm equality.

Trap 1: Using cross multiplication on equations that are NOT proportions. Example: 3/x+2=5 is not a proportion (no fraction on right side before the equal sign). Don't cross multiply; instead isolate: 3/x=3 → x=1. Trap 2: Forgetting to distribute after cross multiplying. If you get 3(x+2)=5, expand: 3x+6=5 → 3x=-1 → x=-1/3. Trap 3: Confusing cross multiplication with finding common denominators. Both work, but cross multiplication is faster for simple proportions. Use cross multiplication only when both sides are fractions.

Check your work: if x=5 in 3/x=12/20, then 3/5=0.6 and 12/20=0.6. ✓ Equal.

Cross multiplication saves 30-60 seconds per question by eliminating the need to find common denominators or multiply entire equations by LCD. Over a full math section, that time saved adds up. Students who know cross multiplication answer proportion questions with confidence and speed; others waste time or solve incorrectly.

Drill this for two days before the test. On test day, cross multiplication becomes your fraction-solving weapon.