ACT Math Complex Fractions: Simplify Without Confusion Using One Clear Method

A complex fraction is a fraction with fractions in the numerator and/or denominator. Example: (1/2)/(3/4). Step 1: Rewrite the main division bar as a division operation. (1/2)÷(3/4). Step 2: Apply division rule: multiply by the reciprocal. (1/2)×(4/3)=4/6=2/3. This two-step method converts any complex fraction into a simple multiplication problem, eliminating confusion.

Larger example: (1+(1/2))/(2-(1/3)). Simplify numerator: 1+(1/2)=3/2. Simplify denominator: 2-(1/3)=5/3. Now: (3/2)/(5/3)=(3/2)×(3/5)=9/10. Break complex fractions into steps.

Mistake 1: Forgetting to flip the denominator's fraction when multiplying by reciprocal. (1/2)÷(3/4) becomes (1/2)×(4/3), not (1/2)×(3/4). Mistake 2: Not simplifying the numerator and denominator before dividing. (1+(1/2))/(2-(1/3)) must be simplified first to (3/2)/(5/3). Mistake 3: Losing track of operations when complex fractions contain multiple levels. Always work from innermost operations outward, step by step.

Create a reference card showing the two-step method and one worked example. Reference it daily until the process becomes automatic.

Problem 1: (1/2)/(3/4)=(1/2)×(4/3)=4/6=2/3. Problem 2: (2/3)/(4/5)=(2/3)×(5/4)=10/12=5/6. Problem 3: (1+(1/3))/(2)=(4/3)/2=(4/3)×(1/2)=4/6=2/3. Problem 4: (1/2)/(1-(1/4))=(1/2)/(3/4)=(1/2)×(4/3)=4/6=2/3. Problem 5: ((1/2)+(1/3))/((1/4)+(1/5)). Numerator: 1/2+1/3=5/6. Denominator: 1/4+1/5=9/20. (5/6)/(9/20)=(5/6)×(20/9)=100/54=50/27. Problem 6: (1-1/2)/(1+1/2)=(1/2)/(3/2)=(1/2)×(2/3)=2/6=1/3. Simplify each, showing all steps clearly.

Find six complex fraction problems from a practice test. For each, apply the two-step method, simplify at each stage, and verify your final answer. By the sixth problem, complex fractions will feel manageable.

Complex fraction questions appear on some ACT Math tests, usually in questions 45-60. These problems test fraction manipulation skills. Students who master the two-step simplification method pick up 1 point on the math section because the method is mechanical and reliable.

Drill complex fractions daily this week. Each day, simplify five complex fractions. By test day, you should simplify any complex fraction within 90 seconds by following the two-step method.