Complex fractions

Make fractions within fractions easier to read and simplify. This precalculus algebra set develops two reliable methods: combine each part into one fraction before dividing, or multiply the entire numerator and denominator by a common denominator.

Practice progresses from numerical complex fractions to algebraic forms with sums, two variables and hidden domain restrictions. You will identify the main fraction bar, distinguish a reciprocal of a sum from a sum of reciprocals, and check restrictions arising from both inner denominators and the overall denominator. A work-rate problem reinforces the meaning of division through units.

Getting ready

Review fraction division, least common denominators, factoring and original restrictions. Write a clear main numerator and denominator on scratch paper before carrying out any cancellation.

Reviewing your work

Detailed explanations compare methods and multiply results back when helpful. Single-select and select-all questions test reasoning as well as calculation. This set stays with algebraic expressions and basic rates; interpreting difference quotients and functions belongs to later topics.

Complex fractions