Operations with Complex Fractions

From the study guide

Course Outline

  1. Multiplication of Algebraic Fractions
  2. Division of Algebraic Fractions
  3. Simplifying Complex Fractions
  4. Automotive Mechanics Applications

1. Multiplication of Algebraic Fractions

★ Must-know

📐 Formula - The multiplication of algebraic fractions follows ab⋅cd=acbd\frac{a}{b}\cdot\frac{c}{d}=\frac{ac}{bd}.

  • 🔄 The multiplication procedure is:
    1. Multiply the numerators and denominators
    2. Factor the resulting expressions
    3. Cancel common factors

Further detail

  • In the example x−22x⋅3xx2−4\frac{x-2}{2x}\cdot\frac{3x}{x^2-4}, using x2−4=(x−2)(x+2)x^2-4=(x-2)(x+2) gives 32(x+2)=32x+4\frac{3}{2(x+2)}=\frac{3}{2x+4}.

Memory Hook

Multiply across, factor, cancel, simplify

2. Division of Algebraic Fractions

★ Must-know

📐 Formula - The division of algebraic fractions follows ab÷cd=adbc\frac{a}{b}\div\frac{c}{d}=\frac{ad}{bc}.

  • 🔄 The division procedure is:
    1. Multiply by the reciprocal of the divisor
    2. Factor the expressions
    3. Simplify common factors

Further detail

  • In the example x2+2x+13x3÷2x+2x2\frac{x^2+2x+1}{3x^3}\div\frac{2x+2}{x^2}, factoring and simplifying gives x+16x\frac{x+1}{6x}.

Memory Hook

Multiplication combines corresponding parts, whereas division multiplies by the reciprocal

3. Simplifying Complex Fractions

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Practice quiz preview

1. Which expression correctly represents the product of the algebraic fractions ab\frac{a}{b} and cd\frac{c}{d}?

2. What is the correct procedure for multiplying algebraic fractions?

3. Which expression correctly represents the quotient of the algebraic fractions ab\frac{a}{b} and cd\frac{c}{d}?

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Flashcard preview

What is the formula for multiplying algebraic fractions?

ab⋅cd=acbd\frac{a}{b} \cdot \frac{c}{d} = \frac{ac}{bd}

What is the first step in multiplying algebraic fractions?

Multiply the numerators and denominators.

What do you do after multiplying numerators and denominators in algebraic fractions?

Factor the resulting expressions.

What is the final step when multiplying algebraic fractions?

Cancel common factors.

What is the formula for dividing algebraic fractions?

ab÷cd=adbc\frac{a}{b}\div\frac{c}{d}=\frac{ad}{bc}

What is the first step in dividing algebraic fractions?

Multiply by the reciprocal of the divisor.

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Frequently asked questions

What does the Operations with Complex Fractions study guide cover?

It covers the core concepts of Operations with Complex Fractions, organized by topic with the key definitions, explanations and takeaways, so it's easier to learn and remember.

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How many questions are in the Operations with Complex Fractions quiz?

The practice quiz has 8 multiple-choice questions, each with an explanation. Use it to check what you know and find your gaps.

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How do I study Operations with Complex Fractions with flashcards?

There are 20 flashcards on Operations with Complex Fractions, with a question on the front and the answer on the back. Try to recall each answer before you flip, and let spaced repetition bring back the ones you miss.

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