Algebraic Fractions Term 3 Flashcards

Questions and Answers

How do you simplify algebraic fractions?

Find the highest common factor of both the denominator and numerator, then divide both parts of the fraction by that number.

What should you do if there are no obvious common factors when simplifying a fraction?

Factorise either the denominator, the numerator, or both to find the common factors.

How do you add or subtract algebraic fractions?

You need to have a common denominator between both fractions before you can add or subtract the numerators.

How do you find a common denominator of two fractions?

Multiply the fractions by each other's denominators. Signup and view all the answers

How do you multiply algebraic fractions?

Multiply the numerators by each other and multiply the denominators by each other. Then simplify if necessary. Signup and view all the answers

How do you divide algebraic fractions?

Turn the second fraction upside down and then multiply the two fractions. Signup and view all the answers

How do you solve equations with fractions of x on both sides?

Multiply both sides of the equation by the lowest common multiple of both denominators, then solve the equation as normal. Signup and view all the answers

What is the first step to solve equations where the unknown is in both the numerator and denominator?

Turn the answer of the equation into a fraction by dividing it by 1, then cross-multiply both sides. Signup and view all the answers

What should you do in Step 2 when solving equations with the unknown in both numerator and denominator?

Get the variable onto one side using inverse operations, isolate the variable, divide both sides by the number of x's, and simplify the fraction. Signup and view all the answers

How do you solve algebraic fractional equations?

Add, multiply, subtract, or divide the algebraic fractions, then multiply the answer by the denominator and use inverse operations to find the variable. Signup and view all the answers

Study Notes

Simplifying Algebraic Fractions

Identify the highest common factor (HCF) of the numerator and denominator.
Divide both the numerator and denominator by the HCF to simplify the fraction.

No Obvious Common Factors

If no apparent common factors exist, factorize the denominator, numerator, or both to identify common factors.

Adding and Subtracting Algebraic Fractions

Establish a common denominator before performing addition or subtraction on the fractions.

Finding a Common Denominator

The common denominator can be found by multiplying the denominators of the involved fractions.

Multiplying Algebraic Fractions

Multiply the numerators together and the denominators together.
Simplify the resulting fraction if necessary.

Dividing Algebraic Fractions

Invert (turn upside down) the second fraction and then multiply the two fractions together.

Solving Equations with Fractions

Multiply both sides of the equation by the lowest common multiple (LCM) of the denominators present in the fractions.
After multiplying, solve the equation using standard techniques.

Solving Equations with Unknowns in Both Numerator and Denominator: Step 1

Convert the answer of the equation into a fraction format (e.g., by dividing by 1).
Cross-multiply to eliminate the fractions from the equation.

Solving Equations with Unknowns in Both Numerator and Denominator: Step 2

Use inverse operations to isolate the variable on one side of the equation.
Leave the non-variable side as a fraction and simplify it as needed.

Solving Algebraic Fractional Equations

Perform the necessary operations (addition, multiplication, subtraction, division) on the algebraic fractions.
Multiply the result by the denominator and apply inverse operations to isolate and find the variable.

Description

Test your understanding of simplifying algebraic fractions with these flashcards. Each card covers essential concepts, including finding common factors and factorization techniques. Perfect for Term 3 Maths review!