**How To Simplify Fractions Algebra** – Objective Simplify algebraic expressions involving algebraic fractions Grade 6 Prior knowledge Fraction operations (numbers) Algebra manipulation (including factoring squares) Duration If algebraic skills are strong (expansion and factoring squares), content can be taught in 60 minutes with hands-on time. Resources Print Slides: 4, 6, 8, 10, 12 Learning Progression Tools What will students learn? How do students learn? (Works and Differentiation) Review basic algebra skills needed to solve quadratics (expanding brackets and simple factoring) Have students print slides 4 and 6. Work independently to solve (repeat previous knowledge of the content). All teachers are confident in these two basic skills. Students can mark their work using slides 5 and 7. match the eight factors with the expressions. This can be used to emphasize the role of the negative sign (note the expression x2 ± 3x – 18). Printout of slide 8 for students. Various Practices in Quadratic Factoring. Print 10 slides for students. 20 Simplifying Fractions by Finding Common Factors Give students slide 12. Using slide 13 shows how to find the common factor in each term and then simplify the quotient for each term to the lowest level. Students copy the example and write notes on the method in the white box. 5 Simplifying Fractions by Factoring Slide 14 shows how to simplify factoring expressions and then find common factors to cancel. Students copy the example and write notes on the method in the white box. Students complete the questions on slide 12 independently. Check the answers on slide 15. Reflection questions on slide 16. SAMS does not have OCR exam questions that test these skills separately. Further learning is needed to add/subtract algebraic fractions and solve equations involving algebraic fractions before considering the relevant exam questions. Next steps Adding and subtracting algebraic fractions Solving equations involving algebraic fractions PLC Assessment/Modified Specification/Target 6/Algebra/Algebraic Fractions

5(y + 4t – 2) x(x2 + 2) (t + 2) (t + 4) (x – 5) (x + 3) (2x + 1) (x – 4) (2t – 3) ( t + 5) Multiplication – AQA Basic Student Sheet 1

## How To Simplify Fractions Algebra

X2 + 6x + 8 x2 + x − 20 ( x + 6 ) ( x + 3 ) ( x + 4 ) ( x − 4 ) ( x − 6 ) ( x + 2 ) ( x − 3 ) ( ) factorize the expression x + 5 ) x2 + 3x − 18 x2 − 3x − 18 Student sheet 3

### How To Divide Fractional Algebraic Expressions: 8 Steps

Pair the factors with the expression x2 + 6x + 8 x2 + x − 20 ( x + 6 ) ( x + 3 )( x + 4 )( x − 4 )( x − 6 )( x + 2 )( x − 3 ) ( x + 5 ) x2 + 3x − 18 x2 − 3x − 18

Factoring All but two of these can be factored; say they use parentheses – and how do you explain why the other two don’t work? SILVER x2 + 7x + 10 x2 + 4x + 6 x2 + 3x − 18 x2 + x − 42 x2 + 10x + 25 x2 + 3x x2 + 16 x2 − 16 x2 − x Want a challenge? All but one of these can be factored… GOLD 2×2 + 7x + 3 3×2 + x − 2 3×2 + x 4×2 − 25 9×2 + 16 4×2 − 8x − 5 The factoring screen changes color to green; which does not blush. If you have colored pencils… Student Sheet 4

Factoring All but two of these can be factored; say they use parentheses – and how do you explain why the other two don’t work? SILVER x2 + 7x + 10 x2 + 4x + 6 x2 + 3x − 18 x2 + x − 42 x2 + 10x + 25 x2 + 3x x2 + 16 x2 − 16 x2 − x Want a challenge? All but one of these can be factored… GOLD 2×2 + 7x + 3 3×2 + x − 2 3×2 + x 4×2 − 25 9×2 + 16 4×2 − 8x − 5 Click the box to see if it factors. If it turns red, it won’t. If it turns green, you know what to do…

### Equations With Algebraic Fractions

Practice example 3 𝑎𝑏 + 6 𝑏 2 3 𝑏𝑐 -12 𝑏𝑑 12 𝑎𝑏 4 𝑎𝑏 4 𝑎𝑏 3 𝑏 17𝑥 𝑥 2 −𝑥−2 Write the algebraic fraction in simplest terms. 3𝑏+ 𝑏 𝑏 2 −𝑏−2 The area of a rectangle is 4x 2 −7x−15 square units, and the width is x-3 units. What is the length of the rectangle? Student page 5

Find the common factor in each term. Simplify the factors as low as possible for each term. 3𝑎𝑏+6 𝑏 2 3𝑏𝑐−12𝑏𝑑 Each of the 4 terms in the fraction is a multiple of 3. They also have a “b”. Therefore, each term is divisible by 3 and b. All 4 terms have nothing else in common, so this is complete. 1 2 3𝑎𝑏+6 𝑏 2 3𝑏𝑐−12𝑏𝑑 1 4 𝑎+2𝑏 𝑐−4𝑑

Look for multiples of certain letters in each expression – can you factor the expression if there are no such letters? Simplify the factors as low as possible for each term. 3𝑏+ 𝑏 𝑏 2 −𝑏−2 Both terms are quadratic in b. Both can be factored. Both have the same full parentheses, so they cancel out in the numerator and denominator. (𝑏+1)(𝑏+2) (𝑏−2)(𝑏+1) (𝑏+1)(𝑏+2) (𝑏−2)(𝑏+1) = 𝑏+2 𝑏−2

### Reducing Rational Expressions To Lowest Terms (video)

Write algebraic fractions in the simplest language. 12. -4𝑐 𝑎+ 2𝑐 𝑥+1 𝑥+2 𝑥+2 𝑥−5 𝑥+5 𝑥−1

16 Thinking. The area of a rectangle is 4𝑥 2 −7𝑥−15 square units, and the width is x-3 units. What is the length of the rectangle? Area ÷ width = length, so: 4𝑥 2 −7𝑥−15 𝑥−3 Factor and sum: (4𝑥+5)(𝑥−3) 𝑥−3 The length is 4x+5 units.

We log user data and share it with processors to operate this website. To use this website, you must agree to our Privacy Policy, including our cookie policy. This question is about how to simplify algebraic fractions and is popular in GCSE non-calculus maths papers. They are either easy… or very difficult. The example in the picture shows the following expression as “2x the square of …” and this type of question is considered very difficult.

## Lesson Video: Simplifying Algebraic Fractions

Here are a few videos to explain factoring and it’s a basic skill you’ll need most of the time. As with most algebra topics, it is difficult to give specific examples because they all deal with different types of questions. However, if you can simplify algebraic fractions using factoring, this can help with higher level problems.

If you want to ask for more information, or if you are not sure about anything, ask in the comment section.

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### Equivalent Algebraic Fractions Simplifying Algebraic Fractions

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Non-necessary cookies are any cookies that are not necessary for the operation of the website and are used to collect personal data of the user through special analytics, advertisements and other embedded content. It is mandatory to obtain user consent before enabling these cookies on your website. Algebraic fractions are exactly what they sound like: fractions where you find terms that involve algebra. It’s important to remember that the rules you learned about fractions still apply to algebraic fractions, so make sure you’re comfortable with the following topics before continuing.

#### Algebra 1 Unit 6 Lesson 12 Simplifying Mixed Fractions

This is the simplest form in short, requiring only the cancellation of such conditions.

Step 1: First, we need to factor the numerator and denominator of the fraction. (Check out factoring squares here)

Step 2: cancel our fraction, in this case we can cancel (a