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Algebraic fractions handout, Cheat Sheet of Mathematics

Mathematics

Algebraic fractions handout GCSE

Typology: Cheat Sheet

2022/2023

Uploaded on 02/05/2026

arushi-7
arushi-7 🇬🇧

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19-06-2023
ALGEBRAIC FRACTIONS
ALGEBRAIC FRACTIONS
Algebraic fractions refer to fractions containing numbers and variables.
Common terms refer to algebraic expressions of the form 𝑥, (𝑎𝑥 + 𝑏) or 𝑎𝑥 − 𝑏
where 𝑎and 𝑏are integers.
Mathematical operations are same as those with fractions containing numbers only
Simplification
Equivalent
Multiplication
Division
Addition/Subtraction
Rules and steps are similar to
number fractions.
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Download Algebraic fractions handout and more Cheat Sheet Mathematics in PDF only on Docsity!

ALGEBRAIC FRACTIONS

ALGEBRAIC FRACTIONS

Algebraic fractions refer to fractions containing numbers and variables.

Common terms refer to algebraic expressions of the form 𝑥, (𝑎𝑥 + 𝑏) or 𝑎𝑥 − 𝑏

where 𝑎 and 𝑏 are integers.

Mathematical operations are same as those with fractions containing numbers only

 Simplification

 Equivalent

 Multiplication

 Division

 Addition/Subtraction

Rules and steps are similar to

number fractions.

SIMPLIFICATION

Identify common expressions for cancellation

Terms of the form 𝑎𝑥 ± 𝑏

Same powers of the variable

Common numerical factors

ଶ

ଶ

ଶ

ଶ

ସ

ଶ

ଷ

ଶ

ଶ

ଷ

ଶ

ଷ

ଶ

ଶ

SIMPLIFICATION

Cancelling common expressions using Factorization

ଶ

− 4

Factorize

denominator

FRACTION ARITHMETIC

Multiplication: Multiply the numerators, multiply the denominators and simplify

Division: Take the reciprocal of the fraction after division sign, change the division to

multiplication. This changes the problem to multiplication.

ଶ

×

×

Factorize

× 𝑛 =

Simplify

Multiply

ଶ

  • 𝑥 − 15

÷

ଶ

  • 9𝑥

ଶ

  • 𝑥 − 15

× (3𝑥

ଶ

× 3𝑥(𝑥 + 3) =

× 3𝑥

Reciprocal

Factorize

Factorize

Simplify

Multiply

PRACTICE PROBLEMS

ଶ

ଶ

÷

ଶ

ଶ

ଶ

÷

ଶ

ଶ

ଶ

− 4

÷

ଶ

  • 2𝑥

ଶ

×

ଶ

ଶ

ଶ

ଶ

×

ଶ

ଶ

÷

ଶ

ଶ

×

ଶ

ଶ

ସ

÷

ଷ

ଶ

ଶ

FRACTION ARITHMETIC

Addition/Subtraction: Take a common denominator (CD) followed by equivalent

fractions and combining the terms in the numerator. Finally simplify the expression.

× 2

× 2

× 3

× 3

× 𝑥

× 𝑥

× (𝑥 − 1)

× (𝑥 − 1)

Combine

like terms

Combine

like terms

FRACTION ARITHMETIC

Find the common denominator using Factorization

ଶ

Factorize the

denominator

× 1

× 1

Combine

like terms

ଶ

− 1

Expand the

denominator

× (2𝑥 + 1)

× (2𝑥 + 1)

MATCH EQUIVALENT EXPRESSIONS

Sl.No. Expression-I Sl.No. Expression-II

ଶ

ଶ

P

ଶ

  • 6𝑥 + 8

ଶ

ଶ

𝑥 Q

ଶ

ଶ

R

ଶ

ଶ

− 11𝑥 − 21

2 𝑥 S

ଶ

ଶ

1 R

2 P

3 S

4 Q

PRACTICE PROBLEMS

ଶ

The function 𝑓 is defined as:

ଶ

Show that 𝑓 𝑥 =

஺

௫ିଶ

where 𝐴 is an expression to

be found in its simplest form.

Write as a single fraction, simplify fully:

5 − 𝑥 + 2 ÷

ଶ

Simplify fully:

ଶ

PRACTICE PROBLEMS

Solve the equation:

Solve:

ଶ

Solve the equation:

Solve the equation:

PRACTICE PROBLEMS

Solve the equation:

Solve

Solve

Solve:

PRACTICE PROBLEMS

For positive values of 𝑥

Work out 𝑓 𝑥 + 1 − 𝑓 𝑥

Answer should be given in simplest form.

Circle the expression that is equivalent to

ଶ

Circle the expression that is equivalent to

ଶ

ଶ

Simplify fully:

ଶ

PRACTICE PROBLEMS

Suppose Toby forms an equation:

Solve for 𝑥.

Solve the equation