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Level 5-6 Algebra - Equations - Fractional

Solve fractional equations in KS3 algebra. Clear denominators, use inverse operations, and check solutions by substitution to handle fractions, mixed numbers, and negatives confidently.

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Fascinating Fact:

For example, if a recipe uses 3/4 of a cup of flour per cake, then the equation (3/4) × x = 6 helps you find how many cakes can be made with 6 cups of flour.

In KS3 Maths, fractional equations include fractions with unknowns. You will clear denominators by multiplying through, use inverse operations to isolate the variable, keep both sides balanced, and check by substitution.

Key Terms

Fractional equation: An equation where numbers or coefficients are fractions, for example (2/3)x = 8.
Common denominator: A shared multiple of denominators used to remove fractions by multiplying both sides.
Reciprocal: The number that multiplies to 1, e.g., the reciprocal of 3/4 is 4/3.

Frequently Asked Questions (Click to see answers)

How do I solve a fractional equation like (2/3)x = 8?

Multiply both sides by the reciprocal 3/2: (2/3)x × 3/2 = 8 × 3/2. This gives x = 12.

What if there are fractions on both sides of the equation?

Find the lowest common multiple (LCM) of the denominators and multiply every term by it to clear fractions, then solve step by step.

How can I check my answer to a fractional equation?

Substitute your value back into the original equation, work carefully with fractions, and confirm both sides are equal.

Try These Related Quizzes

1 .

According to the dictionary what is the purpose of a fraction?

To complicate maths

To annoy teachers

To confuse students

To represent part of a whole

All the other answers might be true but we did ask for what the DICTIONARY tells us!

2 .

Where can the 'numerator' in a fraction be found?

Above the line

Below the line

Either above or below the line

Anywhere but where it ought to be

One way to remember numerators and denominators is this - NUmerators are Never Under and Denominators are Down

3 .

Where can the 'denominator' in a fraction be found?

Above the line

Below the line

Either above or below the line

Hiding

One way to remember numerators and denominators is this - NUmerators are Never Under and Denominators are Down

4 .

If a fraction has a numerator (above the line) that is greater than the denominator (below the line) then it is what type of fraction?

Important

Impossible

Improbable

Improper

¹¹?₃ is an example of an improper fraction; ³?₁₁ is an example of a proper fraction

5 .

Look at this fractional equation: ^a⁄₃ = ⁹⁄₂. To solve the equation what would you do first?

Multiply a x 9

Multiply 3 x 2

Multiply a x 9 AND multiply 3 x 2

Multiply a x 2 AND multiply 3 x 9

To cross multiply, you multiply the denominator on the right hand side with the numerator on the left hand side and then vice versa with the other numbers. This gets you to the position of 2 x a = 3 x 9

6 .

In the equation 2 x a = 3 x 9 which of these is not correct?

2 x a = 27

2a = 3 x 9

2a = 27

a = 14.5

The correct answer is a = 13.5

7 .

Look at this fractional equation: ^a⁄₉ = ⁹⁄₄. Which of the following steps is incorrect?

4 x a = 9 x 9

4a = 81

a = 81/4

a = 20

The correct answer is a = 20.25

8 .

Look at the following fractional equation and decide what is the correct value for a: ^a⁄₆ = ⁷⁄₄.

6.5

8.5

10.5

12.5

If you got it wrong then look through the workings in questions 6 and 7 above

9 .

Look at the following fractional equation and decide what is the correct value for a: ⁹⁄_a = 18.

0.5

162

It might make it easier to think of the above equation as ⁹?_a = ¹⁸?₁

10 .

Look at the following fractional equation and decide what is the correct value for a: ^a⁄₃ = ⁵⁄₆

2.5

3.5

We divide 6 by 2 to get the denominator 3, so we divide 5 by 2 to get the numerator (a) which is 2.5

You can find more about this topic by visiting BBC Bitesize - Equations

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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