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Algebraic Fractions Operations

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Algebraic Fractions Operations

Simplify each answer where possible. Show your working for calculation questions. Assume all denominators are non-zero.

Understanding algebraic fractions

1.Before adding two algebraic fractions with different denominators, what should you usually find?

A common denominator
The sum of the denominators
A common numerator
The largest numerator

2.Select every statement that is correct about algebraic fractions.

They follow the usual fraction rules.
When adding, you add the denominators.
Addition and subtraction often require equivalent fractions with a common denominator.
A variable may appear in a denominator.

3.Complete the statements: With a shared denominator, add or subtract the and retain the . Then check whether the result can be .

Fractions with a shared denominator

4.Simplify 4/x + 7/x.

5.Simplify (3a + 2)/b − (a − 4)/b.

6.Simplify 6/(x + 5) + 2/(x + 5).

Fractions with different denominators

7.State a lowest common denominator for 3/m + 2/n.

8.Combine and simplify 2/x + 1/(4x).

9.Work out 4/(x + 2) − 1/(x − 2), and simplify.

10.Simplify 5/(3a) + 1/(6a) − 2/(9a).

Apply and explain

11.Simplify (x + 4)/(x − 2) + (x − 3)/(x + 2).

12.A rectangular display has dimensions 5/p metres by 2/q metres. A second display has dimensions 3/p metres by 1/q metres. Find the difference between their areas, taking the first display's area minus the second's.

13.Match each calculation to the most suitable first step.

1. 5/r + 2/r
2. 1/c + 1/d
3. 1/(2s) + 3/(5s)
4. (t + 3)/t − 4/t

D. Subtract the numerators over the shared denominator.
A. Find a common denominator for 2s and 5s.
C. Find a common denominator for c and d.
B. Add the numerators over the shared denominator.

14.Explain why fractions such as 2/u and 3/v cannot usually be added by combining their numerators and keeping either original denominator.

15.A common error is to add both the numerators and denominators when calculating 2/a + 1/b. State why this is incorrect and give the correct simplified result.

16.Find and simplify 3/(2x) + 1/(3x).