Ever wondered if fractions with letters work like ordinary fractions?
Ngozi gets ₦x pocket money. She saves half of it and spends a third on data. How much is that altogether? x/2 + x/3 — and it adds up exactly like 12 + 13 = 56, giving 5x/6.
Revision notes
Fractions with letters follow the same rules as number fractions — simplify, add, subtract and evaluate them.
Ngozi gets ₦x pocket money. She saves half of it and spends a third on data. How much is that altogether? x/2 + x/3 — and it adds up exactly like 12 + 13 = 56, giving 5x/6.
An algebraic fraction has letters in it, like 6x/9 or (x + 2)/5. Simplify it just like 69 = 23: divide top and bottom by a common factor. So 6x/9 = 2x/3.
For (4x + 8)/4, factorise the top first: 4(x + 2)/4 = x + 2.
But (x + 8)/4 is NOT x + 2 — 4 is not a factor of the whole top. Test x = 4: (4 + 8)/4 = 3, but 4 + 2 = 6.
🔑 Key idea: Only cancel a factor of the WHOLE top and the WHOLE bottom.
Use the LCM of the denominators, just as with numbers. For x/2 + x/3 the LCM is 6: 3x/6 + 2x/6 = 5x/6.
When a top has two terms, multiply the WHOLE top: (x + 1)/2 + (x − 3)/4 = [2(x + 1) + (x − 3)]/4 = (2x + 2 + x − 3)/4 = (3x − 1)/4.
Never add the denominators: x/2 + x/3 is not 2x/5.
🔑 Key idea: Same denominator first, then combine the tops.
To evaluate, substitute and work out the top and bottom separately. (x + 4)/(x − 2) at x = 5 is 9 ÷ 3 = 3.
A fraction is undefined when its bottom is zero, because we can't divide by zero.
(x + 4)/(x − 2) is undefined when x − 2 = 0, that is when x = 2.
🔑 Key idea: Undefined means the denominator is zero.
Simplify x/3 + 2x/5.
Step 1: Use a common denominator
LCM of 3 and 5 = 15
x/3 = 5x/15, 2x/5 = 6x/15
5x/15 + 6x/15 = 11x/15
Why? Algebraic fractions follow exactly the same rules as ordinary fractions.
Answer: 11x/15
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