Original independent learning guide. Not official KICD content.
Why equivalent fractions matter
Multiplying both the numerator and denominator by the same non-zero number changes the number of parts without changing the amount. For example, 1/2 = 2/4 = 4/8. A drawing of equal-sized rectangles makes this visible: more dividing lines create smaller pieces, but the shaded area stays the same.
Worked example: add 2/3 and 1/6
The denominators 3 and 6 describe different-sized pieces. Rewrite 2/3 as 4/6 by multiplying numerator and denominator by 2. Now add the sixths: 4/6 + 1/6 = 5/6. Do not add the denominators: the pieces remain sixths. Estimate first if useful: 2/3 is already more than a half, and adding 1/6 should give a result below 1.
Compare before calculating
To compare 3/4 and 5/8, write both in eighths: 3/4 = 6/8. Six eighths is larger than five eighths, so 3/4 > 5/8. Comparing numerators alone would have led to the wrong conclusion. A common denominator makes the comparison fair.
Check and explain
After solving a question, explain what one part represents. If a sum of two positive fractions is smaller than either addend, something has gone wrong. Simplify an answer only by dividing both numerator and denominator by a common factor. Ask a teacher to check a method that you cannot explain in words.
Practice questions
Calculate 1/2 + 1/3.
Which is larger, 2/3 or 3/5? Explain.
A learner reads 3/8 of a book on Monday and 1/4 on Tuesday. What fraction is read altogether?
Answers and explanations
Use sixths: 3/6 + 2/6 = 5/6.
Use fifteenths: 2/3 = 10/15 and 3/5 = 9/15. Therefore 2/3 is larger.
1/4 = 2/8, so the total is 5/8. This assumes both fractions describe the same book and the pages read do not overlap.
