Fractions and Decimals • Topic 1 of 7

Proper Fractions

A proper fraction has a numerator smaller than its denominator, so its value lies between 0 and 1 — for example 3/4 or 2/5. The numerator counts how many parts you have; the denominator says how many equal parts make one whole. Proper fractions describe a quantity less than a whole, so they appear in part-of-a-whole, ratio and probability questions. Always reduce a fraction to lowest terms by dividing the numerator and denominator by their greatest common factor, which makes comparing and combining fractions far easier.

✅ Solved examples

1. Which of these is a proper fraction: 5/3, 7/7, 2/9, 8/5?
A proper fraction has numerator < denominator. Only 2/9 satisfies this (2 < 9); the others are equal to or greater than 1.
2. What fraction of a day is 6 hours?
A day has 24 hours, so 6 hours is 6/24. Dividing numerator and denominator by 6 gives 1/4.
3. Simplify 12/18 to lowest terms.
The GCF of 12 and 18 is 6. Dividing both by 6 gives 2/3.
4. Is 4/4 a proper fraction?
No. Its numerator equals its denominator, so 4/4 = 1, which is not less than 1.

✏️ Practice — try these, take hints as needed

1. Which is a proper fraction: 9/4, 3/8, 5/5, 11/2?
A proper fraction has numerator < denominator.
Compare the top and bottom of each.
3 < 8.
3/8.
2. Simplify 15/25 to lowest terms.
Find the GCF of 15 and 25.
The GCF is 5.
Divide both by 5.
3/5.
3. What fraction of an hour is 20 minutes?
An hour is 60 minutes.
Write 20/60.
Divide both by 20.
1/3.
4. Reduce 24/36 to lowest terms.
Find the GCF of 24 and 36.
It is 12.
Divide both by 12.
2/3.
5. A pizza is cut into 8 equal slices and 3 are eaten. What fraction is left?
Slices left = 8 − 3 = 5.
Write this over the total 8.
Check whether 5/8 reduces (it does not).
5/8.

📝 Topic test — 8 questions

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