Number System (Classes VI-VIII) • Topic 4 of 6

Fractions & Decimals

Fractions and decimals are, by a distance, the topics where upper-primary children carry the most stubborn misconceptions, and CTET knows it. The headline error is whole-number thinking applied to fractions: a child decides 1/4 is bigger than 1/2 because 4 is bigger than 2, not seeing that a bigger denominator cuts the whole into smaller pieces. In decimals the mirror error is longer-is-larger, where 0.65 is judged greater than 0.7 because it has more digits. A third is adding denominators (1/2 + 1/3 = 2/5), which ignores that you must first make the parts equal-sized via a common denominator. A teacher counters all three with the area or fraction-strip model so children SEE the size of a part, and stresses that 0.7 = 0.70 to defeat the place-value confusion in decimals. The exam usually gives a child's wrong comparison or sum and asks for the misconception or the correct value, so keep the maths exact and the diagnosis ready.

✅ Solved examples

1. Add 1/2 + 1/3.
LCM of 2 and 3 is 6, so 1/2 = 3/6 and 1/3 = 2/6. Adding the numerators: 3/6 + 2/6 = 5/6.
2. A child says 0.65 is greater than 0.7. What is the misconception?
The longer-is-larger error: the child treats more digits as more value. But 0.7 = 0.70, and 70 hundredths is greater than 65 hundredths, so 0.7 > 0.65. Lining up the decimal places (or using 0.70) makes it clear.
3. Which is greater, 1/2 or 1/4, and why might a child get it wrong?
1/2 is greater, because dividing a whole into 2 parts gives bigger pieces than dividing into 4. A child may pick 1/4 by whole-number thinking, reasoning 4 > 2.
4. Convert 3/4 to a decimal.
3/4 = 3 divided by 4 = 0.75. Equivalently 3/4 = 75/100 = 0.75.

✏️ Practice — try these, take hints as needed

1. Add 2/5 + 1/10.
LCM of 5 and 10 is 10.
Convert 2/5 to tenths first.
1/2 (2/5 = 4/10, so 4/10 + 1/10 = 5/10 = 1/2)
2. A child writes 1/2 + 1/3 = 2/5. What error is this?
Look at how the denominators were handled.
Parts must be equal-sized first.
The child added numerators and denominators directly; you must use a common denominator. The correct answer is 5/6.
3. Arrange in ascending order: 0.5, 0.45, 0.405.
Write each to three decimal places.
Compare 500, 450, 405 thousandths.
0.405, 0.45, 0.5
4. Convert 0.25 to a fraction in lowest terms.
0.25 = 25/100.
Divide top and bottom by 25.
1/4

📝 Topic test — 8 questions

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