As society grew more complex, measuring became just as important as counting. If a farmer divides a field of wheat among his three children, how much does each get? If a recipe calls for half a cup of ghee, how do we represent that mathematically?

Step-by-step solution

Idea: Whole numbers count whole things. To describe a part of one whole, we write a fraction: the denominator tells how many equal parts the whole is cut into, and the numerator tells how many parts we take.

1. The field is one whole shared equally into 3 parts, so each child gets 1 ÷ 3 = 13 of the field.½ mark
2. Half a cup means the cup is cut into 2 equal parts and one part is used: 12 cup. Numbers like 13 and 12 are called fractions.½ mark

Check: 13 + 13 + 13 = 1: the three shares make the whole field ✓.

Answer to write in the exam

Common mistakes that cost marks

• Writing 31 instead of 13: the number of parts (3) goes in the denominator.
• Saying each child gets 3 parts; each gets 1 of the 3 equal parts.
• Writing half as 0.2 instead of 0.5 or 12.

How this can come in the exam

Try one yourself

A pizza is shared equally by 5 friends. What fraction does each get, and what fraction do two of them get together?

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