By dividing the whole chikki into 6 equal parts in different ways, we get 1/6 chikki pieces of different shapes. Are they of the same size?

Question

Homi · Accepted Answer

Fractions mean dividing a whole into equal parts.

Step 1 — Look at the first way to cut

Look at the first picture. We see one whole chikki. It is cut into 6 equal pieces. Each piece is a small rectangle. Each small rectangle is $\frac{1}{6}$ of the whole chikki.

Diagram 1

Step 2 — Look at the second way to cut

Now look at the second picture. We see the same whole chikki. It is also cut into 6 equal pieces. Each piece is a small triangle. Each small triangle is $\frac{1}{6}$ of the whole chikki.

Diagram 2

Step 3 — Compare the sizes

In both ways, the chikki is cut into 6 equal parts. One part from the first way is $\frac{1}{6}$ of the whole. One part from the second way is also $\frac{1}{6}$ of the whole. Both pieces are $\frac{1}{6}$ of the same whole chikki. So, their sizes must be equal. Their shapes are different. But their amount of chikki is the same.

Step 4 — See other fractions

The diagram shows 6 equal pieces. Let us take 2 of these $\frac{1}{6}$ pieces. We get $\frac{1}{6} + \frac{1}{6}$ of the chikki. This is $\frac{2}{6}$ of the chikki. We can simplify $\frac{2}{6}$ .

$\frac{2}{6}$

$= \frac{2 \div 2}{6 \div 2}$

$\boxed{\frac{1}{3}}$

So, the diagram also helps us see that $\frac{1}{3}$ of the chikki is made of two $\frac{1}{6}$ pieces.

Answer

(i) Yes, these are of same size. (ii) It shows 1/3 chikki.

Question 2

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