Fraction pieces

In your book, Maths Mela (Chapter 2), Gurpreet is playing with his fraction kit. The kit has strips all the same length as one whole, cut into pieces: halves, thirds, fourths, fifths, sixths, eighths and twelfths. How many 1/5 pieces make a whole? 5 of them, because a whole cut into 5 equal pieces has 5 fifths.

Gurpreet makes a whole from two different kinds of pieces: one 1/2 piece and two 1/4 pieces. This works because when a 1/2 piece is broken into 2 equal parts, each part is a 1/4 piece. So 2 pieces of 1/4 are as long as 1 piece of 1/2, and one 1/2 with two 1/4s fills the whole.

We can ask how many small pieces fit into a bigger one. A 1/3 piece broken into 2 equal parts gives two 1/6 pieces, so two 1/6s make 1/3. Two 1/8s make 1/4, and four 1/8s make 1/2.

Twelfths are the smallest pieces. Six 1/12s make 1/2 (because 12 twelfths make the whole, and half of 12 is 6). Four 1/12s make 1/3, three 1/12s make 1/4, and two 1/12s make 1/6.

Now we can make a whole from mixed pieces. One 1/2, one 1/4 and three 1/12s make a whole: the 1/2 and the 1/4 leave one 1/4 empty, and three 1/12s fill it. Four 1/6s and four 1/12s also make a whole: four 1/6s are 2/3, and four 1/12s are the last 1/3.