Fractions beyond one

In your book, Maths Mela (Chapter 2), Raman's father makes nice soft parathas. Before serving them he cuts each paratha into halves (2 equal parts) or into fourths (4 equal parts). Maa took 5 pieces of 1/2 paratha. How much paratha did she eat? 5 halves is written 5/2. Two halves make 1 whole paratha, so 4 halves make 2 parathas, and there is 1 half more. So 5/2 = 2 + 1/2, and we write it as 2 1/2 (two and a half) parathas. A number like 2 1/2, a whole number with a fraction, is called a mixed number.

We can show this on a number line. Split the gap between 0 and 1 into 2 equal parts; each part is 1/2. Keep going past 1 in steps of 1/2: 1/2, 2/2 (which is 1), 3/2, 4/2 (which is 2), 5/2. So 5 halves takes us to 5/2, halfway between 2 and 3. Radhika took 6 halves: 6/2 = 3 parathas exactly.

Another day, Raman's father cut all the parathas into fourths. Four 1/4 pieces make 1 whole. Dadaji took 9 pieces of 1/4 paratha: 9/4. 8 fourths make 2 whole parathas, and 1 fourth is left, so 9/4 = 2 1/4 parathas. On the number line, split each gap from one whole number to the next into 4 equal parts, and count 9 steps of 1/4.

Raman's family of 6 ordered 2 pizzas and cut each into 3 equal slices, one slice each. Dadiji and Dadaji gave their slices to Raman, so he had 3 slices of 1/3: 3/3 = 1 whole pizza. Maa and Baba gave theirs to Radhika, so she too had 1 whole pizza. Raman could eat only 2 slices, so he gave 1 to Radhika. Now Radhika has 4 slices: 4/3 = 1 + 1/3 = 1 1/3 pizzas.

When the top number is bigger than the bottom number, the fraction is more than 1 whole. The book also asks: an ant is 1/4 cm long; how long is a line of 16 such ants? 16 fourths is 16/4. Every 4 fourths make 1 cm, and 16 is four 4s, so the line is 4 cm long.