Question 18

Arrange these fraction words in order of size from the smallest to the biggest in the empty box below:

One and a half, three quarters, one and a quarter, half, quarter, two and a half.

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

Do it once more! Fill in the blank boxes.

Now, can you find the lengths of the various blue lines shown below? Fill in the boxes as well.

1. Here, the fractional unit is dividing a length of 1 unit into three equal parts. Write the fraction that gives the length of the blue line in the box or in your notebook.

Here, a unit is divided into 5 equal parts. Write the fraction that gives the length of the blue lines in the respective boxes or in your notebook.

Now, a unit is divided into 8 equal parts. Write the appropriate fractions in your notebook.

Write down all the fractions you marked on the number line earlier.

Now, let us classify these in two groups:

Did you notice something common between the fractions that are greater than 1?

What do you observe?

• Are the lengths $\dfrac{1}{2}$ and $\dfrac{2}{4}$ equal?
• Are the lengths $\dfrac{2}{4}$ and $\dfrac{4}{8}$ equal?

Now, check whether $\dfrac{1}{3}$ and $\dfrac{2}{6}$ are equivalent fractions or not, using paper strips.

Answer the following questions after looking at the fraction wall:

Are the lengths $\dfrac{1}{2}$ and $\dfrac{3}{6}$ equal?

Answer the following questions after looking at the fraction wall:

Are $\dfrac{2}{3}$ and $\dfrac{4}{6}$ equivalent fractions? Why?

Answer the following questions after looking at the fraction wall:

How many pieces of length $\dfrac{1}{6}$ will make a length of $\dfrac{1}{2}$?

Answer the following questions after looking at the fraction wall:

How many pieces of length $\dfrac{1}{6}$ will make a length of $\dfrac{1}{3}$?

Context: Anil was in a group where 2 cakes were divided equally among 5 children.

Q. Now, if there are 10 children in my group, how many cakes will I need so that they get same amount of cake as Anil?

What if we put two such groups together? One group where 2 cakes are divided equally between 5 children, and another group again with 4 cakes and 10 children.

Find some more fractions equivalent to $\dfrac{1}{2}$. Write them in the boxes here:

Suppose the number of children is kept the same, but the number of units that are being shared is increased? What can you say about each child's share now? Why? Discuss how your reasoning explains $\dfrac{1}{5} < \dfrac{2}{5}$, $\dfrac{3}{7} < \dfrac{4}{7}$, and $\dfrac{1}{2} < \dfrac{5}{8}$.

Now, decide in which of the two groups will each child get a larger share:

1. Group 1: 3 glasses of sugarcane juice divided equally among 4 children. Group 2: 7 glasses of sugarcane juice divided equally among 10 children.
2. Group 1: 4 glasses of sugarcane juice divided equally among 7 children. Group 2: 5 glasses of sugarcane juice divided equally among 7 children.

Which groups were easier to compare? Why?

Find equivalent fractions for the given pairs of fractions such that the fractional units are the same.

a. $\dfrac{7}{2}$ and $\dfrac{3}{5}$

b. $\dfrac{8}{3}$ and $\dfrac{5}{6}$

c. $\dfrac{3}{4}$ and $\dfrac{3}{5}$

d. $\dfrac{6}{7}$ and $\dfrac{8}{5}$

e. $\dfrac{9}{4}$ and $\dfrac{5}{2}$

f. $\dfrac{1}{10}$ and $\dfrac{2}{9}$

g. $\dfrac{8}{3}$ and $\dfrac{11}{4}$

h. $\dfrac{13}{6}$ and $\dfrac{1}{9}$

Context: Meena's father made some chikki. Meena ate $\dfrac{1}{2}$ of it and her younger brother ate $\dfrac{1}{4}$ of it.

Q. How much of the total chikki is remaining?

Try adding $\dfrac{4}{7} + \dfrac{6}{7}$ using a number line. Do you get the same answer?

Try doing this same exercise using the number line.

Puzzle!

1. Can you find three different fractional units that add up to 1?

   It turns out there is only one solution to this problem (up to changing the order of the 3 fractions)! Can you find it? Try to find it before reading further.