Fractions

Find out and discuss the words for fractions that are used in the different languages spoken in your home, city, or state. Ask your grandparents, parents, teachers, and classmates what words they use for different fractions, such as for one and a half, three quarters, one and a quarter, half, quarter, and two and a half, and write them here:

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

It turns out that this problem has six solutions! Can you find at least one of them? Can you find them all? You can try using similar reasoning as in the cases of two and three fractional units—or find your own method!

Once you find one solution, try to divide a circle into parts like in the figure above to visualise it!

Fill in the blanks with fractions.

1. Three guavas together weigh 1 kg. If they are roughly of the same size, each guava will roughly weigh ___ kg.

A wholesale merchant packed 1 kg of rice in four packets of equal weight. The weight of each packet is ___ kg.

Four friends ordered 3 glasses of sugarcane juice and shared it equally among themselves. Each one drank ___ glass of sugarcane juice.

The big fish weighs $\frac{1}{2}$ kg. The small one weighs $\frac{1}{4}$ kg. Together they weigh ___ kg.

The figures below show different fractional units of a whole chikki. How much of a whole chikki is each piece?

Continue this table of $\frac{1}{2}$ for 2 more steps.

Can you create a similar table for $\frac{1}{4}$?

Make $\frac{1}{3}$ using a paper strip. Can you use this to also make $\frac{1}{6}$?

Draw a picture and write an addition statement as above to show:

a. 5 times $\frac{1}{4}$ of a roti

b. 9 times $\frac{1}{4}$ of a roti

Match each fractional unit with the correct picture:

On a number line, draw lines of lengths $\frac{1}{10}$, $\frac{3}{10}$, and $\frac{4}{5}$.

Write five more fractions of your choice and mark them on the number line.

How many fractions lie between 0 and 1? Think, discuss with your classmates, and write your answer.

What is the length of the blue line and black line shown below? The distance between 0 and 1 is 1 unit long, and it is divided into two equal parts. The length of each part is $\frac{1}{2}$. So the blue line is $\frac{1}{2}$ units long. Write the fraction that gives the length of the black line in the box.

Write the fraction that gives the lengths of the black lines in the respective boxes.

How many whole units are there in $\frac{7}{2}$?

How many whole units are there in $\frac{4}{3}$ and in $\frac{7}{3}$?

Figure out the number of whole units in each of the following fractions:

a. $\frac{8}{3}$

b. $\frac{11}{5}$

c. $\frac{9}{4}$

Can all fractions greater than 1 be written as such mixed numbers?

Write the following fractions as mixed fractions (e.g., $\frac{9}{2} = 4\frac{1}{2}$):

a. $\frac{9}{2}$

b. $\frac{9}{5}$

c. $\frac{21}{19}$

d. $\frac{47}{9}$

e. $\frac{12}{11}$

f. $\frac{19}{6}$

Write the following mixed numbers as fractions:

a. $3 \frac{1}{4}$

b. $7 \frac{2}{3}$

c. $9 \frac{4}{9}$

d. $3 \frac{1}{6}$

e. $2 \frac{3}{11}$

f. $3 \frac{9}{10}$

Are $\frac{3}{6}$, $\frac{4}{8}$, $\frac{5}{10}$ equivalent fractions? Why?

Write two equivalent fractions for $\frac{2}{6}$.

$\frac{4}{6} = \dots\dots\dots\dots\dots$ (Write as many as you can)

Three rotis are shared equally by four children. Show the division in the picture and write a fraction for how much each child gets. Also, write the corresponding division facts, addition facts, and, multiplication facts.

Fraction of roti each child gets is ______. Division fact: Addition fact: Multiplication fact:

Compare your picture and answers with your classmates!

Draw a picture to show how much each child gets when 2 rotis are shared equally by 4 children. Also, write the corresponding division facts, addition facts, and multiplication facts.

Anil was in a group where 2 cakes were divided equally among 5 children. How much cake would Anil get?

Find the missing numbers:

a. 5 glasses of juice shared equally among 4 friends is the same as ___ glasses of juice shared equally among 8 friends.

b. 4 kg of potatoes divided equally in 3 bags is the same as 12 kgs of potatoes divided equally in ___ bags.

c. 7 rotis divided among 5 children is the same as ___ rotis divided among ___ children.

Express the following fractions in lowest terms:

a. $\frac{17}{51}$

b. $\frac{64}{144}$

e. $\frac{126}{147}$

d. $\frac{525}{112}$

Compare the following fractions and justify your answers:

a. $\frac{8}{3}$, $\frac{5}{2}$

b. $\frac{4}{9}$, $\frac{3}{7}$

c. $\frac{7}{10}$, $\frac{9}{14}$

d. $\frac{12}{5}$, $\frac{8}{5}$

e. $\frac{9}{4}$, $\frac{5}{2}$

Write the following fractions in ascending order.

a. $\frac{7}{10}$, $\frac{11}{15}$, $\frac{2}{5}$

b. $\frac{19}{24}$, $\frac{5}{6}$, $\frac{7}{12}$

Write the following fractions in descending order.

a. $\frac{25}{16}$, $\frac{7}{8}$, $\frac{13}{4}$, $\frac{17}{32}$

b. $\frac{3}{4}$, $\frac{12}{5}$, $\frac{7}{12}$, $\frac{5}{4}$

Add the following fractions using Brahmagupta's method:

a. $\frac{2}{7} + \frac{5}{7} + \frac{6}{7}$

b. $\frac{3}{4} + \frac{1}{3}$

c. $\frac{2}{3} + \frac{5}{6}$

d. $\frac{2}{3} + \frac{2}{7}$

e. $\frac{3}{4} + \frac{1}{3} + \frac{1}{5}$

f. $\frac{2}{3} + \frac{4}{5}$

g. $\frac{4}{5} + \frac{2}{3}$

h. $\frac{3}{5} + \frac{5}{8}$

i. $\frac{9}{2} + \frac{5}{4}$

j. $\frac{8}{3} + \frac{2}{7}$

k. $\frac{3}{4} + \frac{1}{3} + \frac{1}{5}$

l. $\frac{2}{3} + \frac{4}{5} + \frac{3}{7}$

m. $\frac{9}{2} + \frac{5}{4} + \frac{7}{6}$

Rahim mixes $\frac{2}{3}$ litres of yellow paint with $\frac{3}{4}$ litres of blue paint to make green paint. What is the volume of green paint he has made?

Geeta bought $\frac{2}{5}$ meter of lace and Shamim bought $\frac{3}{4}$ meter of the same lace to put a complete border on a table cloth whose perimeter is 1 meter long. Find the total length of the lace they both have bought. Will the lace be sufficient to cover the whole border?

$\frac{5}{8} - \frac{3}{8}$

$\frac{7}{9} - \frac{5}{9}$

$\frac{10}{27} - \frac{1}{27}$

Carry out the following subtractions using Brahmagupta's method:

a. $\frac{8}{15} - \frac{3}{15}$

b. $\frac{2}{5} - \frac{4}{15}$

c. $\frac{5}{6} - \frac{4}{9}$

d. $\frac{2}{3} - \frac{1}{2}$

Subtract as indicated:

a. $\frac{13}{4}$ from $\frac{10}{3}$

b. $\frac{18}{5}$ from $\frac{23}{3}$

c. $\frac{29}{7}$ from $\frac{45}{7}$

Solve the following problems:

a. Jaya's school is $\frac{7}{10}$ km from her home. She takes an auto for $\frac{1}{2}$ km from her home daily, and then walks the remaining distance to reach her school. How much does she walk daily to reach the school?

b. Jeevika takes $\frac{10}{3}$ minutes to take a complete round of the park and her friend Namit takes $\frac{13}{4}$ minutes to do the same. Who takes less time and by how much?

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

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

Answer the following questions after looking at the fraction wall:

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

Answer the following questions after looking at the fraction wall:

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

Answer the following questions after looking at the fraction wall:

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

Answer the following questions after looking at the fraction wall:

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

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?

Q. 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 $\frac{1}{2}$. Write them in the boxes here:

Equally divide the rotis in the situations shown below and write down the share of each child. Are the shares in each of these cases the same? Why?

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 $\frac{1}{5} < \frac{2}{5}$, $\frac{3}{7} < \frac{4}{7}$, and $\frac{1}{2} < \frac{5}{8}$.

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. $\frac{7}{2}$ and $\frac{3}{5}$

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

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

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

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

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

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

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

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

Q. How much of the total chikki is remaining?

Try adding $\frac{4}{7} + \frac{6}{7}$ 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.