Question 35

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?

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

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

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

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?