Fractions | FIO

Question 30

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

Solution

To compare fractions, we make their bottom numbers the same.

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

Step 1 — Find Common Bottom Number We need a common bottom number. Let us find the smallest common multiple of 3 and 2. Multiples of 3 are 3, 6, 9, ... Multiples of 2 are 2, 4, 6, ... The smallest common multiple is 6.

$\boxed{\text{Common bottom number} = 6}$

Step 2 — Make Equivalent Fractions We change both fractions. They will have the same bottom number. For $\frac{8}{3}$ : $\frac{8}{3} = \frac{8 \times 2}{3 \times 2}$ $= \frac{16}{6}$ For $\frac{5}{2}$ : $\frac{5}{2} = \frac{5 \times 3}{2 \times 3}$ $= \frac{15}{6}$

Step 3 — Compare Top Numbers Now we look at the top numbers. We compare the new top numbers. We compare 16 and 15. 16 is bigger than 15. So, $\frac{16}{6}$ is bigger than $\frac{15}{6}$ . This means $\frac{8}{3}$ is bigger than $\frac{5}{2}$ .

$\boxed{\frac{8}{3} > \frac{5}{2}}$

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

Step 1 — Find Common Bottom Number We need a common bottom number. Let us find the smallest common multiple of 9 and 7. Multiples of 9 are 9, 18, 27, 36, 45, 54, 63, ... Multiples of 7 are 7, 14, 21, 28, 35, 42, 49, 56, 63, ... The smallest common multiple is 63.

$\boxed{\text{Common bottom number} = 63}$

Step 2 — Make Equivalent Fractions We change both fractions. They will have the same bottom number. For $\frac{4}{9}$ : $\frac{4}{9} = \frac{4 \times 7}{9 \times 7}$ $= \frac{28}{63}$ For $\frac{3}{7}$ : $\frac{3}{7} = \frac{3 \times 9}{7 \times 9}$ $= \frac{27}{63}$

Step 3 — Compare Top Numbers Now we look at the top numbers. We compare the new top numbers. We compare 28 and 27. 28 is bigger than 27. So, $\frac{28}{63}$ is bigger than $\frac{27}{63}$ . This means $\frac{4}{9}$ is bigger than $\frac{3}{7}$ .

$\boxed{\frac{4}{9} > \frac{3}{7}}$

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

Step 1 — Find Common Bottom Number We need a common bottom number. Let us find the smallest common multiple of 10 and 14. Multiples of 10 are 10, 20, 30, 40, 50, 60, 70, ... Multiples of 14 are 14, 28, 42, 56, 70, ... The smallest common multiple is 70.

$\boxed{\text{Common bottom number} = 70}$

Step 2 — Make Equivalent Fractions We change both fractions. They will have the same bottom number. For $\frac{7}{10}$ : $\frac{7}{10} = \frac{7 \times 7}{10 \times 7}$ $= \frac{49}{70}$ For $\frac{9}{14}$ : $\frac{9}{14} = \frac{9 \times 5}{14 \times 5}$ $= \frac{45}{70}$

Step 3 — Compare Top Numbers Now we look at the top numbers. We compare the new top numbers. We compare 49 and 45. 49 is bigger than 45. So, $\frac{49}{70}$ is bigger than $\frac{45}{70}$ . This means $\frac{7}{10}$ is bigger than $\frac{9}{14}$ .

$\boxed{\frac{7}{10} > \frac{9}{14}}$

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

Step 1 — Denominators are Same The bottom numbers are already equal. Both fractions have a bottom number of 5.

Step 2 — Compare Top Numbers We just compare the top numbers. The top number of the first fraction is 12. The top number of the second fraction is 8. We know that 12 is bigger than 8. So, $\frac{12}{5}$ is bigger than $\frac{8}{5}$ .

$\boxed{\frac{12}{5} > \frac{8}{5}}$

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

Step 1 — Find Common Bottom Number We need a common bottom number. Let us find the smallest common multiple of 4 and 2. Multiples of 4 are 4, 8, ... Multiples of 2 are 2, 4, 6, ... The smallest common multiple is 4.

$\boxed{\text{Common bottom number} = 4}$

Step 2 — Make Equivalent Fractions We change both fractions. They will have the same bottom number. The fraction $\frac{9}{4}$ already has 4 as its bottom number. For $\frac{5}{2}$ : $\frac{5}{2} = \frac{5 \times 2}{2 \times 2}$ $= \frac{10}{4}$

Step 3 — Compare Top Numbers Now we look at the top numbers. We compare the new top numbers. We compare 9 and 10. 9 is smaller than 10. So, $\frac{9}{4}$ is smaller than $\frac{10}{4}$ . This means $\frac{9}{4}$ is smaller than $\frac{5}{2}$ .

$\boxed{\frac{9}{4} < \frac{5}{2}}$

Answer

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. $\frac{9}{4} < \frac{5}{2}$

More questions in FIO

Fill in the blanks with fractions.

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

Q10

Match each fractional unit with the correct picture:

Q11

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

Q12

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

Q13

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

Q14

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.

Q15

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

Q16

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

Q17

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

Q18

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

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

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

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

Q19

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

Q20

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. $\frac{19}{6}$

Q21

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

Q22

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

Q23

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

Q24

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

Q25

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!

Q26

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.

Q27

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

Q28

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.

Q29

Express the following fractions in lowest terms:

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

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

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

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

Q30

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

Q31

Write the following fractions in ascending order.

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

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

Q32

Write the following fractions in descending order.

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

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

Q33

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

Q34

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?

Q35

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?

Q36

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

Q37

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

Q38

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

Q39

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

Q40

Subtract as indicated:

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

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

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

Q41

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?