# F**ractions**

**Exercise 7.4**

*Questions with (*) sign are open-ended questions.*

1). Write shaded portion as fraction. Arrange them in ascending and descending order using correct sign ‘<’, ‘=’, ‘>’ between the fractions:

(a).

(b).

(c) Show ^{2}/_{6}, ^{4}/_{6}, ^{8}/_{6}, and ^{6}/_{6} on the number line. Put appropriate signs between the fractions given.

Answer:

2). Compare the fractions and put an appropriate sign.

(*) 3). Make five more such pairs and put appropriate signs.

Answer:

4). Look at the figures and write ‘<’ or ‘>’, ‘=’ between the given pairs of fractions. Make five more such problems and solve them with your friends.

Answer:

5). How quickly can you do this? Fill appropriate sign. ( ‘<’, ‘=’, ‘>’)

(a). ½ □ ^{1}/_{5} (b). ^{2}/_{4} □ ^{3}/_{6}

(c). ^{3}/_{5} □ ^{2}/_{3} (d). ¾ □ ^{2}/_{8}

(e). ^{3}/_{5} □ ^{6}/_{5} (f). ^{7}/_{9} □ ^{3}/_{9}

(g). ¼ □ ^{2}/_{8} (h). ^{6}/_{10} □ ^{4}/_{5}

(i). ¾ □ ^{7}/_{8} (j). ^{6}/_{10} □ ^{3}/_{5}

(k). ^{5}/_{7} □ ^{15}/_{21}

Answer:

6). The following fractions represent just three different numbers. Separate them into three groups of equivalent fractions, by changing each one to its simplest form.

(a). ^{2}/_{12} (b). ^{3}/_{15}

(c). ^{8}/_{50} (d). ^{16}/_{100}

(e). ^{10}/_{60} (f). ^{15}/_{75}

(g). ^{12}/_{60} (h). ^{16}/_{96}

(i). ^{12}/_{75} (j). ^{12}/_{72}

(k). ^{3}/_{18} (i) ^{4}/_{25}

Solution:

a). ^{2}/_{12}

^{2}/_{12} = ^{2 ÷ 2} / _{12÷ 2} = ^{1}/_{6}

(b). ^{3}/_{15}

^{3}/_{15} = ^{3 ÷3} /_{15 ÷ 3} = ^{1}/_{5}

(c). ^{8}/_{50}

^{8}/_{50} = ^{8 ÷ 2} / _{50 ÷ 2 }= ^{4}/_{25}

(d). ^{16}/_{100}

^{16}/_{100} = ^{16 ÷ 4}/_{100÷ 4} = ^{4}/_{25}

(e). ^{10}/_{60}

^{10}/_{60} = ^{10 ÷ 10}/_{60 ÷ 10} = ^{1} / _{6}

(f). ^{15}/_{75}

^{15}/_{75} = ^{15 ÷ 15}/_{75 ÷ 15} = ^{1}/_{5}

(g). ^{12}/_{60}

^{12}/_{60} = ^{12 ÷ 12} / _{60 ÷ 12} = ^{1}/_{5}

(h). ^{16}/_{96}

^{16}/_{96} = ^{16 ÷ 16} /_{96 ÷ 16} = ^{1}/_{6}

(i). ^{12}/_{75}

^{12}/_{75} = ^{12 ÷ 3} / _{75 ÷ 3} = ^{4} / _{25}

(j). ^{12}/_{72}

^{12}/_{72} = ^{12 ÷ 12} / _{72 ÷ 12} = ^{1}/_{6}

(k). ^{3}/_{18}

^{3}/_{18} = ^{3 ÷ 3 }/ _{18 ÷ 3} = ^{1}/_{6}

(i) ^{4}/_{25}

^{4}/_{25} = ^{4}/_{25}

7). Find answers to the following. Write and indicate how you solved them.

(a) Is ^{5}/_{9} equal to ^{4}/_{5}?

(b) Is ^{9}/_{16} equal to ^{5}/_{9}?

(c) Is ^{4}/_{5} equal to ^{16}/_{20}?

(d) Is ^{1}/_{15} equal to ^{4}/_{30}?

8). Ila read 25 pages of a book containing 100 pages. Lalita read ^{2}/_{5} of the same book. Who read less?

Pages read by Ila = 25/100 = 25 ÷ 25 / 100 ÷ 25 = 1/4

Pages read by Lalita = 2/5

1 X 5 = 5

4 X 2 = 8

5 < 8

¼ < 2/5

Ans: Ila read the less.

9). Rafiq exercised for ^{3}/_{6} of an hour, while Rohit exercised for ¾ of an hour. Who exercised for a longer time?

Exercise time of Rafiq = 3/6 = 3 ÷ 3/ 6 ÷ 3 = ½

Exercise time of Rohit = ¾

1 X 4 = 4

2 X 3 = 6

4 < 6

½ < ¾

3/6 < ¾

Ans: Rohit exercised for longer time.

10). In class A of 25 students, 20 passed with 60% or more marks; in another class B of 30 students, 24 passed with 60% or more marks. In which class was a greater fraction of students getting with 60% or more marks?

For class A

Students passed with 60% or more marks = 20/25

= 20 ÷5 / 25 ÷ 5

= 4/5

For class B

Students passed with 60% or more marks = 24/30

= 24 ÷6 / 30 ÷ 6

= 4/5

Comparing both the fractions 4/5 = 4/5

Ans: Both the classes A and B have same fraction.

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