These NCERT Solutions for Class 6 Maths Chapter 7 Fractions Ex 7.4 Questions and Answers are prepared by our highly skilled subject experts.

## NCERT Solutions for Class 6 Maths Chapter 7 Fractions Exercise 7.4

Question 1.

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

(c) Show \(\frac{2}{6}, \frac{4}{6}, \frac{8}{6}, \frac{6}{6}\) on the number line. Put appropriate signs between the fractions given.

Answer:

The fractions represented by the shaded portions are as follows:

(a) \(\frac{3}{8}, \frac{6}{8}, \frac{4}{8}, \frac{1}{8}\)

(b) \(\frac{8}{9}, \frac{4}{9}, \frac{6}{9}, \frac{6}{9}\)

When we compare two fractions

Note:

Like Fractions: If the denominator is same, the fraction with the greater numerator is greater.

Unlike Fractions: If the denominator is not same, we first get their equivalent fractions with a denominator which is the L.C.M of the denominators of both the fractions.

The above fractions in (a) and (b) are like fractions as they have the same denominator.

When comparing fractions with same denominator,

So, arranging the fractions in ascending order, we have

(a) \(\frac{1}{8}<\frac{3}{8}<\frac{4}{8}<\frac{6}{8}\)

(b) \(\frac{3}{9}<\frac{4}{9}<\frac{6}{9}<\frac{8}{9}\)

(c) Let us represent the fractions \(\frac{2}{6}, \frac{4}{6}, \frac{8}{6}, \frac{6}{6}\) on the number line.

Again these comparisons are between the like fractions, so numerator will dictate the sign:

Question 2.

Compare the fractions and put an appropriate sign.

Answer:

(a) Here, we have Tike fractions’ so we compare them by their numerators only.

(b) Here, we have ‘unlike fractions’ with same numerators, so we compare them with their denominators only.

(c) Like fractions, so we compare by their numerators only.

(d) ‘Unlike fractions’ with same nemerators so we compare them by their denominators, only.

Question 3.

Make five more such pairs and put appropriate signs.

Answer:

Question 4.

Look at the figures and write ‘<’ or ‘>’, ‘=’ between the given pairs of fractions.

Make five more such problems and solve them with you friends.

Answer:

(a) <

(b) >

(c) >

(d) =

(e) <

Question 5.

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

Answer:

(a) | If the numerator is same, then the smaller of the denominator fraction is bigger | > |

(b) | \(\frac{2}{4}=\frac{1}{2}\) and \(\frac{3}{6}=\frac{1}{2}\) | = |

(c) | These are unlike fractions, So, \(\frac{3}{5}=\frac{9}{15}\) and \(\frac{2}{3}=\frac{10}{15}\) | < |

(d) | \(\frac{3}{4}=\frac{3}{4}\) and \(\frac{2}{8}=\frac{1}{4}\) | > |

(e) | Like fraction | < |

(f) | Like fraction | > |

(g) | \(\frac{1}{4}=\frac{1}{4}\) and \(\frac{2}{8}=\frac{1}{4}\) | ^{=} |

(h) | \(\frac{6}{10}=\frac{3}{5}\) and \(\frac{4}{5}=\frac{4}{5}\) | < |

(i) | Unlike fraction | < |

(j) | \(\frac{6}{10}=\frac{3}{5}\) | = |

(k) | \(\frac{5}{7}=\frac{15}{21}\) | ^{=} |

Question 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.

Answer:

Simplifying the fractions into simplest form.

Totally these are three graps of equivalent fractions 1

\(\frac { 1 }{ 6 }\) = (i) (v) (viii) (x) (xi)

\(\frac { 1 }{ 5 }\) = (ii) (vi) (vii)

\(\frac { 4 }{ 25 }\) = (iii) (iv) (ix) (xii)

Question 7.

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

(a) Is \(\frac { 5 }{ 9 }\) equal to \(\frac { 4 }{ 5 }\) ?

(b) Is \(\frac { 9 }{ 16 }\) equal to \(\frac { 5 }{ 9 }\) ?

(c) Is \(\frac { 4 }{ 5 }\) equal to \(\frac { 16 }{ 20 }\) ?

(d) Is \(\frac { 1 }{ 15 }\) equal to \(\frac { 4 }{ 30 }\) ?

Answer:

We need to first simplify each fraction. After simplification if they are equal, else it is not equal

(a) Not equal

(b) Not equal

(c) Equal

(d) Not equal

Question 8.

Ila read 25 pages of a book containing 100 pages. Lalita read \(\frac { 2 }{ 5 }\) of the same book. who read less?

Answer:

Total number of pages in the book = 100 pages

Number of pages read by Ila = 25 pages

Fraction of pages read by Ila = \(\frac { 25 }{ 100 }\)

= \(\frac { 1 }{ 4 }\)

Lauta read \(\frac { 2 }{ 5 }\) of the same book

So, basically we need to compare the fraction \(\frac { 1 }{ 4 }\) and \(\frac { 2 }{ 5 }\)

Since, they are unlike fractions, we need to find LCM of 4 and 5 which is 20.

So \(\frac{1}{4}=\frac{5}{20}\)

\(\frac{2}{5}=\frac{8}{20}\)

Now, 8 > 5

So Ila read lesser than Lauta.

Question 9.

Rafiq exercised for \(\frac { 3 }{ 6 }\) of an hour, while Rohit exercised for \(\frac { 3 }{ 4 }\) of an hour. Who exercised for a longer time?

Answer:

Rafiq = \(\frac { 3 }{ 6 }\)

Rohit = \(\frac { 3 }{ 4 }\)

We need to compare the fractions. Since these are unlike fraction, we need to calculate the LCM and 4 and 6. LCM of 4 and 6 is 12.

Rafiq = \(\frac{3}{6}=\frac{6}{12}\)

Rahit = \(\frac{3}{4}=\frac{9}{12}\)

\(\frac{9}{12}>\frac{6}{12}\)

∴ Rohit exercised for a longer time than Rafiq.

Question 10.

In a 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?

Answer:

Total number of students in class A = 25 Number of students passed in first class in class A = 20.

Fraction of students of class A who passed in first class = \(\frac{20}{25}=\frac{4}{5}\)

Total number of students in class B = 30 Number of students passed in first class = 24.

Fraction of students of class B who passed in first class = \(\frac{24}{30}=\frac{4}{5}\)

Both class A and B have the same fraction of students who passed in first class.