Chapter 4: Fractions and Decimals

Ans: Neelam's father needs $1\dfrac{3}{4}{\text{m}}\left( {\dfrac{7}{4}{\text{m}}} \right)$ of cloth for the skirt of Neelam's new dress  

$\dfrac{1}{2}{\text{m}}$ for the scarf.

Total cloths buy by her father

 $= \dfrac{7}{4}m + \dfrac{1}{2}m$

   $= \dfrac{7}{4}m + \dfrac{{1 \times 2}}{{2 \times 2}}m$

   $= \dfrac{7}{4}m + \dfrac{2}{4}m$ 

$= \dfrac{{(7 + 2)}}{4}m$

$= \dfrac{9}{4}m$ or $2\dfrac{1}{3}m$

The total cloth Neelam should buy is $\dfrac{9}{4}{\text{m}}$ or $2\dfrac{1}{3}{\text{m}}$

Ans: Equal denominators added.

Ans: Numerator and denominator are added.

Ans: Know that $1{\text{m}} = 100{\text{cm}}$

$1{\text{cm}} = \dfrac{1}{{100}}{\text{m}}$

Now,

$1$ meters $40$ centimeters $ + 60$ centimeters.

$= 1{\text{m}} + \dfrac{{40}}{{100}}{\text{m}} + \dfrac{{60}}{{100}}{\text{m}}$

$1{\text{m}} + 0.40{\text{m}} + 0.60{\text{m}} = 2.00{\text{m}}$

So, $2.6{\text{m}} > 2.0{\text{m}}$

Ans:

Match the correct following

Column I	Column II
(i) $\dfrac{6}{4}$	(D)
(ii) $\dfrac{6}{{10}}$	(A)
(iii) $\dfrac{6}{6}$	(E)
(iv) $\dfrac{6}{{16}}$	(B)

Ans: From the of collection $0,1,2,3,4,5 \to 1,2,3,4,5$ is natural numbers

The fraction that represents the number of natural numbers to the total numbers $= \dfrac{5}{6}$ 

The whole numbers are $0,1,2,3,4$and $5$.

The fraction that represents the number of whole numbers to the total numbers $= \dfrac{6}{6}$

Ans: Total collection of numbers $- 3, - 2, - 1, 0, 1, 2, 3$ and out of these $1, 2$ and $3$ is natural number and $0, 1, 2$ and $3$ are whole number and $- 3, - 2, - 1,0,1,2,3$ are integers.

Ans: Let one fraction be $x$ . 

Another fraction be $\dfrac{7}{{11}} - x$ Now, according to question, 

$x - \left( {\dfrac{7}{{11}} - x} \right) = \dfrac{2}{{11}}$

$x - \dfrac{7}{{11}} + x = \dfrac{2}{{11}}$

$\dfrac{{11x}}{{11}} - \dfrac{7}{{11}} + \dfrac{{11x}}{{11}} = \dfrac{2}{{11}}$

$\dfrac{{11x - 7 + 11x}}{{11}} = \dfrac{2}{{11}}$

$22x - 7 = \dfrac{2}{{11}} \times 11$

$22x - 7 = 2$

$22x = 2 + 7 = 9$

$x = \dfrac{9}{{22}}$

Thus, the fraction is $\dfrac{9}{{22}}$ and another fraction is

$\dfrac{7}{{11}} - \dfrac{9}{{22}} = \dfrac{{7 \times 2}}{{11 \times 2}} - \dfrac{9}{{22}}$

$= \dfrac{{14 - 9}}{{22}}$

$= \dfrac{5}{{22}}$ 

Pair of fractions are $\dfrac{9}{{22}}$ and $\dfrac{5}{{22}}$.

Ans: Since, we know that the measurement of a straight angle is ${180^\circ }$ and a right angle is ${90^\circ }$. The required fraction is $\dfrac{{{{90}^\circ }}}{{{{180}^\circ }}} = \dfrac{1}{2}$.

The fraction of straight angle is a right angle is $\dfrac{1}{2}$.

Ans: 

fractions whose numerators are less than the denominators are called proper fractions. (Numerator < denominator) and fraction is less than one.

fractions with the numerator either equal to or greater than the denominator are called improper fractions. (Numerator = denominator or, Numerator > denominator) and the fraction is greater and equal than one.

Now, cards in Bag -I

(i) $\dfrac{3}{7}$

(iv) $\dfrac{8}{9}$

(v) $\dfrac{5}{6}$

(vi) $\dfrac{6}{{11}}$

(viii) $\dfrac{{19}}{{25}}$

(ix) $\dfrac{2}{3}$and (x) $\dfrac{{13}}{{17}}$

Cards in Bag-II

(ii) $\dfrac{4}{4}$ and (vii) $\dfrac{{18}}{{18}}$

Cards in Bag -III

(iii) $\dfrac{9}{8}$

NCERT Exemplar solutions for Class 6 Mathematics Chapter 4 Fractions and Decimals consists of a fraction which is a number that represents a fraction of a total. This complete may be a single item or a set of items. Fractions with 10, 100 denominators, etc. can be written in the correct order, using a decimal point, called decimal or decimal numbers. Let us now consider some of the concepts discussed in this Chapter.

• Multiplication and division of fractions and other concepts, such as types of fractions.

•  How to change different fractions to like fractions

•  How to compare more than two fractions.

•  How to turn a decimal into a fraction.

•  Converting a fraction into a decimal, adding, and subtracting decimal.

•  Decimal multiplication by 10, 100, 100, etc.

•  Decimal multiplication by a whole number, decimal multiplication by the decimal.