NCERT Exemplar for Class 6 Maths Solutions Chapter 4 Fractions & Decimals

In examples 1 and 2, write the correct answer from the given four options:

Example 1. Which of the following fractions is the smallest?

(A) ${\displaystyle \frac{11}{9}}$

(B) ${\displaystyle \frac{11}{7}}$

(C) ${\displaystyle \frac{11}{10}}$

(D) ${\displaystyle \frac{11}{6}}$

Ans: Option (C) is correct

The following fraction of ${\displaystyle \frac{11}{9}}=1.22$

For, ${\displaystyle \frac{11}{7}}=1.57$

For, ${\displaystyle \frac{11}{10}}=1.1$

For, ${\displaystyle \frac{11}{6}}=1.83$

In the following fractions ${\displaystyle \frac{11}{10}}$ have smallest value

So, the option (C) is correct.

Example 2: 0.7625 lies between

(A) $0.7$ and $0.76$

(B) $0.77$ and $0.78$

(C) $0.76$ and $0.761$

(D) $0.76$ and $0.763$

Ans:  Option (D) is correct.

By using the number line the $0.7625$ is lies between $0.76$ and $0.763$

Example 3: Fill in the blanks so that the statement is true:

Decimal $8.125$is equal to the fraction______

Ans:${\displaystyle \frac{65}{8}}$ or $8{\displaystyle \frac{1}{8}}$ 

fraction for the decimal point is $8.125={\displaystyle \frac{8125}{1000}}$

Example 4: Fill in the blanks so that the statement is true:

$6.45-3.78=$_____

Ans: $2.67$

The subtract the numbers get $6.45-3.78=2.67$

Example 5: State true or false:

The fraction $14{\displaystyle \frac{2}{5}}$ is equal to $\mathbf{14}.\mathbf{2}.$

Ans: The given statement is false.

For fraction is $14{\displaystyle \frac{2}{10}}=14.2$ 

Example 6: Fill in the blanks using > or <

${\displaystyle \frac{8}{45}}\mathrm{\_}\mathrm{\_}{\displaystyle \frac{16}{89}}$

Ans: For the fraction ${\displaystyle \frac{8}{45}}={\displaystyle \frac{8\times 2}{45\times 2}}={\displaystyle \frac{16}{90}}$

Now, ${\displaystyle \frac{16}{90}}<{\displaystyle \frac{16}{89}},$ 

Therefore,  ${\displaystyle \frac{8}{45}}<{\displaystyle \frac{16}{89}}$

Example 7: Express ${\displaystyle \frac{12}{25}}$ as a decimal.

Ans: The fraction for ${\displaystyle \frac{12}{25}}={\displaystyle \frac{12\times 4}{25\times 4}}$

$={\displaystyle \frac{48}{100}}=0.48$

Decimal for the fraction ${\displaystyle \frac{12}{25}}$ is $0.48$

Example 8: Convert $\mathbf{5809}\mathbf{g}$ to kg.

Ans: Since $1000\text{g}=1\text{kg},$

$\text{So, }5809\text{g}={\displaystyle \frac{5809}{1000}}\text{kg}$

$=5.809\text{kg}.$ 

Example 9: Round off $\mathbf{87}.\mathbf{952}$ to tenths place. 

Ans: For rounding off to tenths place, we look at the hundredths place. 

Here the digit is $5$. So, the digit at the tenths place will be increased by $1$

Hence, rounding off $87.952$ to tenths place, we get $88.0$

Example 10: Add the fractions $5{\displaystyle \frac{3}{8}}$ and ${\displaystyle \frac{5}{16}}$

Ans: For the addition of fraction 

Rewrite the mixed fraction

$5{\displaystyle \frac{3}{8}}+{\displaystyle \frac{5}{16}}={\displaystyle \frac{43}{8}}+{\displaystyle \frac{5}{16}}$

$={\displaystyle \frac{43\times 2}{8\times 2}}+{\displaystyle \frac{5}{16}}={\displaystyle \frac{86}{16}}+{\displaystyle \frac{5}{16}}$

$={\displaystyle \frac{86+5}{16}}={\displaystyle \frac{91}{16}}=5{\displaystyle \frac{11}{16}}$

Example 11: What should be added to $37.28$ to obtain $\mathbf{46}.\mathbf{8}$?

Ans:  Let the missing number is $x$

So, $37.28+x=46.8$

$x=46.8-37.28$

$=9.52$

Hence, the required number to be added to $37.28is9.52$

Example 12: Arrange the following in ascending order.

$2.2,2.023,2.0226,22.1,20.42$

Ans: To arrange them from the smallest to the greatest number. 

We arrange them as follows 

using the idea of place value and comparing their digits at different places

$2.0226<2.023<2.2<20.42<22.1.$

Example 13: Gorang purchased $2kg280g$ apples, $3kg375g$ bananas, $225g$ grapes and $5kg385g$ oranges. Find the total weight of the fruits purchased by Gorang in kg.

Ans: Since $1\text{kg}=1000\text{g}$

Weight of apples $=2\text{kg}280\text{g}=2280\text{g}$ 

Weight of bananas $=3\text{kg}375\text{g}=3375\text{g}$

Weight of grapes $=225\text{g}$

Weight of oranges $=5\text{kg}385\text{g}=5385\text{g}$

Total weight $=2280\text{g}+3375\text{g}+225\text{g}+5385\text{g}\text{ = }11265g$

Thus, total weight $=11265\text{g}={\displaystyle \frac{11265}{1000}}\text{kg}$

$=11.265\text{kg}$

Example 14: What is wrong in the following?

${\displaystyle \frac{7}{4}}+{\displaystyle \frac{5}{2}}={\displaystyle \frac{7+5}{4+2}}={\displaystyle \frac{12}{6}}=2$

Ans: Writing ${\displaystyle \frac{7}{4}}+{\displaystyle \frac{5}{2}}={\displaystyle \frac{7+5}{4+2}}$ is wrong. It should be as follows:

Converting into like fractions

${\displaystyle \frac{7}{4}}+{\displaystyle \frac{5}{2}}={\displaystyle \frac{7}{4}}+{\displaystyle \frac{10}{4}}$ 

Only numerators are added

${\displaystyle \frac{7+10}{4}}={\displaystyle \frac{17}{4}}$ 

In Questions 1 to 20, out of the four Options, only one Answer is Correct Choose the correct answer

1. The fraction which is not equal to ${\displaystyle \frac{4}{5}}$ is

(A) ${\displaystyle \frac{40}{50}}$

(B) ${\displaystyle \frac{12}{15}}$

(C) ${\displaystyle \frac{16}{20}}$

(D) ${\displaystyle \frac{9}{15}}$

Ans: Option D is right

Check option $A\Rightarrow {\displaystyle \frac{40÷10}{50÷10}}={\displaystyle \frac{4}{5}}$

Check option $\text{B}\Rightarrow {\displaystyle \frac{12}{15}}={\displaystyle \frac{4}{5}}$

Check option $\text{C}\Rightarrow {\displaystyle \frac{16}{20}}={\displaystyle \frac{4}{5}}$

Check option $\text{D}\Rightarrow {\displaystyle \frac{9}{15}}={\displaystyle \frac{3}{5}}$

2. The two consecutive integers between which the fraction ${\displaystyle \frac{5}{7}}$ lies are

(A) $\mathbf{5}$ and $\mathbf{6}$

(B) $\mathbf{0}$ and $\mathbf{1}$

(C) $\mathbf{5}$ and $7$

(D) $\mathbf{6}$ and $\mathbf{7}$

Ans: Option B is right

Fundamental from fraction, if the value of a numerator of each fraction implies less than this value of denominator, ever lies between and $0$ and $1$.

Hence, ${\displaystyle \frac{5}{7}}$ are lies between $0$ and $1$.

3. When ${\displaystyle \frac{1}{4}}$ is written with denominator as $\mathbf{12}$, its numerator is

(A) $\mathbf{3}$

(B) $\mathbf{8}$

(C) $\mathbf{24}$

(D) $\mathbf{12}$

Ans: Option A is right

Since, $\Rightarrow {\displaystyle \frac{1}{4}}\times {\displaystyle \frac{3}{3}}={\displaystyle \frac{3}{12}}$

4. Which of the following is not in the lowest form?

(A) ${\displaystyle \frac{7}{5}}$

(B) ${\displaystyle \frac{15}{20}}$

(C) ${\displaystyle \frac{13}{33}}$

(D) ${\displaystyle \frac{27}{28}}$

Ans: Option B is right

In case of ${\displaystyle \frac{5}{7}}$, the common factor of $7$ and $5$ is $1$.

Hence, already given in the simplest form.

In case of ${\displaystyle \frac{15}{20}}$, the common factor of $15$ and $20$ is $4.$

In case of ${\displaystyle \frac{13}{33}}$, the common factor of $13$ and $33$ is $1$.

Hence, already given in the simplest form.

In case of ${\displaystyle \frac{27}{28}}$, the common factor of $27$ and $28$ is $1$.

Hence, already given in the simplest form.

Hence, ${\displaystyle \frac{15}{20}}$ not given in the simplest form.

5. If ${\displaystyle \frac{5}{8}}={\displaystyle \frac{20}{p}}$, then value of $p$ is

(A) $\mathbf{23}$

(B) $\mathbf{2}$

(C) $\mathbf{32}$

(D) $\mathbf{16}$

Ans: Option $\text{C}$ is right

${\displaystyle \frac{5}{8}}={\displaystyle \frac{20}{\text{p}}}$

$\Rightarrow 5\times \text{p}=20\times 8$

$\Rightarrow \text{p}={\displaystyle \frac{20\times 8}{5}}$

$\Rightarrow \text{p}=4\times 8=32$

Hence, Value of $\text{p}$ is 32

6. Which of the following is not equal to the others?

(A) ${\displaystyle \frac{6}{8}}$

(B) ${\displaystyle \frac{12}{16}}$

(C) ${\displaystyle \frac{15}{25}}$

(D) ${\displaystyle \frac{18}{24}}$

Ans: Option $\text{C}$ is right

Check option $\text{A}\Rightarrow {\displaystyle \frac{6}{8}}={\displaystyle \frac{3}{4}}$

Check option $\text{B}\Rightarrow {\displaystyle \frac{12÷4}{16÷4}}={\displaystyle \frac{3}{4}}$

Check option $\text{C}\Rightarrow {\displaystyle \frac{15÷5}{25÷5}}={\displaystyle \frac{3}{5}}$

Check option D $\Rightarrow {\displaystyle \frac{18÷6}{24÷6}}={\displaystyle \frac{3}{4}}$

Thus, Option $\text{C}$ is not equal to the other option.

7. Which of the following fractions is the greatest?

(A) ${\displaystyle \frac{5}{7}}$

(B) ${\displaystyle \frac{5}{6}}$

(C) ${\displaystyle \frac{5}{9}}$

(D) ${\displaystyle \frac{5}{8}}$

Ans: Option B is right

In the above option given that, among the entire fraction with same numerator, the one with smaller denominator will be greatest.

Thus, required fraction is ${\displaystyle \frac{5}{6}}$.

8. Which of the following fractions is the smallest?

(A) ${\displaystyle \frac{7}{8}}$

(B) ${\displaystyle \frac{9}{8}}$

(C) ${\displaystyle \frac{3}{8}}$

(D) ${\displaystyle \frac{5}{8}}$

Ans: Option C is right

In the above option given that, among the entire fraction with same denominator, the one with smaller numerator will be smallest.

Thus, required fraction is ${\displaystyle \frac{3}{8}}$.

9. Sum of ${\displaystyle \frac{4}{17}}$ and ${\displaystyle \frac{15}{17}}$ is

(A) ${\displaystyle \frac{19}{17}}$

(B) ${\displaystyle \frac{11}{17}}$

(C) ${\displaystyle \frac{19}{34}}$

(D) ${\displaystyle \frac{2}{17}}$

Ans: Option A is right 

${\displaystyle \frac{4}{17}}$ and ${\displaystyle \frac{15}{17}}$

Take the LCM of denominators

$\Rightarrow {\displaystyle \frac{4}{17}}+{\displaystyle \frac{15}{17}}={\displaystyle \frac{4+15}{17}}$

$={\displaystyle \frac{19}{17}}$

Thus, required fraction is ${\displaystyle \frac{19}{17}}$.

10. On subtracting ${\displaystyle \frac{5}{9}}$ from ${\displaystyle \frac{19}{9}}$, the result is

(A) ${\displaystyle \frac{24}{9}}$

(B) ${\displaystyle \frac{14}{9}}$

(C) ${\displaystyle \frac{14}{18}}$

(D) ${\displaystyle \frac{14}{0}}$

Ans: Option B is right 

${\displaystyle \frac{5}{9}}$ from ${\displaystyle \frac{19}{9}}$

Take the LCM of denominators

   $\Rightarrow {\displaystyle \frac{19}{9}}-{\displaystyle \frac{5}{9}}={\displaystyle \frac{19-5}{9}}$

   $={\displaystyle \frac{14}{9}}$ 

Thus, required fraction is ${\displaystyle \frac{14}{9}}$.

11. $0.7499$lies between

(A) $0.7$and $0.74$

(B)$0.75$ and $0.79$

(C) $\mathbf{0}.\mathbf{749}\mathbf{and}\mathbf{0}.\mathbf{75}$

(D) $\mathbf{0}.\mathbf{74992}\mathbf{and}\mathbf{0}.\mathbf{75}$

Ans: Option $\text{C}$ is right

$0.7499$ is successor of $0.749$and predecessor of $0.75$

Thus, $0.749$lies between $0.749$and $0.75$

12. $\mathbf{0}.\mathbf{023}$lies between

(A) $0.2and0.3$

(B)$\mathbf{0}.\mathbf{02}\mathbf{and}\mathbf{0}.\mathbf{03}$

(C)$\mathbf{0}.\mathbf{03}\mathbf{and}\mathbf{0}.\mathbf{029}$

(D)$\mathbf{0}.\mathbf{026}\mathbf{and}\mathbf{0}.\mathbf{024}$

Ans: Option B is right

Thus, $0.023$lies between $0.02$and $0.03$

13. ${\displaystyle \frac{11}{7}}$ can be expressed in the form

(A) $7{\displaystyle \frac{1}{4}}$

(B) $4{\displaystyle \frac{1}{7}}$

(C) $1{\displaystyle \frac{4}{7}}$

(D) $11{\displaystyle \frac{1}{7}}$

Ans: Option $\text{C}$ is right

The mix fraction of ${\displaystyle \frac{11}{7}}$ is $1{\displaystyle \frac{4}{7}}$

14. The mixed fraction $5{\displaystyle \frac{4}{7}}$ can be expressed as

(A) ${\displaystyle \frac{33}{7}}$

(B) ${\displaystyle \frac{39}{7}}$

(C) ${\displaystyle \frac{33}{4}}$

(D) ${\displaystyle \frac{39}{4}}$

Ans: Option B is right

  $\because 5{\displaystyle \frac{4}{7}}={\displaystyle \frac{(7\times 5)+4}{7}}$

   $={\displaystyle \frac{35+4}{7}}$

   $={\displaystyle \frac{39}{5}}$ 

15. $0.07+0.008$ is equal to

(A) $\mathbf{0}.\mathbf{15}$

(B)$\mathbf{0}.\mathbf{015}$

(C)$\mathbf{0}.\mathbf{078}$

(D)$\mathbf{0}.\mathbf{78}$

Ans: Option $\text{C}$ is right

Sum of $0.07+0.008$ is $\mathbf{0}.\mathbf{078}$

16. Which of the following decimals is the greatest?

(A) $\mathbf{0}.\mathbf{182}$

(B)$\mathbf{0}.\mathbf{0925}$

(C)$\mathbf{0}.\mathbf{29}$

(D)$\mathbf{0}.\mathbf{038}$

Ans: Option $\text{C}$ is right

Convert the above option into like decimal as $0.1820,0.0925,0.2900$and $0.0380.$

Thus, comparing the value of like decimal value, $0.2900$ is the greatest among the given option.

17. Which of the following decimals is the smallest?

(A) $\mathbf{0}.\mathbf{27}$

(B)$\mathbf{1}.\mathbf{5}$

(C)$\mathbf{0}.\mathbf{082}$

(D)$\mathbf{0}.\mathbf{103}$

Ans: Option $\text{C}$ is right

Convert the above option into like decimal as $0.270,1.500,0.082\text{ and }0.103.$

Thus, comparing the value of like decimal value, $0.082$is the smallest among the given option.

18. $13.572$correct to the tenths place is

(A) $\mathbf{10}$

(B)$\mathbf{13}.\mathbf{57}$

(C)$\mathbf{14}.\mathbf{5}$

(D)$\mathbf{13}.\mathbf{6}$

Ans: Option D is right

Round off the number $13.572$is $13.6$

19. $15.8-6.73$ is equal to

(A) $\mathbf{8}.\mathbf{07}$

(B)$\mathbf{9}.\mathbf{07}$

(C)$\mathbf{9}.\mathbf{13}$

(D)$\mathbf{9}.\mathbf{25}$

Ans: Option B is right

Subtraction of $15.8-6.73$is $\mathbf{9}.\mathbf{07}$

20. The decimal $0.238$ is equal to the fraction

  (A) ${\displaystyle \frac{119}{500}}$

  (B) ${\displaystyle \frac{238}{25}}$

  (C) ${\displaystyle \frac{199}{25}}$

  (D) ${\displaystyle \frac{119}{50}}$ 

Ans: Option A is right

Thus, $0.238$

fraction for $0.238$

   $\Rightarrow {\displaystyle \frac{238}{1000}}={\displaystyle \frac{238÷2}{1000÷2}}$

   $={\displaystyle \frac{119}{500}}$ 

Thus, required option ${\displaystyle \frac{119}{500}}.$

In Questions 21 to 44, fill in the blanks to make the Statements True

21. A number representing a part of a_____is called a fraction.

Ans: A number representing a part of a whole is called a fraction.

22. A fraction with denominator greater than the numerator is called a ____fraction.

Ans: A fraction with denominator greater than the numerator is called a proper fraction

23. fractions with the same denominator are called ____ fractions.

Ans: fractions with the same denominator are called like fractions.

24. $13{\displaystyle \frac{5}{18}}$ Is a ____ fraction.

Ans: $13{\displaystyle \frac{5}{8}}$ Is a mix fraction.

25. ${\displaystyle \frac{18}{8}}$ Is a______ fraction.

Ans: ${\displaystyle \frac{18}{5}}$ Is a improper fraction

26. ${\displaystyle \frac{7}{19}}$ Is a_____ fraction.

Ans: ${\displaystyle \frac{7}{19}}$ Is a proper fraction.

27. ${\displaystyle \frac{5}{8}}$ and ${\displaystyle \frac{3}{8}}$ Are _____ proper fractions.

Ans: ${\displaystyle \frac{5}{8}}$ and ${\displaystyle \frac{3}{8}}$ Are like proper fractions.

28. ${\displaystyle \frac{6}{11}}$ and ${\displaystyle \frac{6}{13}}$ Are____ proper fractions.

Ans: ${\displaystyle \frac{6}{11}}$ and ${\displaystyle \frac{6}{13}}$ are unlike proper fractions.

29. The fraction ${\displaystyle \frac{6}{15}}$ in simplest form is______

Ans: Given fraction is ${\displaystyle \frac{6}{15}}={\displaystyle \frac{6÷3}{15÷3}}={\displaystyle \frac{2}{5}}$

The fraction ${\displaystyle \frac{6}{15}}$ in simplest form is ${\displaystyle \frac{2}{5}}$

30. The fraction ${\displaystyle \frac{17}{34}}$ in simplest forms is_____

Ans: Given fraction is ${\displaystyle \frac{17}{34}}={\displaystyle \frac{17÷17}{34÷17}}={\displaystyle \frac{1}{2}}$

The fraction ${\displaystyle \frac{17}{34}}$ in simplest form is ${\displaystyle \frac{1}{2}}$

31. ${\displaystyle \frac{18}{135}}$ and ${\displaystyle \frac{90}{675}}$ Are proper, unlike and _____ fractions.

Ans: ${\displaystyle \frac{18}{135}}$ and ${\displaystyle \frac{90}{675}}$ Are proper, unlike and equivalent fractions.

32. $8{\displaystyle \frac{2}{7}}$ Is equal to the improper fraction_____

Ans: Given fraction is 

  $8{\displaystyle \frac{7}{2}}={\displaystyle \frac{(8\times 7)+7}{2}}$

  $={\displaystyle \frac{56+2}{7}}$

   $={\displaystyle \frac{58}{7}}$ 

$8{\displaystyle \frac{2}{7}}$ Is equal to the improper fraction ${\displaystyle \frac{58}{7}}$

33. ${\displaystyle \frac{87}{7}}$ Is equal to the mixed fraction _____

Ans: By long division the quotient and reminder will be $12\text{and}3$

 ${\displaystyle \frac{87}{7}}$ Is equal to the mixed fraction $12{\displaystyle \frac{3}{7}}$

34. $9+{\displaystyle \frac{2}{10}}+{\displaystyle \frac{6}{100}}$ Is equal to the decimal number_____

Ans: The LCM of $10$ and $100$ is$100$.

Hence, $9+{\displaystyle \frac{2}{10}}+{\displaystyle \frac{6}{100}}$

$={\displaystyle \frac{9\times 100+2\times 10+6}{100}}$

$\Rightarrow {\displaystyle \frac{962}{100}}=9.26$

35. Decimal $\mathbf{16}.\mathbf{25}$are equal to the fraction _____

Ans: Now, $16.25$

$\Rightarrow {\displaystyle \frac{1625}{100}}={\displaystyle \frac{1625÷25}{100÷25}}={\displaystyle \frac{65}{4}}$

Decimal $16.25$are equal to the fraction ${\displaystyle \frac{65}{4}}$.

36. fraction ${\displaystyle \frac{7}{25}}$ is equal to the decimal number

Ans: Given fraction is 

  ${\displaystyle \frac{7}{25}}={\displaystyle \frac{7\times 4}{25\times 4}}$

   $={\displaystyle \frac{28}{100}}$

   $=0.28$ 

fraction ${\displaystyle \frac{7}{25}}$ is equal to the decimal number $0.28$

37. ${\displaystyle \frac{17}{9}}+{\displaystyle \frac{41}{9}}=$

Ans: Explanation,

For the fractions denominator is same so add only numerator

$\Rightarrow {\displaystyle \frac{17}{9}}+{\displaystyle \frac{41}{9}}={\displaystyle \frac{17+41}{9}}={\displaystyle \frac{58}{9}}$

So,

${\displaystyle \frac{17}{9}}+{\displaystyle \frac{41}{9}}={\displaystyle \frac{58}{9}}$

38. ${\displaystyle \frac{67}{14}}-{\displaystyle \frac{14}{14}}=$

Ans: Explanation,

For the fractions denominator is same so subtract only numerator

$\Rightarrow {\displaystyle \frac{67}{14}}-{\displaystyle \frac{24}{14}}={\displaystyle \frac{67-24}{14}}={\displaystyle \frac{43}{14}}$

Hence,

${\displaystyle \frac{67}{14}}-{\displaystyle \frac{24}{14}}={\displaystyle \frac{43}{14}}$

39. ${\displaystyle \frac{17}{2}}+3{\displaystyle \frac{1}{2}}=$

Ans: Explanation,

Rewrite the mixed fraction and add the numerator

$\Rightarrow {\displaystyle \frac{17}{2}}+3{\displaystyle \frac{1}{2}}={\displaystyle \frac{17}{2}}+{\displaystyle \frac{7}{2}}={\displaystyle \frac{17+7}{2}}$

$\Rightarrow {\displaystyle \frac{24}{2}}={\displaystyle \frac{24÷2}{2÷2}}=12$

Hence, ${\displaystyle \frac{17}{2}}+3{\displaystyle \frac{1}{2}}=12$

40. $9{\displaystyle \frac{1}{4}}-{\displaystyle \frac{5}{4}}=$

Ans: Explanation,

Rewrite the mixed fraction and subtract the numerator

   $\Rightarrow 9{\displaystyle \frac{1}{4}}-{\displaystyle \frac{5}{4}}={\displaystyle \frac{37}{4}}-{\displaystyle \frac{5}{4}}$

   $={\displaystyle \frac{37-5}{4}}={\displaystyle \frac{32}{4}}$

   $\Rightarrow {\displaystyle \frac{32÷4}{4÷4}}=8$ 

Therefore, $9{\displaystyle \frac{1}{4}}-{\displaystyle \frac{5}{4}}=8$

41. $4.55+9.73=$

Ans: Add the numbers

$4.55+9.73=14.28$

42. $8.76-2.68=$

Ans: Subtract the numbers

$8.76-2.68=6.08$

43. The value of 50 coins of 50 paisa $=$ Rs____

Ans: $50\times 50=2500$ paisa

   $\Rightarrow \text{ Rs}\text{. }{\displaystyle \frac{2500}{100}}=\text{ Rs}\text{.}{\displaystyle \frac{2500÷100}{100÷100}}$

   $=\text{ Rs}\text{. }25$ 

The value of 50 coins of 50 paisa $=$ Rs. 25

44. 3 Hundredths $+3$tenths $=$

Ans: 3 Hundredths $=0.03$

3 tenths$=0.3$

3 Hundredths $+3$ tenths $=0.33$

In Each of the Questions 45 to 65, state Whether the Statement is True or False

45. fractions with the same numerator are called like fractions. 

Ans: The given statement is False 

The correct statement is fractions with the same denominator are called like fractions.

46. fraction ${\displaystyle \frac{18}{39}}$ is in its lowest form.

Ans: The statement is False

Because the fraction is in lowest form is

${\displaystyle \frac{18}{39}}\Rightarrow {\displaystyle \frac{18÷3}{39÷3}}={\displaystyle \frac{6}{13}}$

47. fractions ${\displaystyle \frac{15}{39}}$ and ${\displaystyle \frac{45}{117}}$ are equivalent fractions.

Ans: The statement is True

It is divide by same number

${\displaystyle \frac{45}{117}}\Rightarrow {\displaystyle \frac{45÷3}{117÷3}}={\displaystyle \frac{15}{39}}$

So, Both are equivalent.

48. The sum of two fractions is always a fraction.

Ans: The statement is True

Let, two fraction ${\displaystyle \frac{17}{9}}$ and ${\displaystyle \frac{41}{9}}$

${\displaystyle \frac{17}{9}}+{\displaystyle \frac{41}{9}}={\displaystyle \frac{58}{9}}$

Explanation,

$\Rightarrow {\displaystyle \frac{17}{9}}+{\displaystyle \frac{41}{9}}={\displaystyle \frac{17+41}{9}}={\displaystyle \frac{58}{9}}$, 

This is a fraction.

49. The result obtained by subtracting a fraction from another fraction is necessarily a fraction.

Ans: The statement is False

Let, two fraction ${\displaystyle \frac{24}{14}}$ and ${\displaystyle \frac{67}{14}}$

${\displaystyle \frac{24}{14}}-{\displaystyle \frac{67}{14}}=-{\displaystyle \frac{43}{14}}$

Explanation, 

$\Rightarrow {\displaystyle \frac{24}{14}}-{\displaystyle \frac{67}{14}}={\displaystyle \frac{24-67}{14}}=-{\displaystyle \frac{43}{14}}$, 

which is not a fraction.

50. If a whole or an object is divided into a number of equal parts, then each part represents a fraction.

Ans: The statement is True

51. The place value of a digit at the tenths place is 10 times the same digit at the one's place.

Ans: The given statement is False

The place value of a digit at the tenths place is ${\displaystyle \frac{1}{10}}$ times the same digit at the one's place.

${\displaystyle \frac{x}{10}}=10x$, it is not possible.

52. The place value of a digit at the hundredths place is ${\displaystyle \frac{1}{10}}$ times the same digit at the tenths place.

Ans: The given statement is True

53. The decimal $3.725$is equal to $3.72$ correct to two decimal places.

Ans: The given statement is False

Since, $5$are at thousandths place.

$3.725$is written as $3.73,$correct two decimal place.

54. In the decimal form, fraction ${\displaystyle \frac{25}{8}}=3.125$.

Ans: The statement is True

${\displaystyle \frac{25}{8}}={\displaystyle \frac{25\times 125}{8\times 125}}$

$={\displaystyle \frac{3125}{1000}}=3.125$ 

55. The decimal $23.2=23{\displaystyle \frac{2}{5}}$.

Ans: The given statement is False

$23.2={\displaystyle \frac{232}{10}}$

$={\displaystyle \frac{232÷2}{10÷2}}={\displaystyle \frac{116}{5}}$ 

By Long division method the quotient and reminder is $23\text{and}1$.

The correct statement 

The decimal $23.2=23{\displaystyle \frac{1}{5}}$.

56. The fraction represented by the shaded portion in the adjoining figure is ${\displaystyle \frac{3}{8}}$.

Ans: The given explanation is true.

The figure shows that, number of total part is$8$ and out of these$3$parts is shaded.

The required fraction is ${\displaystyle \frac{3}{8}}$

57. The fraction represented by the un-shaded portion in the adjoining figure is ${\displaystyle \frac{5}{9}}$.

Ans: The given statement for the figure is false.

The figure shows that, number of total part is $9$ and out of these $4$ parts is un-shaded.

The required fraction is ${\displaystyle \frac{4}{9}}$.

58. ${\displaystyle \frac{25}{19}}+{\displaystyle \frac{6}{19}}={\displaystyle \frac{31}{38}}$

Ans: The addition of the fraction is False

Denominator is same for the fractions so by adding the numerator 

$\Rightarrow {\displaystyle \frac{25}{19}}+{\displaystyle \frac{6}{19}}={\displaystyle \frac{25+6}{19}}={\displaystyle \frac{31}{19}}$

$\Rightarrow {\displaystyle \frac{31}{19}}\ne {\displaystyle \frac{31}{38}}$ 

59. ${\displaystyle \frac{8}{18}}-{\displaystyle \frac{8}{15}}={\displaystyle \frac{8}{3}}$

Ans: The subtract of the fraction is False

Cross multiply the both fraction with each other.

$\Rightarrow {\displaystyle \frac{8}{18}}-{\displaystyle \frac{8}{15}}={\displaystyle \frac{8\times 15-8\times 18}{18\times 15}}$

$={\displaystyle \frac{120-144}{270}}={\displaystyle \frac{-24}{270}}$

$=-{\displaystyle \frac{4}{45}}$ 

$\Rightarrow -{\displaystyle \frac{4}{45}}\ne {\displaystyle \frac{8}{3}}$

60. ${\displaystyle \frac{7}{12}}+{\displaystyle \frac{11}{12}}={\displaystyle \frac{3}{2}}$

Ans: The addition of the fraction is True

$\Rightarrow {\displaystyle \frac{7}{12}}+{\displaystyle \frac{11}{12}}={\displaystyle \frac{7+11}{12}}$

$={\displaystyle \frac{18÷6}{12÷6}}={\displaystyle \frac{3}{2}}$ 

61. $3.03+0.016=3.019$

Ans: The addition of the numbers is False

$\Rightarrow 3.030+0.016=3.046$

$\Rightarrow 3.046\ne 3.019$ 

62. $\mathbf{42}.\mathbf{28}-\mathbf{3}.\mathbf{19}=\mathbf{39}.\mathbf{09}.$

Ans: The subtraction of the two numbers is True

63. ${\displaystyle \frac{16}{25}}>{\displaystyle \frac{13}{25}}$

Ans: The statement is True

Given fraction are like fraction. 

Comparing the numerator, we get ${\displaystyle \frac{16}{25}}>{\displaystyle \frac{13}{25}}$

64. $19.25<19.053$

Ans: The given fraction type is False

Since, convert the $19.25$and $19.053$ in like decimal. It's become $19.250$ and $19.053.$

Compare the place value $19.250<19.053$, we get hundred place of $19.250$ is $2$ and the hundred place of $19.053$ is $0$

Hence, the statement is $19.25>19.053$

65. $13.730=13.73$

Ans: The given number is True

Since, convert the $13.730$ and $13.73$in like decimal. It's become $13.730$ and $13.730$

So,$13.730=13.73$

In Each of the Questions 66 to 71, fill in the Blanks Using '>', '<' or '=':

66. ${\displaystyle \frac{11}{16}}\dots {\displaystyle \frac{14}{15}}$

Ans: The L.C.M. of $16$ and $15$ is $2\times 2\times 2\times 2\times 3\times 5=240$

Make it as like a fraction, multiply in numerator and denominator with the same digit

${\displaystyle \frac{11}{16}}\times {\displaystyle \frac{15}{15}}={\displaystyle \frac{165}{240}}$

${\displaystyle \frac{14}{15}}\times {\displaystyle \frac{16}{16}}={\displaystyle \frac{224}{240}}$

${\displaystyle \frac{224}{240}}>{\displaystyle \frac{165}{240}}\text{ So, }{\displaystyle \frac{11}{16}}<{\displaystyle \frac{14}{15}}$

67. ${\displaystyle \frac{8}{5}}\dots {\displaystyle \frac{95}{14}}$

Ans: The L.C.M of $15$ and $14$ is $2\times 3\times 5\times 7=210$

Make it as like a fraction, multiply in numerator and denominator with the same digit

${\displaystyle \frac{8}{15}}\times {\displaystyle \frac{14}{14}}={\displaystyle \frac{112}{210}}$

${\displaystyle \frac{95}{14}}\times {\displaystyle \frac{15}{15}}={\displaystyle \frac{1425}{210}}$

${\displaystyle \frac{1425}{210}}>{\displaystyle \frac{112}{210}}$

Therefore,  ${\displaystyle \frac{8}{15}}<{\displaystyle \frac{95}{14}}$

68. ${\displaystyle \frac{12}{75}}\dots {\displaystyle \frac{32}{200}}$

Ans: The L.C.M of $75$ and $200$is $2\times 2\times 2\times 3\times 5\times 5=600$

Make it as like a fraction, multiply in numerator and denominator with the same digit

${\displaystyle \frac{12}{75}}\times {\displaystyle \frac{8}{8}}={\displaystyle \frac{96}{600}}$

${\displaystyle \frac{32}{200}}\times {\displaystyle \frac{3}{3}}={\displaystyle \frac{96}{600}}$

${\displaystyle \frac{96}{600}}={\displaystyle \frac{96}{600}}$ 

Hence, ${\displaystyle \frac{12}{75}}={\displaystyle \frac{32}{200}}$

69. $3.25\dots 3.4$

Ans: Since, convert the $3.25$and $3.4$in like decimal. It's become $3.25$ and $3.40$

Compare the place value of $3.25$and $3.40,$we get tenth place of $3.25$ is $2$ and the tenth place of $3.40$is $4$

Hence,$3.25<3.4$

70. ${\displaystyle \frac{18}{15}}\dots 1.3$

Ans: Since, convert $1.3$ into fraction from, we get ${\displaystyle \frac{13}{10}}$

${\displaystyle \frac{18}{15}}\dots ..{\displaystyle \frac{13}{10}}$

The L.C.M. of $15$ and $10$ is $2\times 3\times 5=30$

Make it as like a fraction, multiply in numerator and denominator with the same digit

${\displaystyle \frac{18}{15}}\times {\displaystyle \frac{10}{10}}={\displaystyle \frac{180}{150}}\text{ and }{\displaystyle \frac{13}{10}}\times {\displaystyle \frac{15}{15}}={\displaystyle \frac{195}{150}}$

${\displaystyle \frac{180}{150}}<{\displaystyle \frac{195}{150}}\text{ So, }{\displaystyle \frac{18}{15}}<1.3$

71. $6.25\dots {\displaystyle \frac{25}{4}}$

Ans: Since, convert $1.3$into fraction from, we get ${\displaystyle \frac{625}{100}}$

$\Rightarrow {\displaystyle \frac{625}{100}}={\displaystyle \frac{625÷25}{100÷25}}={\displaystyle \frac{25}{4}}$

${\displaystyle \frac{25}{4}}\dots .{\displaystyle \frac{25}{4}}$

${\displaystyle \frac{25}{4}}={\displaystyle \frac{25}{4}}$

Therefore, $6.25={\displaystyle \frac{25}{4}}$

72. Write the fraction represented by the shaded portion of the adjoining figure:

Ans: In the given figure, total parts in the figure is divided into $8$ parts and 7 parts are shaded. 

Total parts $=8$

Total shaded parts $=7$

Therefore,

fraction of unshaded portion $={\displaystyle \frac{\text{ Total shaded parts }}{\text{ Total parts }}}$

$={\displaystyle \frac{7}{8}}$

The required fraction is ${\displaystyle \frac{7}{8}}$.

73. Write the fraction represented by the un-shaded portion of the adjoining figure:

Ans: In the given figure, total parts in which figure has been divided into 15 and out of which 4 parts are unshaded.

Total parts $=15$

Total unshaded parts $=4$

Therefore,

fraction of unshaded portion $={\displaystyle \frac{\text{ Total unshaded parts }}{\text{ Total parts }}}={\displaystyle \frac{4}{15}}$

The required fraction is ${\displaystyle \frac{4}{15}}$.

74. Ali divided one fruit cake equally among six persons. What part of the cake he gave to each person?

Ans: Given data 

Number of cake $=1$

Total no. of persons $=6$

Since,

Ali has to divide one fruit cake among 6 people,

$\text{Each person will get}={\displaystyle \frac{\text{ No}\text{. of cake }}{\text{ Total no}\text{. of person }}}$

$={\displaystyle \frac{1}{6}}\text{ part}$

75. Arrange $\mathbf{12}.\mathbf{142},\mathbf{12}.\mathbf{124},\mathbf{12}.\mathbf{104},\mathbf{12}.\mathbf{401}\mathbf{and}\mathbf{12}.\mathbf{214}$in ascending order.

Ans: Given number$12.142,12.124,12.104,12.401\text{and }12.214$ in like decimal.

So, compare the place value of the digit and arrange them, $12.104<12.124<12.142<12.214<12.401$

76. Write the largest four-digit decimal number less than1 using the digits $1,5,3$ and $\mathbf{8}$ once.

Ans: Given whole numbers are$1,5,3,\text{ and }8$.

Arrange them in descending order to make them large, after arranging the number will be $8531.$

To make it a decimal number we will keep the whole number  8531 in the decimal point.

The required number is 0.8531, which is the largest four  -  digit decimal number less than 1.

77. Using the digits $\mathbf{2},\mathbf{4},\mathbf{5}$ and $\mathbf{3}$ once, write the smallest four-digit decimal number. 

Ans: For converting $2,4,5,$and $3$ into smallest four digit decimal number, arrange them in ascending order and then making the numbers decimal, we have to keep the whole numbers in decimal point.

After arranging whole numbers in ascending form it will be $2345.$

To make the number decimal we will keep the numbers in decimal point.

So, the required number is$0.2345$, which is the smallest four digit decimal number.

78. Express ${\displaystyle \frac{11}{20}}$ as a decimal.

Ans: ${\displaystyle \frac{11}{20}}$ is an improper fraction.

To get the denominator as whole number we will multiply denominator by$5$,

${\displaystyle \frac{11}{20}}={\displaystyle \frac{11\times 5}{20\times 5}}={\displaystyle \frac{55}{100}}=0.55$

$0.55$ is in decimal form

79. Express $6{\displaystyle \frac{2}{3}}$ as an improper fraction.

Ans: We will convert the mixed fraction $6{\displaystyle \frac{2}{3}}$ into improper fraction. 

We have,

$6{\displaystyle \frac{2}{3}}={\displaystyle \frac{(6\times 3)+2}{3}}={\displaystyle \frac{18+2}{3}}={\displaystyle \frac{20}{3}}$

Now we got ${\displaystyle \frac{20}{3}}$.

${\displaystyle \frac{20}{3}}$ is an improper fraction.

80. Express $3{\displaystyle \frac{2}{5}}$ as a decimal.

Ans: We will convert the mixed fraction $3{\displaystyle \frac{2}{5}}$ into an improper fraction. 

We have, $3{\displaystyle \frac{2}{5}}={\displaystyle \frac{(3\times 5)+2}{5}}={\displaystyle \frac{15+2}{5}}={\displaystyle \frac{17}{5}}$

Now,

${\displaystyle \frac{17}{5}}={\displaystyle \frac{17\times 2}{5\times 2}}={\displaystyle \frac{34}{10}}=3.4$

81. Express $0.041$as a fraction. 

Ans: We can write 0.041 as ${\displaystyle \frac{0.041}{1}}$.

So, $0.041={\displaystyle \frac{0.041}{1}}$

Multiply numerator and denominator by $\mathbf{1000}$ we have,

$0.041={\displaystyle \frac{0.041\times 1000}{1\times 1000}}$

$={\displaystyle \frac{41}{1000}}$ 

fraction for the decimal is ${\displaystyle \frac{41}{1000}}$

82. Express $6.03$as a mixed fraction.

Ans: We have, $6.03$

$6.03={\displaystyle \frac{603}{100}}=6{\displaystyle \frac{3}{100}}$

The fraction for the decimal is $6{\displaystyle \frac{3}{100}}$

83. Convert $\mathbf{5201}\mathbf{g}$ to kg.

Ans: We know that,

$1\text{Kg}=1000\text{g}$

$1\text{g}={\displaystyle \frac{1}{1000}}\text{kg}$

$5201\text{g}={\displaystyle \frac{1}{1000}}\times 5201\text{kg}$

$\Rightarrow 5201\text{g}={\displaystyle \frac{5201}{1000}}=5.201\text{kg}$

84. Convert $\mathbf{2009}$ paisa to rupees and express the result as a mixed fraction.

Ans: We know that,

1 rupee $=100$ paisa

1 paisa $={\displaystyle \frac{1}{100}}$ rupees

2009 paisa $={\displaystyle \frac{1}{100}}\times 2009$ rupees

$\Rightarrow 2009$ paisa $={\displaystyle \frac{2009}{100}}=20.09$ rupees

The mixed fraction is Rs. $20{\displaystyle \frac{9}{100}}$.

85. Convert $1537cm$ to $\text{m}$ and express the result as an improper fraction.

Ans: We know that,

1 meter $=100$centimeters

1 centimeter $={\displaystyle \frac{1}{100}}$ meter

$1537\text{cm}={\displaystyle \frac{1}{100}}\times 1537\text{m}$

$\Rightarrow 1537\text{cm}={\displaystyle \frac{1537}{100}}\text{m}$

86. Convert $2435m$ to $\text{km}$ and express the result as a mixed fraction.

Ans: We know that

$1\text{km}=1000\text{m}$

$1\text{m}={\displaystyle \frac{1}{1000}}\text{km}$

$2435\text{m}={\displaystyle \frac{1}{1000}}\times 2435\text{km}$

$2435\text{m}={\displaystyle \frac{2435}{1000}}\text{km}=2.435\text{km}$

Dividing numerator and denominator by $5$ we have,

${\displaystyle \frac{2435÷5}{1000÷5}}\text{km}={\displaystyle \frac{487}{200}}\text{km}$

By long division method quotient and reminder is $2\text{and}87$

The mixed fraction is $2{\displaystyle \frac{87}{200}}$

87. Arrange the fractions ${\displaystyle \frac{2}{3}},{\displaystyle \frac{3}{4}},{\displaystyle \frac{1}{2}}$ and ${\displaystyle \frac{5}{6}}$ in ascending order.

Ans: Given fraction is ${\displaystyle \frac{2}{3}},{\displaystyle \frac{3}{4}},{\displaystyle \frac{1}{2}}$ and ${\displaystyle \frac{5}{6}}$

Take the LCM of $3,4,2$and $6$

The $\text{LCM}$ of $3,4,2$and $6$ is $2\times 2\times 3=12$

$\text{Now },{\displaystyle \frac{2\times 4}{3\times 4}}={\displaystyle \frac{8}{12}},$

${\displaystyle \frac{3\times 3}{4\times 3}}={\displaystyle \frac{9}{12}}$

${\displaystyle \frac{1\times 6}{2\times 6}}={\displaystyle \frac{6}{12}},$

${\displaystyle \frac{5\times 2}{6\times 2}}={\displaystyle \frac{10}{12}}$