**Category : **4th Class

**Case 1:** When a decimal is divided by 10. Like \[\text{5456}.\text{32}\div \text{1}0\] The decimal is shifted one digit left. Thus \[\text{5456}.\text{32}\div \text{1}0=\text{545}.\text{632}\]

**Case 2:** When a decimal is divided by 100. Like \[\text{5456}.\text{32}\div \text{1}00\] The decimal is shifted two digit left. Thus\[\text{5456}.\text{32}\div \text{1}00=\text{54}.\text{5632}\]

**Case 3:** When a decimal is divided by 1000. Like\[~\text{5456}.\text{32}\div \text{1}000\] The decimal is shifted three digit left. Thus \[\text{5456}.\text{32}\div \text{1}000=\text{5}.\text{45632}\]

**Note:** As you increase the power of 10 by one, the decimal point shift one digit left.

**For example:** \[5463.23\div {{10}^{1}}=546.323\] \[5463.23\div {{10}^{2}}=54.6323\] \[5463.23\div {{10}^{3}}=5.46323\]

**Divide 786.45 by 100**

**Solution:**

100 contains two zeroes, therefore, shift the point two digit left in the decimal. Thus\[\text{786}.\text{45}\div \text{1}00=\text{7}.\text{8645}\]

- Fraction is a part of a whole. It is represented by a/b when\[b\ne o\].
- Fraction is a part of whole, therefore, it has two parts, upper part is known as NUMERATOR and lower part is known as DENOMINATOR and they are separated by a line known as DIVISION LINE
- The fractions having same denominator are called like fraction.
- The fractions having different denominator are called unlike fraction.
- In addition of like fractions, common denominator is the denominator for the required fraction.
- A decimal number is broadly divided into two parts whole part and decimal part.
- The two parts are separated by a dot (.) called the decimal point.
- From the decimal point as you move on the left the place value of a digit is multiplied by 10 and as you move on the right it is divided by 10.
- When a decimal is multiplied by 10, the decimal is shifted one digit right.
- When a decimal is multiplied by 100, the decimal is shifted two digit right,
- When a decimal is multiplied by 1000, the decimal is shifted three digit right.
- When a decimal is divided by 10, the decimal is shifted one digit left.
- When a decimal is divided by 100, the decimal is shifted two digit left.
- When a decimal is divided by 1000, the decimal is shifted three digit left.

- The term fraction came from the Latin "fractio" that means breaking.
- In ancient Rome, fractions were written using words instead of numbers.
- Indian mathematician wrote fractions without using bar. They wrote just a number above other. It was the Arabians who added the bar separating the two numbers.
- The decimal point was invented by John Napier.
- About 5000 year ago/ Indian mathematicians used a form of decimal numbering.
- China is considered to be the earliest civilization to adopt the concept of Hindu- Arabic numeral system.

**Represent the shaded part of the following figures as fraction and choose what kind of fractions they are?**

Figure (i) Figure (ii)

(a) They are like fractions.

(b) They are unlike fractions.

(c) They are equivalent fractions.

(d) All of these

(e) None of these

**Answer (a)**

**Explanations-**

In the figure (i), 4 parts out of 8 parts are shaded. Thus fractional representation for the shaded part\[=\frac{4}{8}\] In the figure (ii), 6 parts out of 8 parts are shaded. Thus fractional representation for the shaded part\[=\frac{6}{8}\] Both the representations have same denominator. Therefore, they are like fractions.

**Which one of the following is the equivalent fraction of\[\frac{7}{8}\]?**

(a) \[\frac{9}{8}\]

(b) \[\frac{7}{9}\]

(c) \[\frac{35}{40}\]

(d) \[\frac{11}{40}\]

(e) None of these

**Answer (c)**

**Explanation-**

When we multiply both numerator and denominator of the fractionby 5, we get\[\frac{35}{40}\]. Thus,\[\frac{35}{40}\]and\[\frac{7}{8}\]are equivalent fractions.

**Jack:** \[\frac{7}{9}\]and\[\frac{7}{13}\], are like fractions as both has same numerator.

**Cody:** To be like fractions, denominators of the fractions should be same instead of numerator. Who is correct?

(a) Jack

(b) Cody

(c) Both of them are correct

(d) Both of them are partially incorrect

(e) None of these

**Answer (c)**

**Represent the yellow part in the following figure as fraction and find its one equivalent fraction.**

Red | Yellow | Green | Yellow | Red |

(a) \[\frac{22}{60}\]

(b) \[\frac{4}{20}\]

(c) \[\frac{6}{20}\]

(d) \[\frac{32}{60}\]

(e) None of these

**Answer (b)**

**In which one of the following figures shaded part represents\[\frac{1}{5}\]?**

(a)

(b)

(c)

(d)

(e) None of these

**Answer (c)**

**Which one of the following is not a proper fraction?**

(a) \[\frac{1}{5}\]

(b) \[\frac{2}{5}\]

(c) \[\frac{3}{5}\]

(d) \[\frac{7}{5}\]

(e) None of these

**Answer (d)**

**Explanation-**

Numerator is greater than denominator in the fraction\[\frac{7}{5}\].Thus\[\frac{7}{5}\]is an improper fraction.

**\[\frac{p}{q}\]is a fraction. If p is greater than q, which one of the following is correct?**

(a) \[\frac{p}{q}\]is a proper fraction

(b) \[\frac{p}{q}\]is an improper fraction

(c) \[\frac{p}{q}\]is a unit fraction

(d) All of these

(e) None of these

**Answer (b)**

**Explanations-** p is greater than q, therefore,\[\frac{p}{q}\]is an improper fraction.

**How many parts of the following figure would you like to shade such that shaded part of the figure can represents unit fraction?**

(a) One part

(b) Two parts

(c) Three parts

(d) Four parts

(e) None of these

**Answers (a)**

**Convert the given mixed fraction into improper fraction\[7\frac{7}{12}\].**

(a) \[\frac{12}{91}\]

(b) \[\frac{91}{12}\]

(c) \[\frac{7}{12}\]

(d) \[\frac{27}{91}\]

(e) None of these

**Answer (b)**

**Jack:** \[\frac{19}{11}\]is an improper fraction.

**Cody:** \[\frac{19}{11}\]can be changed into mixed fraction. Who is correct?

(a) Jack is correct

(b) Cody is correct

(c) Both of them are correct

(d) Both of them are partially incorrect

(e) None of these

**Answer (c)**

**Find the fraction that should be added to\[\frac{8}{9}\]to get\[\frac{31}{18}\]?**

(a) \[\frac{5}{6}\]

(b) \[\frac{23}{18}\]

(c) \[\frac{7}{9}\]

(d) \[\frac{8}{9}\]

(e) None of these

**Answer (a)**

**Explanations-**

Let the fraction X should be added to\[\frac{8}{9}\] According to the question\[\frac{8}{9}\times X=\frac{31}{18},X=\frac{31}{18}-\frac{8}{9},X=\frac{5}{6}\]

**Zacob has 8 liters of milk. He uses\[2\frac{1}{2}\]liters for pudding and\[2\frac{1}{8}\]liters for curd. What quantity of milk is left with him?**

(a) \[\frac{21}{26}\]

(b)\[\frac{5}{27}\]

(c) \[\frac{8}{27}\]

(d) \[\frac{27}{8}\]

(e) None of these

**Answer (d)**

**Explanations-**

Total milk Zacob has = 8 L Total milk used by Jacob \[=2\frac{1}{2}L+2\frac{1}{8}L\] Or\[(\frac{5}{2}+\frac{17}{8})L=(\frac{20+17}{8})L=\frac{37}{8}L,\], So remaining milk\[=8-\frac{37}{8}=\frac{27}{8}L\]

**Arrange the following in ascending order:**

\[\frac{2}{3},\frac{4}{9},\frac{5}{7},\frac{5}{3}\]

(a) \[\frac{4}{9},\frac{2}{3},\frac{5}{7},\frac{5}{3}\]

(b) \[\frac{2}{3},\frac{4}{9},\frac{5}{3},\frac{5}{7}\]

(c) \[\frac{2}{3},\frac{5}{3},\frac{4}{9},\frac{5}{7}\]

(d)\[\frac{2}{3},\frac{4}{9},\frac{5}{7},\frac{5}{3}\]

(e) None of these

**Answer (a)**

**Find the perimeter of the following figure.**

(a) \[\frac{198}{168}m\]

(b) \[\frac{230}{168}m\]

(c) \[\frac{250}{168}m\]

(d) \[\frac{65}{42}m\]

(e) None of these

**Answer (d)**

** What is the difference of the fractions if shaded part in the following figures are represented as fraction?**

Figure (i) Figure (ii)

(a) \[\frac{7}{10}\]

(b) \[\frac{7}{30}\]

(c) \[\frac{11}{30}\]

(d)\[\frac{14}{30}\]

(e) None of these

**Answers (c)**

**Which one of the following is true for 0.003**

(a) Three-tenth

(b) Three-hundredth

(c) Three-thousandth

(d) Three-ten thousandth

(e) None of these

**Answer (c)**

**Explanation-**

\[0.003=\frac{3}{1000}\] (three-thousandth)

**John makes a rectangular figure and divides it into 100 equal parts. He shades 3 parts out of every 10 parts. Find the correct expression for the shaded part.**

(a) \[\frac{1}{100}\]

(b) \[\frac{10}{100}\]

(c) \[\frac{3}{100}\]

(d) \[\frac{30}{100}\]

(e) None of these

**Answer (d)**

**Explanation-**

John shades 3 parts out of every 10 parts and there are 100 parts in the figure. So he shades 30 parts. Therefore, correct expression for the figure ls\[\frac{30}{100}\].

**Which one of the following is the correct decimal representation for the shaded part in the figure?**

(a) 0.1

(b) 0.2

(c) 0.5

(d) 0.4

(e) None of these

**Answer (c)**

**Which one of the following is correct decimal expression for the place value of 5?**

Ones | Decimal Point | Tenths | Hundredths |

3 | . | 0 | 5 |

(a) 0.5

(b) 0.05

(c) 0.005

(d) 0.0005

(e) None of these

**Answer (b)**

**You have to arrange the digits of the decimal 35.564 in the decimal place value chart. Which one of the following places is suitable for the digit 4? **

(a) Ones

(b) Tens

(c) Hundredths

(d) Thousandths

(e) None of these

**Answer (d)**

**Choose the correct option for 50.203.**

(a)\[50+20+\frac{3}{10}\]

(b) \[50+\frac{2}{10}+\frac{3}{100}\]

(c) \[50+\frac{2}{10}+\frac{3}{1000}\]

(d) \[5+\frac{2}{10}+\frac{3}{100}\]

(e) None of these

**Answer (c)**

**Explications-**

In the decimal 50.203, 5 is at the tens place, 2 is at the tenths place, and 3 is at the hundredths place. Thus, expanded form of 50.203 is\[50+\frac{2}{10}+\frac{3}{1000}\].

**Which one of the following is the equivalent decimal of 623.523?**

(a) 623.52300

(b) 623.5023

(c) 62.3523

(d) 0.623523

(e) None of these

**Answers (a)**

**Expirations-**

If we add zero extreme right to the decimal, the value of the decimal does not get changed. But if we change the place of decimal, the value of the decimal get changed. Therefore, 623.52300 is a equivalent decimal of 623.523.

**215.0A2 and 215.0B3 are two decimals. Which one of the following is not true?**

(a) If A = B, 215.0A2 < 215.0B3

(b) If A >B, 215.0A2 > 215.0B3

(c) If A <B, 215.0A2 < 215.0B3

(d) If A = B, 215.0A2 and 215.0B3 are equivalent decimals.

(e) None of these

**Answer (d)**

**P is the extreme right digit of a decimal. If place value of P is\[\frac{p}{1000}\], how many decimal places the decimal has?**

(a) One

(b) Two

(c) Three

(d) Four

(e) None of these

**Answers (c)**

**Jack:** When we multiply a decimal by 10 we get an equivalent decimal of that decimal.

**John:** When we multiply a decimal by 10 its value is changed. Equivalent decimals have same value therefore; we cannot find an equivalent decimal by multiplying the decimal by 10. Who is correct?

(a) Jack

(b) John

(c) Both are correct

(d) Both are partially incorrect

(e) None of these

**Answers (b)**

**Add: 131.298 + 16.042 + 2.468 + 8.234**

(a) 159.33

(b) 158.033

(c) 258.33

(d) 151.33

(e) None of these

**Answers (b)**

**Explanations-**

\[\begin{align} & \text{131}.\text{289} \\ & \,\,\,\text{16}.0\text{42} \\ & \,\,\,\,\,\,\text{2}.\text{468} \\ & +\,\,\,\text{8}.\text{234} \\ & \overline{\underline{\text{158}.0\text{33}}} \\ \end{align}\]

**Find the value of A. If A = 331.000 ?** **96.042**

(a) 344.345

(b) 453.786

(c) 234.958

(d) 234.876

(e) None of these

**Answer (c)**

**Explanation**

\[\begin{align} & \,\,\,\text{331}.000 \\ & -\text{ 96}.0\text{42} \\ & \,\,\,\overline{\underline{\text{234}.\text{958}}} \\ \end{align}\]

** \[''0.02002\times {{10}^{4}}=200.2''\]In the given expression 0.02002 is multiplied by 104 and the product is 200.2. Jack replaces\[{{10}^{4}}\]P thus he finds the product gets changed and it becomes 2.002. Find the value of P**

(a) \[{{10}^{1}}\]

(b) \[{{10}^{2}}\]

(c)\[{{10}^{5}}\]

(d)\[{{10}^{3}}\]

(e) None of these

**Answer (b)**

**By what number 4562.2 should be divided to obtain the decimal 4.5622?**

(a) 10

(b) 100

(c) 1000

(d) 10000

(e) None of these

**Answer (c)**

**Which one of the following is true for\[0.\text{45}\times \]\[\text{1}00\times \text{56}\]?**

(a) 2205

(b) 1825

(c) 2025

(d) 2520

(e) None of these

**Answer (d)**

*play_arrow*Introduction*play_arrow*Fraction*play_arrow*Conversion of mixed Fraction into Improper Fraction*play_arrow*Comparison of Fraction*play_arrow*Operation on the Fractions*play_arrow*Decimals*play_arrow*Comparison of Decimals*play_arrow*Addition of Decimals*play_arrow*Subtraction of Decimals*play_arrow*Multiplication of Decimals*play_arrow*Division of a Decimal by the Power of 10

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