Multiplication of Decimals
Multiplication of Decimals by Power of 10
Case 1: When a decimal is multiplied by 10. Like\[\text{8}.\text{6542}\times \text{1}0\] The decimal is shifted one digit right. Thus\[\text{8}.\text{6542}\times \text{1}0=\text{86}.\text{542}\]
Case 2: When a decimal is multiplied by 100. Like\[\text{8}.\text{6542}\times \text{1}00\] The decimal is shifted two digit right. Thus\[\text{8}.\text{6542}\times \text{1}00=\text{865}.\text{42}\]
Case 3: When a decimal is multiplied by 1000. Like\[~\text{8}.\text{6542}\times \text{1}000\] The decimal is shifted three digit right. Thus \[\text{8}.\text{6542}\times \text{1}000=\text{8654}.\text{2}\]
Note: As you increase the power of 10 by one, the decimal point shift one digit right.
For example: \[\text{2}.\text{35682}\times \text{1}{{\text{0}}^{2}}=\text{235}.\text{682}\] \[2.35682\times {{10}^{3}}=2356.82\] \[2.35682\times {{10}^{4}}=23568.2\]
\[\mathbf{Multiply:394}\mathbf{.5607\times 1000}\]
Solution:
\[~\text{394}.\text{56}0\text{7}\times \text{1}000=\text{39456}0.\text{7}\]
\[\mathbf{Multiply:100}\mathbf{.15\times 100}\]
Solution:
\[\text{1}00.\text{15}\times \text{1}00=\text{1}00\text{15}\] more...
Subtraction of Decimals
Step 1: Arrange the decimals one below other such that decimal points come in same column.
Step 2: Now subtract the digits.
Step 3: Place the decimal in the decimal column in the difference.
Subtract 96.042 from 231.289
Solution:
Subtract\[\text{231}.\text{289}-\text{96}.0\text{42}=\text{135}.\text{247}\]
A = 10.468, B = 9.234. Find\[\mathbf{A}-\mathbf{B}\]
Solution:
\[\text{A}-\text{B }=\text{ 1}0.\text{468}-\text{9}.\text{234 }=\text{1}.\text{234}\]
Addition of Decimals
Step 1: Arrange the decimals one below other such that decimal points come in same column.
Step 2: Now add the digits.
Step 3: Place a point in the sum in point column.
Add: \[\mathbf{231}.\mathbf{289}+\mathbf{96}.\mathbf{042}+\mathbf{1}.\mathbf{468}+\mathbf{9}.\mathbf{234}\]
Solution:
\[\begin{align} & \,\text{231}.\text{289} \\ & \,\,\,\text{96}.0\text{42} \\ & \,\,\,\,\,\,\,\text{1}.\text{468} \\ & +\text{ 9}.\text{234} \\ & \underline{\overline{\text{338}.0\text{33}}} \\ \end{align}\]
\[\mathbf{2312}\mathbf{.899 + 604}\mathbf{.2146 + 89}\mathbf{.2342}\]
Solution:
\[\begin{align} & \,\text{2312}.\text{899}0 \\ & \,\,\,\,\text{6}0\text{4}.\text{2146} \\ & +\text{ }\,\text{89}.\text{2342} \\ & \underline{\overline{\text{3}00\text{6}.\text{3478}}} \\ \end{align}\]
Comparison of Decimals
Step 1: Compare the whole parts. The decimal having greater whole part is greater.
Note : In case of equal whole parts, follow the step 2.
Step 2: Compare the decimal part, the decimal having greater decimal part is greater.
Compare between 9.2 and 7.9 and find which is greater?
Solution:
Whole part of 9.2 = 9 Whole part of 7.9 =7 \[\text{9}>\text{7}.\text{ So 9}.\text{2}>\text{7}.\text{9}\]
Compare 14.7 and 14.3, which is greater?
Solution:
Whole part of 14.7 =14
Whole part of 14.3 = 14
\[\because \]Both the decimals have same whole part, therefore, compare decimal parts.
The digit at the tenths place in 14.7 = 7
The digit at the tenths place in 14.3 = more...
Decimals
A decimal number is broadly divided into two parts.
(i) Whole number part
(ii) 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 is multiplied by 10 and as you move on the right it is divided by 10.
| Decimal Fraction | Whole Part | Decimal Part |
more...
 Operation on the Fractions
 Addition of Like Fractions
\[\text{Sum of like fractions}=\frac{\text{Sum of numerators}}{\text{common denominator}}\] In addition of like fractions, sum of the numerators will be the numerator for the resulting fraction and the common denominator will be the denominator. \[\frac{P}{R}+\frac{Q}{R}=\frac{P+Q}{R}\]
Add the following fractions.
Solution: \[\frac{3}{11}+\frac{2}{11}+\frac{5}{11}=\frac{10}{11}\]
Add the following fractions:
\[\frac{3}{10}+\frac{2}{10}\]
Solution:
\[\frac{3}{10}+\frac{2}{10}=\frac{5}{10}\]
Addition of Unlike Fractions
Add\[\frac{5}{7}\] and\[\frac{5}{8}\]
Step 1: Convert the fractions into like fractions. \[\frac{5}{7}=\frac{5\times 8}{7\times 8}=\frac{40}{56}\] And \[\frac{5}{8}=\frac{5\times 7}{8\times 7}=\frac{35}{56}\]
Step 2: Add numerator of the fractions\[\text{4}0+\text{35}=\text{75}\].
Step 3: Write the sum as numerator for the required fraction and common denominator as denominator\[\frac{75}{56}\]
more...
 Comparison of Fraction
 Comparison of Like Fractions
Let\[\frac{p}{q}\]and\[\frac{r}{q}\]are like fractions.
If p is greater than \[q,\frac{p}{q}>\frac{r}{q}\]
Compare between\[\frac{\mathbf{7}}{\mathbf{9}}\]and\[\frac{5}{\mathbf{9}}\].Which is greater?
Solution:
\[7>5\] \[\frac{7}{9}>\frac{5}{9}\]
Comparison of Fractions Having Same Numerator
If the two fractions have same numerator, the fraction which has smaller denominator is greater. Like\[\frac{P}{Q}\]is greater than\[\frac{P}{R}\]if\[\text{Q}<\text{R}\].
Find the greatest fraction out of the given fractions:
\[\frac{18}{23},\frac{18}{17},\frac{18}{19},\frac{18}{20},\frac{18}{12}\]
Solution:
\[\frac{18}{12}\]is the greatest fraction among the given fractions. As it has smallest denominator.
Comparison of Unlike Fractions
Compare between\[\frac{7}{13}\]and\[\frac{6}{9}\]
Step 1: Convert the fractions into like fractions.
\[\frac{7\times 9}{13\times 9}=\frac{63}{117}\]
And\[\frac{6\times 13}{9\times more...
 Conversion of mixed Fraction into Improper Fraction
Convert\[11\frac{4}{7}\]into improper fraction
Step 1: Multiply the whole number by the denominator of the fractional part and add the numerator to the resulting number. \[\text{11}\times \text{7}+\text{4}=\text{81}\].
Step 2: Write the resulting number as numerator for the required fraction and denominator is same as the fractional part has\[\frac{81}{7}\].
Convert \[\mathbf{44}\frac{\mathbf{3}}{\mathbf{7}}\] into improper fraction.
Solution: \[\frac{7\times 44+3}{7}=\frac{308+3}{7}=\frac{311}{7}\]
Thus\[44\frac{3}{7}=\frac{311}{7}\]
 Fraction
Fraction is used to indicate a part of a whole. It is represented as \[\frac{a}{b}\] where, a is called numerator and b is called denominator of the fraction. It may be explained as - If a whole is divided into some equal parts, each part is called fraction of the whole and the number which is used to represent the part is called fractional number. Let 4 kg flour is divided into five equal parts. The amount each part will contain is represented as \[\frac{4}{5}\] kg here \[\frac{4}{5}\] is a number which is known as fraction. Thus fraction is a mathematical term which represents part of a whole. Shaded part in the following figures has been represented by fractions.
1 kg corn is divided into five equal parts. Represent the more...
 Introduction
When a figure is divided in equal number of point. The point of the figure a represented by the fraction. In a fraction, numerator represents the required number of parts of figure and denominator represents the total number of points in which the whole figure is divider into.
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