Division of Decimal Numbers - Division of a Decimal Number by Another Decimal Number

Topics

Term - 1
Number System
- Concept of Integers
- Representation of Integers on the Number Line
- Concept for Ordering of Integers
- Addition of Integers
- Subtraction of Integers
- Properties of Addition and Subtraction of Integers
- Multiplication of a Positive and a Negative Integers
- Multiplication of Two Negative Integers
- Product of Three Or More Negative Integers
- Properties of Multiplication of Integers
- Closure Property of Multiplication of Integers
- Closure Property of Multiplication of Integers
- Associative Property of Multiplication of Integers
- Distributive Property of Multiplication of Integers
- Multiplicative Identity of Integers
- Division of Integers
- Properties of Division of Integers
- Statement Problems on Integers Using All Fundamental Operations.
Measurements
- Concept of Perimeter
- Concept of Area
- Properties of a Parallelogram
- Properties of Rhombus
- Properties of Trapezium
- Area of a Parallelogram
- Perimeter of Parallelogram
- Area of a Rhombus
- Area of Trapezium
Algebra
- Algebraic Expressions
- Terms, Factors and Coefficients of Expression
- Types of Algebraic Expressions as Monomials, Binomials, Trinomials, and Polynomials
- Like and Unlike Terms
- Evaluation of Algebraic Expressions by Substituting a Value for the Variable.
- Addition of Algebraic Expressions
- Subtraction of Algebraic Expressions
- Expressions with Variables
- Balancing an Equation
- The Solution of an Equation
Direct and Inverse Proportion
- Concept of Ratio
- Concept of Proportion
- Concept of Direct Proportion
- Concept of Unitary Method
- Concept of Inverse Proportion
Geometry
- Concept of Line
- Concept of Line Segment
- Concept of Ray
- Introduction to Parallel Lines
- Concept of Intersecting Lines
- Concept of Points
- Concept of Angle
- Types of Angles
- Complementary Angles
- Supplementary Angles
- Concept of Linear Pair
- Concept of Vertically Opposite Angles
- Pairs of Lines - Transversal
- Pairs of Lines - Angles Made by a Transversal
- Pairs of Lines - Transversal of Parallel Lines
- The Perpendicular Bisector
- Concept of Angle Bisector
- Angles of Special Measures - 30°, 45°, 60°, 90°, and 120°
Information Processing
- Tetromino
- Route Map
Term - 2
Number System
- The Decimal Number System
- Concept of Tenths, Hundredths and Thousandths in Decimal
- Concept of Place Value
- Conversion between Decimal Fraction and Common Fraction
- Comparing Decimal Numbers
- Representing Decimals on the Number Line
Measurements
- Concept of Circle
- Circumference of a Circle
- Area of Circle
- Area of Pathways
Algebra
- Concept of Exponents
- Laws of Exponents
- Multiplying Powers with the Same Base
- Dividing Powers with the Same Base
- Taking Power of a Power
- Multiplying Powers with Different Base and Same Exponents
- Dividing Powers with Different Base and Same Exponents
- Unit Digit of Numbers in Exponential Form
- Algebraic Expressions
- Terms, Factors and Coefficients of Expression
- Like and Unlike Terms
- Degree of Expressions
Geometry
- Concept of Triangles
- Classification of Triangles (On the Basis of Sides, and of Angles)
- Classification of Triangles based on Sides- Equilateral, Isosceles, Scalene
- Classification of Triangles based on Sides- Equilateral, Isosceles, Scalene
- Classification of Triangles based on Angles: Acute-Angled, Right-Angled, Obtuse-Angled
- Angle Sum Property of a Triangle
- Exterior Angle of a Triangle and Its Property
- Congruence of Triangles
- Congruency of Shapes
- Congruence Among Line Segments
- Congruence of Plane Figures
- Congruence of Angles
- Congruence of Triangles
- Criteria for Congruence of Triangles
- SSS Congruence Criterion
- SAS Congruence Criterion
- ASA Congruence Criterion
- RHS Congruence Criterion
Information Processing
- Tables and Patterns Leading to Linear Functions
- Pascal’s Triangle
Term - 3
Number System
- The Decimal Number System
- Rounding of Decimals
- Addition of Decimal Fraction
- Subtraction of Decimal Fraction
- Multiplication of Decimal Fractions
- Multiplication of Decimal Numbers by 10, 100 and 1000
- Division of Decimal Numbers
- Division of Decimal Numbers by 10, 100 and 1000
- Division of Decimal Fractions
- Division of a Decimal Number by Another Decimal Number
Percentage and Simple Interest
- Basic Concept of Percentage
- Conversion between Percentage and Fraction
- Conversion between Percentage and Fraction
- Converting Decimals to Percentage
- Converting Percentages to Decimals
- Estimation in Percentages
- Interpreting Percentages
- Ratios to Percents
- Increase Or Decrease as Percent
- Profit or Loss as a Percentage
- Calculation of Interest
Algebra
- Concept of Identity
- Geometrical Approach to Multiplication of Monomials
- Expansion of (x + a)(x + b)
- Expansion of (a + b)2 = a2 + 2ab + b2
- Expansion of (a - b)2 = a2 - 2ab + b2
- Expansion of (a + b)(a - b) = a2-b2
- Inequation
- Solving Linear Inequations
- Graphical Representation of Inequation
Geometry
- Concept of Lines Symmetry
- Concept of Reflection Symmetry
- Concept of Reflection Symmetry
- Translational Symmetry
- Concept of Symmetry
- Symmetry Through Transformations
- Concept of Circle
- Construction of a Circle When Its Radius is Known
- Construction of Concentric Circles
Statistics
- Concept of Data Handling
- Collection of Data
- Organisation of Data
- Concept of Representative Values - Average
- Arithmetic Mean - Raw Data
- Concept of Mode
- Concept of Median
Information Processing
- Scheduling
- Flowchart

Notes

Division of a Decimal Number by Another Decimal Number:

While dividing two decimal numbers, first shift the decimal point to the right by an equal number of places in both, to convert the divisor to a whole number. Then divide.
Thus, 2.4 ÷ 0.2 = 24 ÷ 2 = 12.

Let us find $\frac{25.5}{0.5}$ i.e., 25.5 ÷ 0.5.

We have 25.5 ÷ 0.5 = $\frac{255}{10} \div \frac{5}{10} = \frac{255}{10} \times \frac{10}{5} = 51$ .

Thus, 25.5 ÷ 0.5 = 51.

For $\frac{25.5}{0.5}$ , we find that there is one digit to the right of the decimal in 0.5. This could be converted to the whole number by dividing by 10. Accordingly, 25.5 was also converted to a fraction by dividing by 10.

Or, we say the decimal point was shifted by one place to the right in 0.5 to make it 5. So, there was a shift of one decimal point to the right in 25.5 also to make it 255.

Thus, 22.5 ÷ 1.5 = $\frac{22.5}{1.5} = \frac{225}{15}$ = 15.

Example

Find: 6.6 ÷ 2.2

6.6 ÷ 2.2

$= \frac{66}{10} \div \frac{22}{10}$

$= \frac{66}{10} \times \frac{10}{22}$

$= \frac{66 \times 10}{10 \times 22}$

$= \frac{10 \times 66}{10 \times 22}$

$= \frac{10}{10} \times \frac{66}{22}$

$= \frac{1}{1} \times 3$

= 3

Example

Find: 0.0125 ÷ 0.05

0.0125 ÷ 0.05

$= \frac{125}{10000} \div \frac{5}{100}$

$= \frac{125}{10000} \times \frac{100}{5}$

$= \frac{125 \times 100}{10000 \times 5}$

$= \frac{100 \times 125}{10000 \times 5}$

$= \frac{100}{10000} \times \frac{125}{5}$

$= \frac{1}{100} \times 25$

$= \frac{1 \times 25}{100}$

$= \frac{25}{100}$

= 0.25

Example

Find: 0.375 ÷ 1.5

0.375 ÷ 1.5

$= \frac{375}{1000} \div \frac{15}{10}$

$= \frac{375}{1000} \times \frac{10}{15}$

$= \frac{375 \times 10}{1000 \times 15}$

$= \frac{10 \times 375}{1000 \times 15}$

$= \frac{10}{1000} \times \frac{375}{15}$

$= \frac{1}{100} \times 25$

$= \frac{1 \times 25}{100}$

$= \frac{25}{100}$

= 0.25

Example

Each side of a regular polygon is 2.5 cm in length. The perimeter of the polygon is 12.5 cm. How many sides does the polygon have?

The perimeter of a regular polygon is the sum of the lengths of all its equal sides = 12.5 cm.
Length of each side = 2.5 cm.

Thus, the number of sides = $\frac{12.5}{2.5} = \frac{125}{25} = 5$ .

The polygon has 5 sides.

Example

A car covers a distance of 89.1 km in 2.2 hours. What is the average distance covered by it in 1 hour?

Distance covered by the car = 89.1 km.

Time required to cover this distance = 2.2 hours.

So distance covered by it in 1 hour = $\frac{89.1}{2.2} = \frac{891}{22}$ = 40.5 km.

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Division of Decimal Numbers - Division of Decimal Numbers by 10, 100 and 1000

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Topics

Term - 1

Number System

Measurements

Algebra

Direct and Inverse Proportion

Geometry

Information Processing

Term - 2

Number System

Measurements

Algebra

Geometry

Information Processing

Term - 3

Number System

Percentage and Simple Interest

Algebra

Geometry

Statistics

Information Processing

Notes

Division of a Decimal Number by Another Decimal Number:

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Example

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Example

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Division of Decimal Numbers - Division of a Decimal Number by Another Decimal Number

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Topics

Term - 1

Number System

Measurements

Algebra

Direct and Inverse Proportion

Geometry

Information Processing

Term - 2

Number System

Measurements

Algebra

Geometry

Information Processing

Term - 3

Number System

Percentage and Simple Interest

Algebra

Geometry

Statistics

Information Processing

Notes

Division of a Decimal Number by Another Decimal Number:

Example

Example

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