Grade 6
  1. Number System  1.1. Whole Numbers  1.1.1. Place Value and Face Value  1.1.2. Comparing and Ordering Numbers  1.1.3. Rounding Numbers  1.1.4. Properties of Whole Numbers (Associative, Commutative, Distributive)  1.2. Integers  1.2.1. Introduction to Integers  1.2.2. Addition and Subtraction of Integers  1.2.3. Multiplication and Division of Integers  1.2.4. Properties of Integer Operations  1.3. Fractions  1.3.1. Types of Fractions  1.3.2. Equivalent Fractions  1.3.3. Simplification of Fractions  1.3.4. Addition and Subtraction of Fractions  1.3.5. Multiplication and Division of Fractions  1.3.6. Comparing and Ordering Fractions  1.4. Decimals  1.4.1. Understanding Decimals  1.4.2. Conversion between Fractions and Decimals  1.4.3. Addition and Subtraction of Decimals  1.4.4. Multiplication and Division of Decimals  1.4.5. Comparing and Ordering Decimals
  2. Algebra  2.1. Basics of Algebra  2.1.1. Variables and Constants  2.1.2. Expressions and Equations  2.1.3. Algebraic Terms and Coefficients  2.2. Solving Simple Equations  2.2.1. Balancing Equations  2.2.2. Solving One-Step Equations  2.2.3. Solving Two-Step Equations  2.3. Patterns and Sequences  2.3.1. Identifying Patterns  2.3.2. Arithmetic Sequences
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Equivalent Ratios  3.1.3. Simplifying Ratios  3.2. Proportion  3.2.1. Introduction to Proportion  3.2.2. Direct and Inverse Proportions  3.3. Percentages  3.3.1. Converting Ratios to Percentages  3.3.2. Percentage Increase and Decrease  3.3.3. Discount and Profit Calculations  3.3.4. Simple Interest Calculations in Percentages in Ratio and Proportion
  4. Geometry  4.1. Basic Geometric Shapes  4.1.1. Points, Lines, and Angles  4.1.2. Types of Angles  4.1.3. Intersecting and Parallel Lines  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Properties of Triangles  4.2.3. Sum of Angles in a Triangle  4.2.4. Congruence of Triangles  4.3. Quadrilaterals  4.3.1. Types of Quadrilaterals  4.3.2. Properties of Quadrilaterals  4.4. Circles  4.4.1. Radius and Diameter  4.4.2. Circumference and Area  4.4.3. Arcs and Chords  4.4.4. Sector and Segment
  5. Mensuration  5.1. Perimeter  5.1.1. Perimeter of Simple Shapes  5.2. Area  5.2.1. Area of Rectangles and Squares  5.2.2. Area of Triangles and Parallelograms  5.2.3. Area of Composite Figures  5.2.4. Area of Trapezium  5.3. Volume  5.3.1. Volume of Cubes and Cuboids  5.3.2. Volume of Cylinders  5.3.3. Volume of Cones  5.3.4. Surface Area of Simple Solids
  6. Data Handling  6.1. Introduction to Data  6.1.1. Types of Data  6.1.2. Organizing Data  6.1.3. Frequency Distribution  6.2. Graphs and Charts  6.2.1. Bar Graphs  6.2.2. Line Graphs  6.2.3. Pictographs  6.2.4. Pie Charts  6.3. Mean, Median, and Mode  6.3.1. Calculating Mean  6.3.2. Finding Median  6.3.3. Identifying Mode  6.3.4. Range of Data in Mean, Median, and Mode
  7. Probability  7.1. Basics of Probability  7.1.1. Understanding Probability  7.1.2. Probability of Simple Events  7.1.3. Experimental and Theoretical Probability
  8. Practical Geometry  8.1. Construction of Shapes  8.1.1. Constructing Triangles  8.1.2. Constructing Quadrilaterals  8.1.3. Constructing Circles and Arcs  8.2. Symmetry  8.2.1. Line of Symmetry  8.2.2. Rotational Symmetry  8.2.3. Translational Symmetry

Grade 6 → Number System → Decimals ↓


Addition and Subtraction of Decimals


Decimals are an important part of math, and they come in handy in many real-life situations. Understanding how to add and subtract decimals is important for solving problems related to money, measurements, and other numerical data that involve fractions of whole numbers. In this lesson, we'll learn how to handle the addition and subtraction of decimals.

Understanding decimals

Decimals are a way of representing fractions and are defined by the position of the digits in relation to the decimal point. The numbers to the left of the decimal point are whole numbers, and each digit to the right of the decimal point represents a part of a whole.

For example, consider the decimal number: 23.456

23.456
,
| | Tenth (4)
| hundredth (5)
Whole numbers (23)

Here 23 is the whole number. 4 is in the tenths place, 5 is in the hundredths place, and 6 is in the thousandths place.

Adding decimals

Adding decimals is the same as adding whole numbers, but it takes the extra step of aligning the decimal points. This ensures that you are adding digits of the same place value.

Steps to add decimals:

  1. Write the numbers one below the other and keep the decimal points lined up.
  2. Increase each number by zeros so that they have the same number of decimal places.
  3. Add the numbers the same way you add whole numbers, starting with the rightmost digit.
  4. Place the decimal point in the sum just below the other decimal points.

Example:

Add 12.56 and 7.128.

12.560 
+ 7.128 
,
19.688
1 | 2 . 5 6 0 + 7 . 1 2 8 , 19. 6 8 8

The decimal points are lined up, and the sum is calculated as 19.688.

Tips:

  • Always line up the decimal points before you begin adding.
  • Fill in zeros to make the decimal places equal. This will help prevent mistakes.

Subtracting decimals

Subtracting decimals involves the same alignment of decimal points as adding. Following the correct procedure will help you get accurate results.

Steps to subtract decimals:

  1. Write the numbers lined up with the decimal point.
  2. Make sure both numbers have the same number of decimal places by adding zeros where necessary.
  3. Start subtracting from the rightmost digit, just like with whole numbers.
  4. Place the decimal point in the gap just below the other decimal points.

Example:

Subtract 3.56 from 8.459.

8,459 
- 3.560 
,
4,899
8. 4 5 9 - 3 . 5 6 0 , 4. 8 9 9

Here, the decimal points are aligned, and the result is 4.899.

Tips:

  • Make sure the numbers are correctly aligned near the decimal point for accurate subtraction.
  • Convert numbers to the same number of decimal places by adding zeros where necessary.

Importance of decimal place value

Remember, the value of each digit in a decimal number is important when adding or subtracting. Putting it in the wrong place can completely change the value of your calculation.

Example:

Compare the following calculations:

Incorrect connection:
Incorrect: 
12.56
+ 7.128
,
19.688 (wrong!)

Connecting correctly:
Correct:
12.560
+ 7.128
,
19.688
Wrong way 1 2 . 5 6 + 7 . 1 2 8 , 19. 6 8 8 The right way 1 2 . 5 6 0 + 7 . 1 2 8 , 19. 6 8 8

Practice problems

Yoga practice

Solve the following problems:

  1. 23.45 + 5.678
  2. 13.56 + 8.44
  3. 1.2 + 2.6789

Subtraction practice

Solve the following problems:

  1. 10.56 - 4.78
  2. 23.469 - 7.534
  3. 8.002 - 2.111

Connection to the real world

Decimals are often used in everyday life, especially when it comes to money or measurement. For example, when you go shopping and calculate the total amount, decimal values are used to represent cents.

Example:

If you buy items priced at $1.25, $2.50, and $3.75, your total cost will be calculated as follows:

1.25
+2.50
+3.75
,
7.50

Understanding how to add and subtract decimals will help you better manage your expenses and make sure you're getting the correct change.

Conclusion

Adding and subtracting decimals is a basic skill in math that applies in many real-world scenarios. Making sure you align the decimal points and solve the problems properly will produce accurate results. Practice more, follow the steps, and soon, handling decimal operations will become second nature!


Grade 6 → 1.4.3


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Conversion between Fractions and Decimals
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Multiplication and Division of Decimals

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Addition and Subtraction of Decimals

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