Grade 7
  1. Number System  1.1. Integers  1.1.1. Properties of Integers  1.1.2. Operations on Integers  1.1.3. Additive and Multiplicative Inverses  1.1.4. Applications of Integers  1.2. Rational Numbers  1.2.1. Definition of Rational Numbers  1.2.2. Properties of Rational Numbers  1.2.3. Operations on Rational Numbers  1.2.4. Standard Form of Rational Numbers  1.3. Decimals  1.3.1. Operations on Decimals  1.3.2. Converting Between Fractions and Decimals  1.4. Powers and Exponents  1.4.1. Laws of Exponents  1.4.2. Simplifying Expressions with Exponents  1.4.3. Scientific Notation  1.5. Roots  1.5.1. Square Roots  1.5.2. Cube Roots
  2. Algebra  2.1. Expressions  2.1.1. Algebraic Expressions  2.1.2. Simplifying Expressions  2.1.3. Evaluating Expressions  2.2. Linear Equations  2.2.1. Solving Simple Equations  2.2.2. Applications of Linear Equations  2.3. Algebraic Identities  2.3.1. Expanding Using Identities  2.3.2. Simplifying Using Identities
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Simplifying Ratios  3.1.3. Equivalent Ratios  3.2. Proportion  3.2.1. Concept of Proportion  3.2.2. Direct Proportion  3.2.3. Inverse Proportion  3.3. Unitary Method  3.3.1. Solving Problems Using the Unitary Method
  4. Geometry  4.1. Lines and Angles  4.1.1. Types of Angles  4.1.2. Pairs of Angles  4.1.3. Properties of Parallel Lines and a Transversal  4.1.4. Angle Bisectors  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Angle Sum Property  4.2.3. Exterior Angle Property  4.2.4. Pythagoras Theorem  4.3. Congruence of Triangles  4.3.1. Criteria for Congruence  4.3.2. Applications of Congruence  4.4. Quadrilaterals  4.4.1. Types of Quadrilaterals  4.4.2. Properties of Parallelograms  4.4.3. Special Quadrilaterals  4.4.4. Properties of Rectangles and Rhombuses
  5. Mensuration  5.1. Perimeter and Area  5.1.1. Perimeter of Plane Figures  5.1.2. Area of Plane Figures  5.1.3. Area of a Trapezium  5.1.4. Area of a Parallelogram  5.1.5. Area of a Circle  5.1.6. Area of Composite Figures  5.2. Surface Area and Volume  5.2.1. Cubes and Cuboids  5.2.2. Surface Area of Cylinders  5.2.3. Volume of Prisms and Cylinders  5.2.4. Volume and Surface Area of Cones
  6. Data Handling  6.1. Data Collection  6.1.1. Organizing Data  6.1.2. Frequency Distribution  6.2. Graphical Representation of Data  6.2.1. Bar Graphs  6.2.2. Double Bar Graphs  6.2.3. Pie Charts  6.2.4. Histograms  6.2.5. Line Graphs  6.3. Probability  6.3.1. Simple Events  6.3.2. Experimental Probability  6.3.3. Theoretical Probability
  7. Practical Geometry  7.1. Construction of Triangles  7.1.1. Constructing Triangles Given Side Lengths  7.1.2. Constructing Triangles Given Side and Angle  7.1.3. Constructing Right-Angled Triangles  7.2. Construction of Quadrilaterals  7.2.1. Quadrilaterals Given Side Lengths and Angles  7.2.2. Constructing Parallelograms and Rectangles

Grade 7 → Number System → Decimals ↓


Operations on Decimals


In mathematics, decimals are a way of expressing numbers that are not whole, using a point called a decimal point. Decimals are used in many real-life applications such as money, measurement, and much more. Understanding how to perform various operations with decimals is essential in many aspects of life. In this explanation, we will cover the basic operations on decimals: addition, subtraction, multiplication, and division. Each operation requires careful attention to the placement of the decimal point, and we will explore each in detail with examples for better understanding.

Addition of decimals

When adding decimals, the main rule is to line up the decimal points of the numbers you are adding. This ensures that each digit is aligned correctly according to its place value. Here's how you can add decimals:

        3.57
      + 2.68
      ,

Step 1: Align the numbers with the decimal point.

          3.57
        + 2.68
        ,

Step 2: Add the numbers as if they were whole numbers, starting with the rightmost digit.

          3.57
        + 2.68
        ,
          6.25

Result: So, 3.57 + 2.68 = 6.25.

Subtracting decimals

Subtracting decimals is similar to addition. You need to line up the decimal points and then subtract as if they were whole numbers.

        5.83
      - 2.49
      ,

Step 1: Align the numbers with the decimal point.

          5.83
        - 2.49
        ,

Step 2: Subtract the numbers starting from the right.

          5.83
        - 2.49
        ,
          3.34

Result: Thus, 5.83 - 2.49 = 3.34.

Multiplication of decimals

Multiplying decimals requires a slightly different approach. Here, you initially ignore the decimal point and multiply the numbers as if they were whole numbers, then count the decimal places in the original numbers to keep the decimal in the final result.

        2.5
      x 1.3
      ,

Step 1: Ignore the decimal and multiply 25 by 13.

          25
        X13
        ,
        325

Step 2: Count the total number of decimal places in the numbers you are multiplying. (1 place in 2.5 and 1 place in 1.3 = 2 places total).

Step 3: Place the decimal in the result such that there are two digits after the decimal place.

        32.5

Result: Thus, 2.5 x 1.3 = 3.25.

Decimal division

Dividing decimals can be a little more complicated because it involves changing the divisor to a whole number by moving the decimal point. Let's work through an example:

        3.75 ÷ 1.5

Step 1: Move the decimal point in the divisor (1.5) to the right so that it becomes a whole number (15). Move the decimal in the dividend (3.75) the same number of places.

        37.5 ÷ 15

Step 2: Divide by whole numbers: 37.5 ÷ 15 = 2.5

Result: Thus, 3.75 ÷ 1.5 = 2.5.

Practical examples and visualization

Let's visualize the addition of decimals with an SVG rectangle, where each rectangle represents a whole number, and the smaller parts represent tenths and hundredths.

Example of 3.57 + 2.68 giving a sum of 6.25

The rectangles in this visual example show how each part of the decimal corresponds to a part of the total when put together.

Decimal rounding

Sometimes the results may be more precise than necessary, requiring them to be rounded to a certain decimal place.

Example: Round 3.256 to the nearest tenth.

        3.256

Since the hundredths place (5) is 5 or more, we round off the tenths place (2) by one:

        3.3

Result: So 3.256 rounded to the nearest tenth gives 3.3.

This detailed explanation aims to deepen your understanding and ease your calculation ability when handling decimal operations. Be sure to practice these techniques with different numbers to become proficient.


Grade 7 → 1.3.1


U
username
0%
completed in Grade 7

← Prev (1.3)
Decimals
Next (1.3.2) →
Converting Between Fractions and Decimals

Comments 



Operations on Decimals

https://www.buddymath.com/g7/1.3.1?bmal=en