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 ↓


Multiplication and Division of Decimals


Decimals play an important role in our everyday lives. They are present everywhere - from shopping, cooking, money transactions to measuring distances. That is why learning how to multiply and divide decimals is very important.

Multiplying decimals

Multiplying decimals may seem a little complicated at first glance, but it's just like multiplying whole numbers. The trick is to keep track of the decimal point.

Steps to multiply decimals

  1. Ignore the decimal points and multiply the numbers as if they were whole numbers.
  2. Count the total number of decimal places in the two numbers you are multiplying.
  3. Place a decimal point in the answer. The number of decimal places in the result should equal the total number of decimal places in the numbers you multiplied.

Example 1: Multiply 2.5 by 3.6

Let us analyse this:

  1. First, ignore the decimal points and multiply 25 by 36.
  2. Multiplication without decimals: 
    25 × 36 = 900
  3. Now, count the decimal places in the original numbers. 2.5 and 3.6 both have one decimal place each, so the total is two.
  4. Insert a decimal point in our multiplication product, 900. Start at the back and move forward two places:
    So, 2.5 × 3.6 = 9.00
2.5 x 3.6 = 9.00

Example 2: Multiply 0.75 by 0.4

Follow these steps:

  1. Ignore the decimal points and multiply 75 by 4.
  2. Multiplication without decimals: 
    75 × 4 = 300
  3. Total decimal places: 0.75 has two, and 0.4 has one, so there are a total of three decimal places.
  4. Place the decimal point in our product 300 three decimal places to the right:
    Therefore, 0.75 × 0.4 = 0.300
0.75 x 0.4 = 0.300

Dividing decimals

Dividing decimals is a little different than multiplying, but it's also simple once you understand the process.

Steps to divide decimals

  1. Make the divisor (the number you're dividing by) a whole number by moving the decimal point all the way to the right.
  2. Move the decimal point in the dividend (the number being divided) the same number of places.
  3. Place the decimal point directly above the decimal point in the dividend on the answer line.
  4. Divide like whole numbers.

Example 1: Divide 6.25 by 2.5

  1. Convert 2.5 to a whole number by moving the decimal one place to the right: becomes 25.
  2. Moving the decimal point one place to the right in 6.25 will give us 62.5.
  3. Now, divide 62.5 by 25 like whole numbers. Place the decimal point above the answer line: 
    62.5 ÷ 25 = 2.5
6.25 ÷ 2.5 = 2.5

Example 2: Divide 0.81 by 0.3

  1. Move the decimal point to the right one place to make 0.3 a whole number: 0.3 becomes 3.
  2. Move the decimal in 0.81 one place to the right: 0.81 becomes 8.1.
  3. Now, divide 8.1 by 3. Use the division method: 
    8.1 ÷ 3 = 2.7
0.81 ÷ 0.3 = 2.7

Key points to remember

  • Ignore the first decimal point and multiply or divide as for whole numbers.
  • Always adjust the number of decimal places after calculation to get the correct decimal place in your answer.
  • In dividing, make the divisor a whole number by moving the decimal point forward and adjust the dividend accordingly.

Practice problems

Try solving these problems for better understanding:

  • Multiply: 1.9 × 4.8
  • Divide: 9.36 ÷ 0.6
  • Multiply: 0.47 × 3.2
  • Divide: 7.2 ÷ 1.2

Solution:

1. 1.9 × 4.8 = 9.12 2. 9.36 ÷ 0.6 = 15.6 3. 0.47 × 3.2 = 1.504 4. 7.2 ÷ 1.2 = 6

By practicing these techniques you will become more comfortable and master decimal multiplication and division, which is important for everyday applications!


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Addition and Subtraction of Decimals
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Multiplication and Division of Decimals

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