Grade 5
  1. Number Sense and Place Value  1.1. Understanding Large Numbers  1.2. Place Value up to Millions  1.3. Comparing and Ordering Numbers  1.4. Rounding Whole Numbers  1.5. Expanded Form and Standard Form  1.6. Estimation in Calculations
  2. Operations with Whole Numbers  2.1. Addition of Large Numbers  2.2. Subtraction of Large Numbers  2.3. Multiplication Concepts and Strategies  2.4. Division Concepts and Strategies  2.5. Multi-Digit Multiplication  2.6. Long Division  2.7. Order of Operations
  3. Fractions  3.1. Introduction to Fractions  3.2. Equivalent Fractions  3.3. Simplifying Fractions  3.4. Comparing and Ordering Fractions  3.5. Addition and Subtraction of Fractions  3.6. Multiplication of Fractions  3.7. Division of Fractions  3.8. Mixed Numbers and Improper Fractions  3.9. Converting Between Improper Fractions and Mixed Numbers
  4. Decimals  4.1. Understanding Decimals  4.2. Place Value in Decimals  4.3. Comparing and Ordering Decimals  4.4. Rounding Decimals  4.5. Addition and Subtraction of Decimals  4.6. Multiplication of Decimals  4.7. Division of Decimals  4.8. Converting Decimals to Fractions and Vice Versa
  5. Measurement  5.1. Length Measurement (Metric and Customary Units)  5.2. Weight and Mass Measurement  5.3. Volume and Capacity Measurement  5.4. Area of Squares and Rectangles  5.5. Perimeter of Polygons  5.6. Time and Elapsed Time  5.7. Temperature  5.8. Understanding Metric Conversions
  6. Geometry  6.1. Types of Lines and Angles  6.2. Measuring Angles  6.3. Classifying Triangles  6.4. Properties of Quadrilaterals  6.5. Symmetry and Reflection  6.6. Transformations (Translation, Rotation, Reflection)  6.7. Coordinate Plane and Plotting Points  6.8. 3D Shapes and Their Properties  6.9. Nets of 3D Shapes  6.10. Understanding Congruence and Similarity
  7. Data and Probability  7.1. Introduction to Data Collection  7.2. Organizing Data (Tables and Tally Charts)  7.3. Graphs (Bar Graphs, Line Plots, Pictographs)  7.4. Mean, Median, and Mode  7.5. Range of Data  7.6. Introduction to Probability  7.7. Simple Events and Outcomes  7.8. Probability of Independent Events
  8. Ratios and Proportions  8.1. Understanding Ratios  8.2. Writing and Simplifying Ratios  8.3. Equivalent Ratios  8.4. Introduction to Proportions  8.5. Solving Proportion Problems
  9. Algebraic Thinking  9.1. Understanding Variables and Expressions  9.2. Writing Algebraic Expressions  9.3. Simplifying Expressions  9.4. Solving One-Step Equations  9.5. Understanding Patterns and Sequences  9.6. Using the Distributive Property
  10. Financial Literacy  10.1. Introduction to Money and Currency  10.2. Budgeting Basics  10.3. Saving and Spending  10.4. Understanding Interest  10.5. Basic Financial Planning  10.6. Simple vs. Compound Interest

Grade 5 → Decimals ↓


Division of Decimals


Division of decimals is an important topic in maths, especially for class 5 students. It involves dividing numbers containing decimals, and it may seem difficult at first, but with practice and understanding, it becomes easier. Let's dive into this concept and learn how to divide decimals with a series of steps, examples, and different exercises.

Understanding decimals

Before we proceed with division, let's remember what decimals are. Decimals are numbers that include a decimal point (.), which separates the whole number part from the fractional part. For example, the decimal number In 3.75:

  • 3 is the whole number part.
  • 75 is the fractional part.

Decimal numbers can come in various lengths: one decimal place (e.g., 3.4), two decimal places (e.g., 3.45), and so on. They provide a way to express fractions and are often used to express money, measurements, and other things. They can be encountered when dealing with.

Steps to divide decimals

To divide decimals, you can follow several steps. The main idea is to turn the division of decimals into a simpler problem involving whole numbers. Here is a systematic way to divide decimals:

Step 1: Make the denominator a whole number

The divisor is the number you're dividing by. If the divisor is a decimal, you can make the divisor a whole number by multiplying both the divisor and the dividend (the number being divided by) by the same power of 10.

For example, consider the division: 4.5 ÷ 0.3.

The divisor is 0.3. To make it a whole number, multiply it by 10 Then, multiply the dividend by 10 as well:

4.5 × 10 = 45 0.3 × 10 = 3

Now your division problem is 45 ÷ 3.

Step 2: Do the partitioning

When the denominator is a whole number, perform the division as you would with whole numbers. Using the example above:

45 ÷ 3 = 15

Thus, 4.5 ÷ 0.3 equals 15.

Step 3: Place the decimal point

The last step is to correctly place the decimal point in the quotient. Since we multiplied both the divisor and the dividend by the same amount, the quotient will be correctly placed as a whole number. If the decimal places in the original problem are too many, the result will be more complicated. If they were, adjustments may be needed.

Examples and practice problems

Let's look at some more examples to deepen our understanding.

Example 1

Divide 7.2 by 0.4.

First, multiply both numbers by 10 to get whole numbers:

7.2 × 10 = 72 0.4 × 10 = 4

Now divide:

72 ÷ 4 = 18

So, 7.2 ÷ 0.4 = 18.

Example 2

Divide 5.76 by 0.12.

Multiply both numbers by 100 to get whole numbers:

5.76 × 100 = 576 0.12 × 100 = 12

Now divide:

576 ÷ 12 = 48

Therefore, 5.76 ÷ 0.12 = 48.

Exercise

Try these yourself:

  1. 3.5 ÷ 0.5
  2. 8.4 ÷ 2.1
  3. 9.1 ÷ 0.7
  4. 6.05 ÷ 0.11

Remember to follow the steps: make the divisor a whole number, divide, and place the decimal point correctly if necessary.

Visual example

Let's look at a step-by-step visual representation of dividing decimals.

Suppose we have 4.8 ÷ 0.2 Step 1: Multiply by 10 4.8 × 10 = 48 0.2 × 10 = 2 Step 2: Divide with whole numbers 48 ÷ 2 = 24 Answer: 4.8 ÷ 0.2 = 24

Decoding the decimal place

The biggest challenge in dividing decimals is understanding how to place the decimal point in the answer. Here are some tips to help you:

  • If both the divisor and dividend are multiplied by the same power of 10, further adjustment of the decimal place is unnecessary.
  • Carefully count the decimal places in the original numbers to make sure you move them correctly when rounding both numbers.

Why divide decimals?

Decimal division isn't just a math exercise - it has real-world applications too. Whether counting money, taking measurements, or doing tasks that require precision, understanding how to divide decimal numbers is important. For example, if you buy 2.5 metres of fabric and want to divide it equally into 0.5 metre pieces, you need to divide 2.5 by 0.5 to find out how many pieces you will have.

These skills are fundamental and open the door to more advanced math concepts. With regular practice, dividing decimals can become second nature.

Practice with more problems

To become proficient at dividing decimals, it is important to practice constantly. Below are additional problems for self-assessment. Try to solve them using the steps mentioned earlier.

  1. 10.25 ÷ 0.5
  2. 15.6 ÷ 1.3
  3. 22.4 ÷ 2.24
  4. 4.536 ÷ 0.12
  5. 7.87 ÷ 0.31

Take your time and check your answer by multiplying the quotient by the divisor to see if you got the original quotient.

Conclusion

Dividing decimals may seem challenging at first, but with step-by-step methods and enough practice, it becomes manageable. Begin by converting the division problem into a simpler form involving whole numbers, performing the operation, and dividing the decimal correctly. By keeping this in mind, you will master decimal division. These mathematical skills are not only important academically but are also valuable in everyday life.


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Multiplication of Decimals
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Division of Decimals

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