Grade 4
  1. Numbers and Place Value  1.1. Understanding Place Value  1.2. Reading and Writing Large Numbers  1.3. Comparing and Ordering Numbers  1.4. Rounding Numbers  1.5. Understanding Odd and Even Numbers  1.6. Number Patterns and Sequences
  2. Addition and Subtraction  2.1. Addition of Large Numbers  2.2. Subtraction of Large Numbers  2.3. Estimation in Addition and Subtraction  2.4. Word Problems on Addition and Subtraction
  3. Multiplication and Division  3.1. Understanding Multiplication  3.2. Multiplying Multi-Digit Numbers  3.3. Understanding Division  3.4. Dividing Multi-Digit Numbers  3.5. Multiplication and Division Facts  3.6. Word Problems on Multiplication and Division
  4. Factors and Multiples  4.1. Understanding Factors  4.2. Finding Common Factors  4.3. Understanding Multiples  4.4. Finding Common Multiples  4.5. Prime and Composite Numbers  4.6. Prime Factorization  4.7. Greatest Common Factor  4.8. Least Common Multiple
  5. Fractions  5.1. Understanding Fractions  5.2. Equivalent Fractions  5.3. Simplifying Fractions  5.4. Comparing and Ordering Fractions  5.5. Addition of Fractions  5.6. Subtraction of Fractions  5.7. Mixed Numbers and Improper Fractions  5.8. Converting Mixed Numbers to Improper Fractions  5.9. Word Problems on Fractions
  6. Decimals  6.1. Understanding Decimals  6.2. Reading and Writing Decimals  6.3. Comparing and Ordering Decimals  6.4. Rounding Decimals  6.5. Addition of Decimals  6.6. Subtraction of Decimals  6.7. Converting Decimals to Fractions  6.8. Converting Fractions to Decimals  6.9. Word Problems on Decimals
  7. Measurement  7.1. Length  7.1.1. Units of Length  7.1.2. Converting Units of Length  7.1.3. Perimeter  7.1.4. Area  7.1.5. Word Problems on Length  7.2. Weight  7.2.1. Units of Weight  7.2.2. Converting Units of Weight  7.2.3. Word Problems on Weight  7.3. Volume and Capacity  7.3.1. Units of Volume  7.3.2. Converting Units of Volume  7.3.3. Estimating Volume and Capacity  7.3.4. Word Problems on Volume and Capacity  7.4. Time  7.4.1. Reading Time  7.4.2. Units of Time  7.4.3. Converting Units of Time  7.4.4. Calculating Elapsed Time  7.4.5. Word Problems on Time
  8. Geometry  8.1. Properties of Shapes  8.1.1. Types of Angles  8.1.2. Types of Triangles  8.1.4. Symmetry  8.1.5. Lines of Symmetry  8.2. Perimeter and Area  8.2.1. Perimeter of Rectangles  8.2.2. Perimeter of Other Shapes  8.2.3. Area of Rectangles  8.2.4. Area of Other Shapes  8.2.5. Area of Irregular Shapes  8.3. Coordinate Geometry  8.3.1. Understanding Coordinates  8.3.2. Plotting Points on a Grid  8.3.3. Identifying Shapes on a Grid
  9. Data and Graphs  9.1. Types of Data  9.2. Organizing Data  9.3. Reading Bar Graphs  9.4. Drawing Bar Graphs  9.5. Line Plots  9.7. Reading and Interpreting Line Graphs  9.8. Word Problems on Graphs
  10. Money  10.1. Understanding Money  10.2. Addition and Subtraction with Money  10.3. Making Change  10.4. Multiplying and Dividing Money  10.5. Word Problems on Money

Grade 4 → Factors and Multiples ↓


Understanding Multiples


In math, a multiple is the result of multiplying a number by an integer. This is an important concept, especially for students who are beginning to learn about factors and multiples. Understanding multiples can help in mastering other areas of math, such as division, fractions, and even algebra. Let's take a closer look at what multiples are and how we can identify them.

What is multiple?

The multiple of a number is what you get when you multiply it by another whole number. For example, when you multiply 3 by 2, you get 6. Therefore, 6 is a multiple of both 3 and 2.

3 × 2 = 6

Matrices of multiples may seem abstract at first, but they become easier to understand when broken down with the help of examples.

Understanding multiples with visual examples

Let's take a visual approach and see what multiples look like when represented graphically. Consider the number 3 and its first few multiples: 3, 6, 9, 12, and so on.

Here we show you how to multiply a number by an integer:

3 , 6 , 9 , 12 ,

Why are multipliers important?

Understanding multiples of numbers helps us identify patterns in mathematics and solve various mathematical problems, especially in arithmetic and algebra.

For example, when working with fractions, it is often necessary to find common multiples in order to add or subtract fractions:

Example

Suppose you want to add the fractions 1/4 and 1/3. You need to find a common multiple of the denominators 4 and 3.

The multiples of 4 are: 4, 8, 12, 16, 20...

The multiples of 3 are: 3, 6, 9, 12, 15...

The first common multiple of both 4 and 3 is 12.

You can convert fractions like this:

1/4 = 3/12
1/3 = 4/12

Adding these gives:

3/12 + 4/12 = 7/12

Finding multiples

To find the multiples of any number, you just need to multiply it by the whole numbers 1, 2, 3, etc. For example, the multiples of 5 can be found by multiplying 5 by 1, 2, 3, and so on.

5 × 1 = 5 5 × 2 = 10 5 × 3 = 15 5 × 4 = 20 5 × 5 = 25

So the first few multiples of 5 are 5, 10, 15, 20, and 25.

Multiplier in real life

Multipliers appear in many real-world situations. Some examples are:

  • In a bakery, donuts are packed in boxes of 12. Here the numbers 12, 24, 36, etc. are multiples of 12.
  • If you save money in multiples of 10, your savings can be 10, 20, 30, 40 and so on.

Example

A school bus seats 5 students per row, and there are five rows in total. How many students can the bus carry when fully loaded?

You can express this in multiples:

5 × 5 = 25

Therefore, a total of 25 students can sit in the bus.

Diving deeper into multiples

Common multiples

Sometimes, it is useful to find shared factors between two numbers. These are called common factors.

Consider the numbers 4 and 6. The multiples of each are as follows:

  • Multiples of 4: 4, 8, 12, 16, 20...
  • Multiples of 6: 6, 12, 18, 24...

Here the first common multiple of 4 and 6 is 12.

4 6 Common multiple: 12

Least common multiple (LCM)

As shown above, the smallest common multiple shared by two numbers is called the least common multiple (LCM). This is a useful concept for adding or subtracting fractions, aligning schedules, or solving problems that require coordination.

For example, to find the LCM of 8 and 12:

  • Multiples of 8: 8, 16, 24, 32, 40...
  • Multiples of 12: 12, 24, 36, 48...

The least common multiple of 8 and 12 is 24.

Conclusion

Understanding multiples opens the door to many mathematical concepts and applications. Using simple multiplication, we can find multiples of any number and apply this knowledge to real-world problems, such as distributing objects evenly or finding corresponding fractions in fractions.

Learning about common multiples and least common multiples can simplify complex operations and increase a student's mathematical base. As students become more comfortable with multiples, they will find that many aspects of mathematics become more intuitive and manageable.

Keep practicing finding multiples, and soon you'll see these patterns emerge naturally in everyday activities and problems!


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Understanding Multiples

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