Grade 3
  1. Number Sense and Numeration  1.1. Understanding Numbers  1.1.1. Reading and Writing Numbers up to 10,000  1.1.2. Place Value up to Thousands  1.1.3. Comparing and Ordering Numbers  1.1.4. Rounding Numbers to the Nearest Ten and Hundred  1.1.5. Skip Counting by 2s, 5s, 10s, and 100s up to 1,000  1.2. Operations with Whole Numbers  1.2.1. Addition and Subtraction up to 1,000  1.2.2. Multiplication Facts (up to 10 x 10)  1.2.3. Division Facts (up to 100)  1.2.4. Multiplication as Repeated Addition  1.2.5. Division as Equal Sharing  1.2.6. Word Problems with Addition, Subtraction, Multiplication, and Division  1.3. Estimation  1.3.1. Estimating Sums and Differences  1.3.2. Estimating Products and Quotients  1.4. Understanding Even and Odd Numbers
  2. Fractions and Decimals  2.1. Understanding Fractions  2.1.1. Identifying and Representing Fractions  2.1.2. Fractions of a Whole and Part of a Set  2.1.3. Comparing and Ordering Fractions with Like Denominators  2.1.4. Equivalent Fractions  2.1.5. Simple Fraction Word Problems  2.2. Introduction to Decimals  2.2.1. Tenths and Hundredths as Decimals  2.2.2. Relationship between Fractions and Decimals
  3. Measurement  3.1. Length  3.1.1. Measuring in Centimeters and Meters  3.1.2. Comparing and Ordering Lengths  3.1.3. Estimating Lengths  3.1.4. Converting Between Centimeters and Meters  3.2. Mass  3.2.1. Measuring in Grams and Kilograms  3.2.2. Estimating and Comparing Mass  3.3. Capacity  3.3.1. Measuring in Milliliters and Liters  3.3.2. Estimating and Comparing Capacity  3.4. Time  3.4.1. Telling Time to the Nearest Minute  3.4.2. Calculating Elapsed Time  3.4.3. Using a Calendar  3.4.4. Understanding A.M. and P.M.  3.5. Area and Perimeter  3.5.1. Calculating Perimeter of Simple Shapes  3.5.2. Estimating and Measuring Area of Shapes  3.5.3. Finding Area by Counting Squares
  4. Geometry  4.1. Properties of Shapes  4.1.1. Identifying 2D Shapes (Triangles, Quadrilaterals, Circles, etc.)  4.1.2. Identifying 3D Shapes (Cubes, Spheres, Cylinders, etc.)  4.1.3. Describing Attributes of 2D and 3D Shapes  4.1.4. Recognizing Parallel and Perpendicular Lines  4.2. Symmetry and Transformations  4.2.1. Recognizing Lines of Symmetry  4.2.2. Identifying Flips, Slides, and Turns  4.3. Angles  4.3.1. Understanding Right Angles  4.3.2. Comparing Angles (Acute, Right, Obtuse)
  5. Data Management and Probability  5.1. Data Collection and Organization  5.1.1. Collecting Data using Surveys and Experiments  5.1.2. Organizing Data using Tally Charts and Tables  5.2.1. Creating and Interpreting Pictographs  5.2.2. Creating and Interpreting Bar Graphs  5.2.3. Reading Simple Line Graphs  5.3. Probability  5.3.1. Understanding Basic Probability Terms (Certain, Possible, Impossible)  5.3.2. Predicting Outcomes  5.3.3. Simple Probability Experiments
  6. Patterns and Algebra  6.1. Patterns  6.1.1. Identifying and Extending Numeric Patterns  6.1.2. Identifying and Extending Shape Patterns  6.1.3. Creating Patterns Using Rules  6.2. Introduction to Algebra  6.2.1. Understanding Variables as Unknowns  6.2.2. Solving Simple Addition and Subtraction Equations  6.2.3. Using Patterns to Solve Problems
  7. Problem-Solving Skills  7.1. Strategies for Problem-Solving  7.1.1. Using Pictures or Diagrams  7.1.2. Identifying Patterns in Problems  7.1.3. Making Organized Lists  7.1.4. Guessing and Checking  7.1.5. Using Logical Reasoning  7.1.6. Breaking Down Problems into Steps

Grade 3 → Fractions and Decimals → Understanding Fractions ↓


Comparing and Ordering Fractions with Like Denominators


Welcome to the interesting world of fractions! In this detailed explanation, we'll learn how to compare and order fractions with the same denominators. Once you understand the basics, fractions can be a fun and exciting topic. In this lesson, we'll use simple examples and visual aids to help make these concepts easier to understand.

Understanding fractions

Before we move on to comparing and ordering fractions, let's first make sure we understand fractions. A fraction is a way of representing a part of a whole. It consists of two numbers:

  • Numerator: The top part of a fraction, which tells us how many parts there are in the fraction.
  • Denominator: The bottom part of a fraction, which tells us how many equal parts the whole number is divided into.

For example, in the fraction 3/4, the number 3 is the numerator, and 4 is the denominator.

Same denominator

When we say "like denominators," we mean that the fractions have the same denominator. This means that for the fractions we are comparing, the whole fraction is divided into the same number of equal parts. For example, 1/5 and 3/5 are fractions with the same denominator because their denominators are both 5.

Comparing fractions with the same denominators

Comparing fractions with the same denominator is very easy. All you have to do is compare their numerators. Let's look at some examples to make this process clear.

Example 1: Comparing 2/7 and 5/7

Since both fractions have the same denominator (7), we compare their numerators. The numerators are 2 and 5. Since 2 is smaller than 5, we can write:

    2/7 < 5/7

Visually, imagine a pie cut into 7 equal pieces. Two pieces of the pie represent 2/7, while five pieces represent 5/7. Clearly, five pieces are more than two pieces.

2/7 5/7

Example 2: 4/10 and 6/10 comparison

Again, the denominators are the same (10). Compare the numerators: 4 and 6. Since 4 is less than 6, we can say:

    4/10 < 6/10

Imagine a chocolate bar is divided into 10 equal pieces. Having four pieces means you have less chocolate than having six pieces.

4/10 6/10

Putting fractions with the same denominators in order

Now that we've learned how to compare two fractions, we can extend this idea to order a group of fractions with the same denominator from smallest to largest or largest to smallest. Let's see how this is done.

Example 3: Order of 3/8, 5/8 and 4/8

To order these fractions, first list their numerators: 3, 5, and 4. Then, arrange these numbers in order:

    From lowest to highest: 3, 4, 5
    From largest to smallest: 5, 4, 3

So the fractions in order from smallest to largest are:

    3/8, 4/8, 5/8

And from largest to smallest:

    5/8, 4/8, 3/8
3/8 5/8 4/8

Example 4: Sequence of 2/9, 7/9, 5/9 and 0/9

Start by listing the fractions: 2, 7, 5, and 0. Arrange these fractions from smallest to largest:

    From lowest to highest: 0, 2, 5, 7

So, the sequence is this:

    0/9, 2/9, 5/9, 7/9

From highest to lowest:

    From largest to smallest: 7, 5, 2, 0

The order is as follows:

    7/9, 5/9, 2/9, 0/9
0/9 2/9 5/9 7/9

Summary

Understanding fractions with the same denominators is an important step in learning fractions. By simply comparing the numerators, you can easily determine which fraction is larger or smaller when the denominators are the same. Additionally, ordering fractions involves placing them in order from smallest to largest or vice versa by examining their numerators.

As you now know, recognizing like denominators simplifies many mathematical problems. By mastering this comparison and ordering technique, you create a strong foundation for working with more complex fraction operations in the future.

Keep exploring fractions, and soon you'll be able to solve more complex math problems with ease. Happy learning!


Grade 3 → 2.1.3


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Comparing and Ordering Fractions with Like Denominators

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