Grade 2
  1. Number Sense and Operations  1.1. Counting and Number Sequences  1.1.1. Counting up to 100  1.1.2. Counting by 2s, 5s, and 10s  1.1.3. Counting Backward from 20  1.1.4. Odd and even numbers in counting sequences  1.2. Place Value  1.2.1. Understanding ones and tens  1.2.2. Comparing Two-Digit Numbers  1.2.3. Identifying the Value of Each Digit in a Number  1.2.4. Building numbers using tens and ones  1.3. Addition and Subtraction  1.3.1. Basic addition up to 20  1.3.2. Basic subtraction up to 20  1.3.3. Addition with Regrouping  1.3.4. Subtraction with Borrowing  1.3.5. Solving word problems involving addition and subtraction  1.3.6. Addition and Subtraction with Multiples of 10  1.4. Odd and Even Numbers  1.4.1. Identifying Odd and Even Numbers  1.4.2. Understanding patterns in odd and even numbers  1.4.3. Simple operations with odd and even numbers
  2. Fractions and Decimals  2.1. Introduction to Fractions  2.1.1. Understanding halves and quarters  2.1.2. Representing fractions visually  2.1.3. Simple Fraction Comparisons  2.1.4. Writing Simple Fractions  2.1.5. Fractions as part of a whole  2.2. Fraction Equivalency  2.2.1. Understanding Equal Parts  2.2.2. Identifying Equivalent Fractions
  3. Measurement and Data  3.1. Length Measurement  3.1.1. Measuring objects using rulers  3.1.2. Comparing lengths  3.1.3. Estimating lengths  3.1.4. Understanding units of measurement (centimeters and inches)  3.1.5. Relating Length Measurements to Real-World Objects  3.2. Weight and Mass Measurement  3.2.1. Comparing Weights of Objects  3.2.2. Estimating weight in grams and kilograms  3.2.3. Using balance scales for comparison  3.3. Volume and Capacity Measurement  3.3.1. Understanding capacity with cups and liters  3.3.2. Comparing capacities of containers  3.3.3. Introduction to Milliliters  3.4. Time  3.4.1. Reading analog and digital clocks  3.4.2. Understanding hours and minutes  3.4.3. Calculating elapsed time in hours  3.4.4. Days of the week and months of the year  3.4.5. Understanding AM and PM  3.5. Money  3.5.1. Recognizing coins and bills  3.5.2. Counting money up to $1  3.5.3. Simple Addition and Subtraction with Money  3.5.4. Making Change for a Dollar
  4. Geometry and Spatial Reasoning  4.1. Shapes and Their Attributes  4.1.1. Identifying basic shapes (circle, triangle, square, rectangle)  4.1.2. Understanding sides and corners  4.1.3. Distinguishing between 2D and 3D shapes  4.1.4. Recognizing 3D Shapes (Cube, Sphere, Cone, Cylinder)  4.1.5. Composing and Decomposing Shapes  4.2. Symmetry  4.2.1. Understanding Lines of Symmetry  4.2.2. Drawing Symmetrical Shapes  4.2.3. Identifying Symmetrical Objects in the Environment  4.3. Patterns and Spatial Awareness  4.3.1. Recognizing and Creating Patterns  4.3.2. Extending Patterns  4.3.3. Understanding positions (left, right, above, below)  4.3.4. Using a grid to locate objects
  5. Data Handling and Probability  5.1. Collecting and Organizing Data  5.1.1. Using tally marks  5.1.2. Reading Bar Graphs  5.1.3. Simple Pictographs  5.1.4. Creating Bar Graphs from Given Data  5.2. Interpreting Data  5.2.1. Answering questions based on data  5.2.3. Identifying Most and Least in Data Sets  5.3. Introduction to Probability  5.3.1. Understanding likely and unlikely events

Grade 2 → Fractions and Decimals → Introduction to Fractions ↓


Simple Fraction Comparisons


Fractions can be a fun and exciting part of learning math. As you may know, fractions represent parts of a whole. Learning how to compare fractions is very important as it helps us understand which fraction is bigger, which is smaller, or whether they are the same. In this chapter, we will explore some easy ways to compare simple fractions using numbers and shapes.

Understanding fractions

Before we start comparing fractions, let's quickly remember what fractions are. A fraction has two parts: the numerator and the denominator. Here's an example of a fraction with its two parts labeled:

  1
  3
  • The number on top is called the numerator. It tells us how many parts we have.
  • The bottom number is called the denominator. It tells us how many equal parts the whole is divided into.

In the above example, the fraction 1/3 means that we have 1 part out of 3 equal parts.

Comparing fractions

When we compare fractions, we want to know which is greater or whether they are equal. Let's see how we can do this with fractions that have:

  • Same denominator
  • Equal fractions
  • Different numerators and denominators

Fractions with the same denominators

When fractions have the same denominator, it's very easy to compare them. You just have to look at the numerators. The larger the numerator, the larger the fraction.

Suppose we have the following fractions:

  3 5
  8 8

To compare these fractions, compare their numerators:

  • The numerator of 3/8 is 3.
  • The numerator of 5/8 is 5.

Since 5 is greater than 3, 5/8 is greater than 3/8.

We write this comparison as follows:

  3 5
  8 8

Illustrating fractions with like denominators

Let's visualize it with shapes!

In the above scene:

  • The top row represents 3/8 with three green bars.
  • The bottom line represents 5/8 with five blue bars.

Fractions with the same numerator

When fractions have the same numerator, we compare the denominators. The fraction that has the smaller denominator is the larger fraction, because it means the whole fraction is divided into fewer parts.

Consider fractions:

  3 3
  4 5

To compare these, look at the denominators:

  • The denominator of 3/4 is 4.
  • The denominator of 3/5 is 5.

Since 4 is smaller than 5, therefore 3/4 is greater than 3/5.

We write this comparison as follows:

  3 3
  4 5

Looking at fractions with the same numerator

The shapes help make it more clear!

In the above scene:

  • The top row represents 3/4 with three yellow bars.
  • The bottom line represents 3/5 with three red bars.

You can see that each yellow bar is longer than the red bar, which shows that 3/4 is larger than 3/5.

Fractions with different numerators and denominators

Sometimes both the numerator and denominator of fractions are different. To compare these, we find a common denominator so that the fractions look the same. This method is similar to finding similar units to compare measurements.

Let us compare the following fractions:

  1 2
  3 5

To compare these, find a common denominator:

  • The multiples of 3 are: 3, 6, 9, 12, 15, 18, etc.
  • The multiples of 5 are: 5, 10, 15, 20, 25, etc.

15 is the smallest common multiple.

Convert 1/3:
1/3 = (1 × 5) / (3 × 5) = 5/15

Convert 2/5 to:
2/5 = (2 × 3) / (5 × 3) = 6/15

Now compare:

  5 6
 15 15

Therefore, 1/3 is less than 2/5.

Viewing fractions with different denominators

Using shapes will make this method clearer:

In the above scene:

  • The top row represents 1/3 with an orange bar.
  • The bottom row shows 2/5 with two purple bars.

Each purple bar is smaller, but together they take up more space than the orange bar, showing that 2/5 is more than 1/3.

Practice makes perfect

Practice comparing fractions in different ways, including looking at them as parts of a figure. With practice, you'll become comfortable identifying at a glance which fraction is larger or smaller.

Practice problems

1. Compare the fractions and write the correct sign: <, >, or =.

  • 4/9 _____ 5/9
  • 1/2 _____ 2/4
  • 3/7 _____ 2/7
  • 5/6 _____ 3/5

Answer:

  • 4/9 < 5/9
  • 1/2 = 2/4
  • 3/7 > 2/7
  • 5/6 > 3/5

Conclusion

Comparing fractions helps us understand numerical relationships better. Whether the fractions have the same numerator, denominator, or both, the methods discussed here will enable you to identify larger or smaller fractions with confidence. Through practice and visualization, the concept will solidify over time, making it easier to tackle more complex fractions in the future.


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Simple Fraction Comparisons

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