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 ↓


Equivalent Fractions


Fractions are numbers we use to represent parts of a whole. When we talk about fractions, we have two numbers: the top number or numerator and the bottom number, called the denominator. A fraction looks like this: 1 ⁄ 2. The numerator tells us how many parts we're talking about, and the denominator tells us how many equal parts make up a whole.

Equivalent fractions are fractions that may look different, but actually represent the same value or proportion of a whole. This is like saying there are different ways to describe the same amount of dessert on a plate.

Understanding equivalent fractions

Let's start with a simple example to understand equivalent fractions. Imagine that you have a pizza, and it is cut into 4 equal slices. If you ate 2 of those slices, you ate 2 ⁄ 4 of the pizza. Now, if instead, that same pizza was cut into 8 equal slices, and you ate 4 slices, you ate 4 ⁄ 8 of the pizza. You can see with both fractions, 2 ⁄ 4 and 4 ⁄ 8, you ate half of the pizza.

2 out of 4 slices = 4 out of 8 slices

1/2 
,
,
,
,

2/4 4/8

This means that 2 ⁄ 4 and 4 ⁄ 8 are like fractions; they represent the same amount of pizza eaten, even though they look different.

Visual example

How to find equivalent fractions

You can find equivalent fractions by multiplying or dividing both the numerator and denominator by the same number. Remember, we can't change the value of the fraction; we're just finding another way to write it.

Multiplying to find equivalent fractions

If we have a fraction like 1 ⁄ 3 and want to find an equivalent fraction, we can multiply both the numerator and the denominator by the same number. Let's multiply by 2.

1 * 2 2 ---- = ----- 3 * 2 6
1 * 2 2 ---- = ----- 3 * 2 6

So 1 ⁄ 3 is equal to 2 ⁄ 6.

Dividing to find equivalent fractions

Suppose we have a fraction 8 ⁄ 10 To find the equivalent fraction, we can divide the numerator and denominator by the greatest common factor.

8 ÷ 2 4 ---- = ---- 10 ÷ 2 5
8 ÷ 2 4 ---- = ---- 10 ÷ 2 5

Therefore, 8 ⁄ 10 is equal to 4 ⁄ 5.

Why learn about equivalent fractions?

Understanding equivalent fractions can be very helpful when you're adding or subtracting fractions. When fractions have the same denominator, it's easier to add and subtract them like whole numbers.

For example, let's add 1 ⁄ 4 to 1 ⁄ 2 We know from equivalent fractions that 1 ⁄ 2 is the same as 2 ⁄ 4.

1 2 3 - + - = - 4 4 4
1 2 3 - + - = - 4 4 4

So, when using equivalent fractions 1 ⁄ 4 and 1 ⁄ 2 sums to 3 ⁄ 4.

Using equivalent fractions with decimals

Equivalent fractions are also closely related to decimals. For example, the fraction 1 ⁄ 2 is the same as the decimal 0.5. You can convert fractions to decimals and vice versa by understanding their equivalence.

Another example is 3 ⁄ 4, which can be converted to a decimal:

3 ÷ 4 = 0.75
3 ÷ 4 = 0.75

Thus, 3 ⁄ 4 is equal to 0.75.

Practice problem example

Here are some practice problems that will help you understand equivalent fractions further:

  • Find two equivalent fractions for 3 ⁄ 5.
    Solution: 6 ⁄ 10 and 9 ⁄ 15 can be two similar fractions.
  • Determine if 5 ⁄ 8 and 10 ⁄ 16 are similar.
    Solution: Yes, they are equal. If you multiply 5 by 2, you get 10. Multiplying 8 by 2, you get 16.
  • What decimal is equal to 1 ⁄ 4?
    Solution: 0.25

Practicing these types of problems will make it much easier to understand equivalent fractions and use them in everyday mathematical situations.

Conclusion

Equivalent fractions are an important concept in understanding how fractions work. They show that fractions that look different can actually be the same in terms of their true value. Using multiplication and division, one can find multiple equivalent forms of the same fraction and use these concepts to solve problems with a minimum of effort and confusion.

Understanding equivalent fractions is important not just in math, but also in everyday tasks where it's necessary to share and divide quantities equally. This knowledge connects directly to the concepts of measurement, proportional reasoning, and even understanding decimals. So keep practicing, and you'll see how different forms of the same fraction are related and equivalent.


Grade 3 → 2.1.4


U
username
0%
completed in Grade 3

← Prev (2.1.3)
Comparing and Ordering Fractions with Like Denominators
Next (2.1.5) →
Simple Fraction Word Problems

Comments 



Equivalent Fractions

https://www.buddymath.com/g3/2.1.4?bmal=en