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 → Fractions ↓


Simplifying Fractions


A fraction is a way of representing parts of a whole. A fraction consists of two numbers, the numerator and the denominator, where the numerator is the top number and represents a part of the whole, and the denominator is the bottom number and represents the total number of equal parts of the whole.

For example, the fraction 1/4 has a numerator of 1 and a denominator of 4. This fraction means that one of four equal parts is being considered.

What is simplification of fractions?

Simplifying fractions, also known as reducing fractions, is the process of making a fraction as simple as possible. This means writing the fraction in such a way that the numerator and denominator have no common factors other than 1.

For example, the fraction 8/12 can be simplified because both the numerator (8) and the denominator (12) can be divided by a common factor. The simplest form of 8/12 is 2/3.

Steps to simplify fractions

  1. Identify common factors: Find a common factor of both the numerator and denominator. A factor is a number that divides another number without leaving a remainder.

    For example, in the fraction 8/24, the common factors of 8 and 24 are 1, 2, 4, and 8. The greatest common factor is 8.

  2. Divide by the greatest common factor: Divide both the numerator and denominator by the greatest common factor.

    Using our example, divide both 8 and 24 by their greatest common factor, which is 8:

    8 ÷ 8 = 1
24 ÷ 8 = 3

    So the simplified fraction is 1/3.

  3. Check your work: Make sure the new numerator and denominator have no common factors other than 1. If so, repeat the process.

Visual example

Visual depictions can be helpful in understanding fractions better. Consider the fraction 6/8:

6/8

Now simplify 6/8. The common factor is 2:

6 ÷ 2 = 3
8 ÷ 2 = 4

Thus, the simplified form is 3/4:

3/4

Text example

Let's work through some examples of simplifying fractions step by step. This will strengthen your understanding.

Example 1: Simplify 9/12

Step 1: Find the greatest common factor of 9 and 12. The factors of 9 are 1, 3, 9 and the factors of 12 are 1, 2, 3, 4, 6, 12. The greatest common factor is 3.

Step 2: Divide both the numerator and denominator by 3:

9 ÷ 3 = 3
12 ÷ 3 = 4

The simplified fraction is 3/4.

Example 2: Simplify 10/50

Step 1: Find the greatest common factor of 10 and 50. The factors of 10 are 1, 2, 5, 10 and the factors of 50 are 1, 2, 5, 10, 25, 50. The greatest common factor is 10.

Step 2: Divide both the numerator and denominator by 10:

10 ÷ 10 = 1
50 ÷ 10 = 5

The simplified fraction is 1/5.

Example 3: Simplify 18/24

Step 1: Find the greatest common factor of 18 and 24. The factors of 18 are 1, 2, 3, 6, 9, 18 and the factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The greatest common factor is 6.

Step 2: Divide both the numerator and denominator by 6:

18 ÷ 6 = 3
24 ÷ 6 = 4

The simplified fraction is 3/4.

Example 4: Simplify 45/60

Step 1: Find the greatest common factor of 45 and 60. The factors of 45 are 1, 3, 5, 9, 15, 45 and the factors of 60 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. The greatest common factor is 15.

Step 2: Divide both the numerator and denominator by 15:

45 ÷ 15 = 3
60 ÷ 15 = 4

The simplified fraction is 3/4.

Connection to the real world

Simplified fractions are important in real-world scenarios. They make ratios or portions easier to understand and perceive. For example, when sharing a pizza with friends, it is easier to say that you have half a pizza rather than 4/8 of a pizza, even though they represent the same portion.

More practice problems

Here are some more fractions to practice simplification:

  • Simplification 15/45
  • Simplification 25/100
  • Simplification 14/28
  • Simplification 42/56
  • Simplification 27/81

Try solving these problems yourself to develop your skills.

Conclusion

Simplifying fractions is a basic skill in math that makes it easier to understand and work with fractions. By understanding and practicing the steps of finding and dividing the greatest common factor, you can easily simplify any fraction you encounter. With practice, you will become more skilled and confident in handling fractions in different forms.


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Simplifying Fractions

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