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


Fractions are a way of representing parts of a whole. When we talk about fractions, we are discussing how many parts of a certain size there are in something. Fractions can be used in many everyday situations, such as cooking, dividing a pizza, reading a clock, and much more.

What is fraction?

In the simplest sense, a fraction is a number that represents a part of a whole. It is used to show how many parts we have out of a certain number of equal parts. A fraction is made up of two main components: the numerator and the denominator.

Fraction example: Let's look at the fraction 3/4. Here, 3 is the numerator, and 4 is the denominator.

Meter

The numerator is the top number in a fraction. It tells us how many parts we have. In the fraction 3/4, the number 3 is the numerator. This means we have 3 parts.

Divisor

The denominator is the bottom number in a fraction. It tells us how many equal parts the whole number is divided into. In the fraction 3/4, the number 4 is the denominator. This means the whole number is divided into 4 equal parts.

Fraction table:

Whole | Parts taken | Fractions
1 | 1 | 1/1
1 | 2 | 1/2
1 | 3 | 1/3
1 | 4 | 1/4
1 | 5 | 1/5

Reading and writing fractions

When writing or reading fractions we usually say the numerator first and then the denominator. For example:

  • 1/2 is read as "half."
  • 3/4 is read "three quarters."
  • 5/8 is read as "five eighths."
  • 7/10 is read "seven tenths".

Visualization of fractions

Fractions are easier to understand when we can visualize them. Below is an example of a pie chart representation of the fraction 1/4.

In this circle, the shaded area represents 1/4 of the whole.

Similarly, we can represent other fractions also using visual charts.

Equivalent fractions

Sometimes, different fractions can represent the same quantity. Such fractions are called equivalent fractions. For example, 1/2 is equal to 2/4, 3/6 or 4/8. They all mean the same thing.

Example of equivalent fractions:

1/2 = 2/4 = 3/6 = 4/8
Each of these fractions is equivalent. They all represent the same part of a whole.

Comparing fractions

We often have to compare fractions to find out which fraction is bigger and which is smaller. There are several ways we can do this.

Method 1: Common denominator

The primary method of comparing two fractions is to change them to a common denominator. Once the denominators are the same, we can compare the numerators directly.

Example of comparing fractions:

Let's compare 2/3 and 3/4. We can find a common denominator of 12:

2/3 = 8/12 (Multiply both numerator and denominator by 4)
3/4 = 9/12 (Multiply both numerator and denominator by 3)

Now compare: 8/12 < 9/12. Therefore, 2/3 < 3/4.

Method 2: Cross-multiplying

Another method is cross-multiplication. Multiply the numerator of each fraction by the denominator of the other fraction.

Example of cross-multiplication:

Compare 1/3 and 2/5:

1 * 5 = 5
2 * 3 = 6

Since 5 < 6, we conclude that 1/3 < 2/5.

Adding and subtracting fractions

Adding or subtracting fractions requires a common denominator. With the same denominator, you add or subtract fractions.

Adding fractions with the same denominators

Example of adding fractions: 1/4 + 2/4

1/4 + 2/4 = (1+2)/4 = 3/4

Subtracting fractions with the same denominators

Example of subtracting fractions: 3/5 - 1/5

3/5 - 1/5 = (3-1)/5 = 2/5

Adding or subtracting fractions with different denominators

Example: Add 1/2 and 2/3.

Find a common denominator: lcm(2, 3) = 6

1/2 = 3/6 
2/3 = 4/6 

so,
1/2 + 2/3 = 3/6 + 4/6 = 7/6 or 1 1/6

Multiplication of fractions

Multiplying fractions is easier than adding or subtracting. You just multiply the numerators and multiply the denominators.

Example of multiplying fractions: 2/3 and 3/5

(2/3) * (3/5) = (2*3) / (3*5) = 6/15 = 2/5 (after simplification)

Division of fractions

To divide a fraction by another fraction, the first fraction has to be multiplied by the reciprocal of the second fraction.

Example of dividing fractions: divide 4/5 by 2/3

4/5 ÷ 2/3 = 4/5 * 3/2 = (4*3) / (5*2) = 12/10 = 6/5 or 1 1/5 (after simplification)

Converting improper fractions and mixed numbers

An improper fraction is a fraction in which the numerator is greater than or equal to the denominator. A mixed number contains a whole number and a fraction. They can be converted from one to the other.

Conversion example: Convert 7/4 to a mixed number.

7/4 = 1 3/4
1 full part + 3 parts of 4

Conversely, convert a mixed number to an improper fraction:

Example: Convert 1 1/2 to an improper fraction.

1 1/2 = (1*2 + 1)/2 = 3/2

Conclusion

Fractions are a fundamental part of mathematics and provide a means of expressing parts of a whole in different ways. By understanding the various concepts related to fractions - including equivalent fractions, addition and subtraction, multiplication and division, and converting between improper fractions and mixed numbers - you can build a strong foundation for tackling more complex mathematical ideas in the future.


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