Grade 6
  1. Number System  1.1. Whole Numbers  1.1.1. Place Value and Face Value  1.1.2. Comparing and Ordering Numbers  1.1.3. Rounding Numbers  1.1.4. Properties of Whole Numbers (Associative, Commutative, Distributive)  1.2. Integers  1.2.1. Introduction to Integers  1.2.2. Addition and Subtraction of Integers  1.2.3. Multiplication and Division of Integers  1.2.4. Properties of Integer Operations  1.3. Fractions  1.3.1. Types of Fractions  1.3.2. Equivalent Fractions  1.3.3. Simplification of Fractions  1.3.4. Addition and Subtraction of Fractions  1.3.5. Multiplication and Division of Fractions  1.3.6. Comparing and Ordering Fractions  1.4. Decimals  1.4.1. Understanding Decimals  1.4.2. Conversion between Fractions and Decimals  1.4.3. Addition and Subtraction of Decimals  1.4.4. Multiplication and Division of Decimals  1.4.5. Comparing and Ordering Decimals
  2. Algebra  2.1. Basics of Algebra  2.1.1. Variables and Constants  2.1.2. Expressions and Equations  2.1.3. Algebraic Terms and Coefficients  2.2. Solving Simple Equations  2.2.1. Balancing Equations  2.2.2. Solving One-Step Equations  2.2.3. Solving Two-Step Equations  2.3. Patterns and Sequences  2.3.1. Identifying Patterns  2.3.2. Arithmetic Sequences
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Equivalent Ratios  3.1.3. Simplifying Ratios  3.2. Proportion  3.2.1. Introduction to Proportion  3.2.2. Direct and Inverse Proportions  3.3. Percentages  3.3.1. Converting Ratios to Percentages  3.3.2. Percentage Increase and Decrease  3.3.3. Discount and Profit Calculations  3.3.4. Simple Interest Calculations in Percentages in Ratio and Proportion
  4. Geometry  4.1. Basic Geometric Shapes  4.1.1. Points, Lines, and Angles  4.1.2. Types of Angles  4.1.3. Intersecting and Parallel Lines  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Properties of Triangles  4.2.3. Sum of Angles in a Triangle  4.2.4. Congruence of Triangles  4.3. Quadrilaterals  4.3.1. Types of Quadrilaterals  4.3.2. Properties of Quadrilaterals  4.4. Circles  4.4.1. Radius and Diameter  4.4.2. Circumference and Area  4.4.3. Arcs and Chords  4.4.4. Sector and Segment
  5. Mensuration  5.1. Perimeter  5.1.1. Perimeter of Simple Shapes  5.2. Area  5.2.1. Area of Rectangles and Squares  5.2.2. Area of Triangles and Parallelograms  5.2.3. Area of Composite Figures  5.2.4. Area of Trapezium  5.3. Volume  5.3.1. Volume of Cubes and Cuboids  5.3.2. Volume of Cylinders  5.3.3. Volume of Cones  5.3.4. Surface Area of Simple Solids
  6. Data Handling  6.1. Introduction to Data  6.1.1. Types of Data  6.1.2. Organizing Data  6.1.3. Frequency Distribution  6.2. Graphs and Charts  6.2.1. Bar Graphs  6.2.2. Line Graphs  6.2.3. Pictographs  6.2.4. Pie Charts  6.3. Mean, Median, and Mode  6.3.1. Calculating Mean  6.3.2. Finding Median  6.3.3. Identifying Mode  6.3.4. Range of Data in Mean, Median, and Mode
  7. Probability  7.1. Basics of Probability  7.1.1. Understanding Probability  7.1.2. Probability of Simple Events  7.1.3. Experimental and Theoretical Probability
  8. Practical Geometry  8.1. Construction of Shapes  8.1.1. Constructing Triangles  8.1.2. Constructing Quadrilaterals  8.1.3. Constructing Circles and Arcs  8.2. Symmetry  8.2.1. Line of Symmetry  8.2.2. Rotational Symmetry  8.2.3. Translational Symmetry

Grade 6 → Number System → Fractions ↓


Addition and Subtraction of Fractions


Fractions represent parts of a whole. Learning how to add and subtract fractions is an important skill in the world of math. In this guide, we'll learn step by step about adding and subtracting fractions. Let's start by understanding what a fraction is.

Understanding fractions

A fraction has two parts: the numerator and the denominator. The numerator is the top number, and the denominator is the bottom number. For example, in the fraction 3/4, 3 is the numerator, and 4 is the denominator.

   ___3___ ← Part
  , 
   ‾‾‾4‾‾ ← every

The denominator tells us how many parts the whole is divided into, and the numerator shows how many parts we have. A fraction can represent values that are less than or greater than a whole.

Addition of fractions

To add fractions, they must have the same denominator. This shared denominator is called the "common denominator." Let's first look at how we can add fractions with the same denominator.

Adding fractions with the same denominators

If the fractions to be added have the same denominator, then add the numerators and keep the denominator the same.

For example, to add 1/4 and 2/4:

    1 2 1 + 2
   , 
    4 4 4
            = ³/₄

Adding fractions with different denominators

If the fractions have different denominators, follow these steps:

  1. Find a common denominator: Find the least common multiple (LCM) of the denominators.
  2. Convert each fraction: Adjust the fractions to have the same denominator by multiplying both the numerator and denominator by the required numbers.
  3. Add the numerators: Now that the denominators are the same, add the numerators.
  4. Subtract if necessary: Simplify the fraction to its simplest form.

Example: Add 1/3 and 1/6

Step 1: The denominators are 3 and 6. The LCM of 3 and 6 is 6.

Step 2: Change 1/3 to the denominator of 6 Multiply both the numerator and denominator by 2.

    1 × 2
  , 
    3 × 2 6

Which gives us: 2/6

Step 3: Add 2/6 and 1/6:

   2 1 2 + 1
  ,
   6 6 6
          = ³/₆

Step 4: Simplify 3/6 by dividing both the numerator and denominator by 3:

   3/3
, 
   6/3
      = 1/2

Subtraction of fractions

Subtracting fractions works the same as adding. Let's learn how to subtract fractions with the same and different denominators.

Subtracting fractions with the same denominators

If the fractions have the same denominator, you can directly subtract the numerators while keeping the denominator the same.

For example, subtract 3/4 from 5/4:

   5 3 5 - 3
  , 
   4 4 4
          = 2/4

Then simplify 2/4 by dividing both the numerator and denominator by 2:

   2/2
, 
   4/2
      = 1/2

Subtracting fractions with different denominators

If the fractions have different denominators, follow these steps:

  1. Find a common denominator: Find the least common multiple (LCM) of the denominators.
  2. Convert each fraction: Adjust the fractions to have the same denominator by multiplying both the numerator and denominator by the required numbers.
  3. Subtract fractions: Subtract the numerators because the denominators are the same.
  4. Subtract if necessary: Simplify the fraction to its simplest form.

Example: Subtract 2/5 from 3/4

Step 1: The denominators are 4 and 5. The LCM of 4 and 5 is 20.

Step 2: Convert 3/4 and 2/5 to the denominator of 20:

For 3/4 multiply both the numerator and denominator by 5:

    3 × 5
  , 
    4 × 5 20

Which gives us: 15/20

For 2/5 multiply both the numerator and denominator by 4:

    2 × 4
  , 
    5 × 4 20

Which gives us: 8/20

Step 3: Subtract 8/20 from 15/20:

  15 8 15 - 8
 , 
  20 20 20
          = 7/20

The fraction 7/20 is already in its simplest form.

Practice problems

Let's practice adding and subtracting fractions:

Add

  1. 2/7 + 3/7 = ?
  2. 3/8 + 1/4 = ?
  3. 4/5 + 2/9 = ?

Subtraction

  1. 5/12 - 1/12 = ?
  2. 7/10 - 2/5 = ?
  3. 11/15 - 4/15 = ?

Conclusion

Mastering the addition and subtraction of fractions takes practice, but it is essential to developing your mathematical skills. Start with questions with like denominators. Once you are comfortable, move on to questions with unequal denominators.

These concepts are fundamental skills that will help you in advanced math topics like algebra and geometry. Practice regularly and apply these techniques to solve real-world problems involving fractions.


Grade 6 → 1.3.4


U
username
0%
completed in Grade 6

← Prev (1.3.3)
Simplification of Fractions
Next (1.3.5) →
Multiplication and Division of Fractions

Comments 



Addition and Subtraction of Fractions

https://www.buddymath.com/g6/1.3.4?bmal=en