Grade 7
  1. Number System  1.1. Integers  1.1.1. Properties of Integers  1.1.2. Operations on Integers  1.1.3. Additive and Multiplicative Inverses  1.1.4. Applications of Integers  1.2. Rational Numbers  1.2.1. Definition of Rational Numbers  1.2.2. Properties of Rational Numbers  1.2.3. Operations on Rational Numbers  1.2.4. Standard Form of Rational Numbers  1.3. Decimals  1.3.1. Operations on Decimals  1.3.2. Converting Between Fractions and Decimals  1.4. Powers and Exponents  1.4.1. Laws of Exponents  1.4.2. Simplifying Expressions with Exponents  1.4.3. Scientific Notation  1.5. Roots  1.5.1. Square Roots  1.5.2. Cube Roots
  2. Algebra  2.1. Expressions  2.1.1. Algebraic Expressions  2.1.2. Simplifying Expressions  2.1.3. Evaluating Expressions  2.2. Linear Equations  2.2.1. Solving Simple Equations  2.2.2. Applications of Linear Equations  2.3. Algebraic Identities  2.3.1. Expanding Using Identities  2.3.2. Simplifying Using Identities
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Simplifying Ratios  3.1.3. Equivalent Ratios  3.2. Proportion  3.2.1. Concept of Proportion  3.2.2. Direct Proportion  3.2.3. Inverse Proportion  3.3. Unitary Method  3.3.1. Solving Problems Using the Unitary Method
  4. Geometry  4.1. Lines and Angles  4.1.1. Types of Angles  4.1.2. Pairs of Angles  4.1.3. Properties of Parallel Lines and a Transversal  4.1.4. Angle Bisectors  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Angle Sum Property  4.2.3. Exterior Angle Property  4.2.4. Pythagoras Theorem  4.3. Congruence of Triangles  4.3.1. Criteria for Congruence  4.3.2. Applications of Congruence  4.4. Quadrilaterals  4.4.1. Types of Quadrilaterals  4.4.2. Properties of Parallelograms  4.4.3. Special Quadrilaterals  4.4.4. Properties of Rectangles and Rhombuses
  5. Mensuration  5.1. Perimeter and Area  5.1.1. Perimeter of Plane Figures  5.1.2. Area of Plane Figures  5.1.3. Area of a Trapezium  5.1.4. Area of a Parallelogram  5.1.5. Area of a Circle  5.1.6. Area of Composite Figures  5.2. Surface Area and Volume  5.2.1. Cubes and Cuboids  5.2.2. Surface Area of Cylinders  5.2.3. Volume of Prisms and Cylinders  5.2.4. Volume and Surface Area of Cones
  6. Data Handling  6.1. Data Collection  6.1.1. Organizing Data  6.1.2. Frequency Distribution  6.2. Graphical Representation of Data  6.2.1. Bar Graphs  6.2.2. Double Bar Graphs  6.2.3. Pie Charts  6.2.4. Histograms  6.2.5. Line Graphs  6.3. Probability  6.3.1. Simple Events  6.3.2. Experimental Probability  6.3.3. Theoretical Probability
  7. Practical Geometry  7.1. Construction of Triangles  7.1.1. Constructing Triangles Given Side Lengths  7.1.2. Constructing Triangles Given Side and Angle  7.1.3. Constructing Right-Angled Triangles  7.2. Construction of Quadrilaterals  7.2.1. Quadrilaterals Given Side Lengths and Angles  7.2.2. Constructing Parallelograms and Rectangles

Grade 7 → Number System → Rational Numbers ↓


Operations on Rational Numbers


Rational numbers are numbers that can be expressed as the quotient or fraction of two integers. The numerator is an integer and the denominator is a non-zero integer. Examples of rational numbers include fractions such as 1/2 and -3/4, as well as whole numbers, since they can be expressed with a denominator of 1. In this document, we will explore the different operations that can be performed on rational numbers: addition, subtraction, multiplication, and division.

Addition of rational numbers

To add two rational numbers, they must have the same denominator. If they don't, you'll need to find a common denominator by finding the least common multiple (LCM) of the denominators. Then, convert each fraction to an equivalent fraction with the same denominator before adding the numerators.

Example

Let's add these rational numbers: 1/4 + 2/8.

First, find a common denominator. The least common multiple of 4 and 8 is 8.
Convert 1/4 to an equivalent fraction with the denominator 8:
1/4 = (1×2)/(4×2) = 2/8.
Now add 2/8 + 2/8:
Fraction: 2 + 2 = 4.
Resulting fraction: 4/8, which simplifies to 1/2.
1 2 ,

Subtraction of rational numbers

Subtraction is similar to addition. First, make sure the rational numbers have the same denominator. Then, subtract the numerators and keep the denominators the same.

Example

Let's subtract: 3/5 - 1/10

First, find a common denominator. The least common multiple of 5 and 10 is 10.
Convert 3/5 to an equivalent fraction with a denominator of 10:
3/5 = (3×2)/(5×2) = 6/10.
Now, subtract 6/10 - 1/10:
Fraction: 6 - 1 = 5.
Resulting fraction: 5/10, which simplifies to 1/2.
3 5 ,

Multiplication of rational numbers

To multiply two rational numbers, multiply the numerators together and the denominators together. Simplify the result if possible.

Example

Let's multiply: 2/3 × 4/5.

Multiply the fractions: 2 × 4 = 8.
Multiply the denominators: 3 × 5 = 15.
The resulting fraction: 8/15 (already in the simplest form).
2 3

Division of rational numbers

To divide by a rational number, multiply by its reciprocal. The reciprocal of a fraction is obtained by switching its numerator and denominator.

Example

Let's divide: 3/4 ÷ 2/3.

To divide, multiply by the reciprocal of 2/3, which is 3/2.
Multiply 3/4 × 3/2:
Fraction: 3 × 3 = 9.
Denominator: 4 × 2 = 8.
Resulting fraction: 9/8
3 4

Conclusion

Working with rational numbers is a fundamental concept that involves understanding how to perform arithmetic operations such as addition, subtraction, multiplication, and division. The essential step in all these operations is to ensure that you have a common denominator when adding or subtracting and know the inverse when dividing. Practicing with simple fractions helps to strengthen these concepts and improve your numerical fluency.

Now that you understand these operations, try solving some problems yourself to reinforce what you've learned!


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Properties of Rational Numbers
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Standard Form of Rational Numbers

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Operations on Rational Numbers

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