Fractions And Decimals Formulas - Mathematics Class 6

Learn important formulas from the Fractions And Decimals chapter of Class 6 Mathematics with examples, variables and applications.

📐 Fractions And Decimals Formulas

Complete collection of formulas with explanations and examples

Decimal Fraction Relation

$$decimal = numerator / denominator$$

Description: Decimal Fraction Relation is a standard relation used in fractions-and-decimals.

Example:

Apply the relation: decimal = numerator / denominator

Identify the known values, substitute them in the relation, and solve for the unknown quantity.
Result depends on the substituted values.

Applications:

  • Use this when the quantities in the relation are known and the missing quantity is required.

Equivalent Fractions

$$a/b = (a x k)/(b x k)$$

Description: Equivalent Fractions is a standard relation used in fractions-and-decimals.

Variables:

  • k = non-zero multiplier

Example:

Apply the relation: a/b = (a x k)/(b x k)

Identify the known values, substitute them in the relation, and solve for the unknown quantity.
Result depends on the substituted values.

Applications:

  • Use this when the quantities in the relation are known and the missing quantity is required.

Fraction Addition

$$a/b + c/d = (ad + bc)/bd$$

Description: Fraction Addition is a standard relation used in fractions-and-decimals.

Variables:

  • a,b,c,d = integers; b and d are non-zero

Example:

Apply the relation: a/b + c/d = (ad + bc)/bd

Identify the known values, substitute them in the relation, and solve for the unknown quantity.
Result depends on the substituted values.

Applications:

  • Use this when the quantities in the relation are known and the missing quantity is required.

Fraction Multiplication

$$a/b x c/d = ac/bd$$

Description: Fraction Multiplication is a standard relation used in fractions-and-decimals.

Example:

Apply the relation: a/b x c/d = ac/bd

Identify the known values, substitute them in the relation, and solve for the unknown quantity.
Result depends on the substituted values.

Applications:

  • Use this when the quantities in the relation are known and the missing quantity is required.

Quick Reference

Decimal Fraction Relation: $decimal = numerator / denominator$
Equivalent Fractions: $a/b = (a x k)/(b x k)$
Fraction Addition: $a/b + c/d = (ad + bc)/bd$
Fraction Multiplication: $a/b x c/d = ac/bd$

💡 Worked Examples

Step-by-step solutions using Fractions And Decimals formulas

Example 1: Area of Circle

Circle Area Formula
Problem:

Find the area of a circle with radius 7 cm.

Solution:
  1. Given: r = 7 cm
  2. Apply formula: A = πr²
  3. Substitute: A = π × 7²
  4. Calculate: A = π × 49 = 49π cm²
  5. Approximate: A ≈ 49 × 3.14159 ≈ 153.94 cm²
Answer:

Area = 49π cm² ≈ 153.94 cm²

🎯 Practice Problems

Try these problems to test your understanding:

Practice Problem 1

Solve the quadratic equation: x² - 7x + 12 = 0

Practice Problem 2

Find the area of a circle with diameter 14 cm.

Practice Problems

Check Your Formula Recall

Write each formula once, define every variable, then solve one direct substitution problem before moving to mixed questions.

Apply Fractions And Decimals

Pick two formulas from this page and create your own values for the variables. Verify units and signs before calculating.

Derivation Notes

Focus on how the formula is built, not only the final expression. Derivations help with board-exam reasoning and multi-step application questions.

  • Start from the definition or identity used in the chapter.
  • Write assumptions clearly before substituting values.
  • Track units through each step to catch calculation mistakes.

Where These Formulas Are Used

Board Exam Problems

Use these formulas for direct numerical questions, proof-based steps, and short-answer reasoning in Mathematics.

Competitive Practice

Memorize the condition of use for each formula so you can identify the right expression quickly under timed practice.

Related Formula Chapters

Basic Geometry 2 formulas Data Handling 1 formulas Fractions And Decimals 4 formulas Mensuration 3 formulas Number Sense 4 formulas

These Fractions And Decimals formulas help students revise concepts quickly and apply equations accurately in exam-style problems.

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