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Grade 7
Ratio and Proportion
Ratio
Comparison of Ratios

Grade 7

1. Rational Numbers

1.1. Understanding Rational Numbers

1.2. Standard Form of a Rational Number

1.4. Comparison of Rational Numbers

1.5. Representation of Rational Numbers on the Real Line

1.6. Addition and Subtraction of Rational Numbers

1.6.1. Addition of Rational Numbers

1.6.2. Additive Inverse of a Rational Number

1.6.3. Subtraction of Rational Numbers

1.7. Multiplication and Division of Rational Numbers

1.7.1. Multiplication Of Rational Numbers

1.7.2. Reciprocal of Rational Number

1.7.3. Division Of Rational Numbers

1.8. Rational Numbers Lying Between Two Rational Numbers

1.9. Simplifying Rational Numbers

1.10. Word Problems on Rational Numbers

2. Integers

2.1. Introduction to Integers

2.2. Representation of Integers on a Number Line

2.3. Successor and Predecessor of an Integer

2.4. Comparing Integers

2.5. Number of Integers Between Two Given Integers

2.6. Absolute Value of an Integer

2.7. Operations on Integers

2.7.1. Addition and Subtraction of Integers

2.7.1.1. Addition of Integers

2.7.1.2. Addition of Integers on the Number Line

2.7.1.3. Properties of Addition of Integers

2.7.2. Subtraction of Integers

2.7.2.1. Subtraction of Integers on the Number Line

2.7.2.2. Properties of Subtraction of Integers

2.7.2.3. Multiplication and Division of Integers

2.7.2.3.1. Multiplication of Integers

2.7.2.3.2. Properties of Multiplication of Integers

2.7.2.3.3. Division of Integers

2.7.2.3.4. Properties of Division of Integers

2.7.2.4. Mixed Operations of Integers

2.7.2.5. Word Problems on Integers

3. Fractions

3.1. Identifying Like and Unlike Fractions

3.2. Unit Fraction

3.3. Proper, Improper and Mixed Fractions

3.3.1. Understand Proper, Improper and Mixed Fractions

3.3.2. Convert Improper Fractions to Mixed Fractions

3.3.3. Convert Mixed Fractions to Improper Fractions

3.4. Equivalent Fractions

3.5. Simplest Form of a Fraction

3.6. Comparing Fractions

3.6.1. Comparing Like Fractions

3.6.2. Comparing Fractions with Same Numerator

3.6.3. Comparing Unlike Fractions

3.7. Operations on Fractions

3.7.1. Addition of Fractions

3.7.1.1. Addition of Like Fractions

3.7.1.2. Addition of Unlike Fractions

3.7.1.3. Addition of Mixed Fractions

3.7.2. Subtraction of Fractions

3.7.2.1. Subtraction of Like Fractions

3.7.2.2. Subtraction of Unlike Fractions

3.7.2.3. Subtraction of Mixed Fractions

3.7.3. Simplify Expressions involving Addition and Subtraction

3.7.4. Multiplication of Fractions

3.7.4.1. Simplify Expressions involving Multiplication

3.7.4.2. Use of 'OF'

3.7.5. Division of Fractions

3.7.5.1. Reciprocal of a Fraction

3.7.5.2. Simplify Expressions involving Division

3.7.6. Simplification by Using Operations

3.7.7. Word Problems on Fractions

3.7.7.1. Word Problems on Addition of Fractions

3.7.7.2. Word Problems on Subtraction of Fractions

3.7.7.3. Word Problems on Addition and Subtraction of Fractions

3.7.7.4. Word Problems on Multiplication of Fractions

3.7.7.5. Word Problems on Division of Fractions

4. Decimals

4.1. Introduction to Decimals

4.2. Reading a Decimal Number

4.3. Place Value Chart

4.4. Expanded Form of Decimal Numbers

4.5. Like and Unlike Decimals

4.6. Like, Unlike And Equivalent Decimals

4.7. Comparing Decimals

4.8. Ordering Decimals

4.9. Relate Decimals and Fractions

4.9.1. Convert Decimals to Fractions

4.9.1.1. Convert Decimals to Proper Fractions

4.9.1.2. Convert Decimals to improper Fractions

4.9.1.3. Convert Decimals to Mixed Fractions

4.9.2. Convert Fractions to Decimals

4.9.2.1. Convert Fractions with Denominators as Powers of 10 to Decimals

4.9.2.2. Convert Any Fractions to Decimals

4.10. Conversion of Metric Units Using Decimals

4.11. Addition and Subtraction of Decimals

4.11.1. Addition of Decimals

4.11.2. Subtraction of Decimals

4.11.3. Mixed Operations on Decimals: Addition and Subtraction

4.11.4. Word Problems on Addition and Subtraction of Decimals

4.12. Multiplication and Division of Decimals

4.12.1. Multiplication of Decimals

4.12.1.1. Multiplication of a Decimal by 10, 100, 1000 etc

4.12.1.2. Multiplication of a Decimal by a Whole Number

4.12.1.3. Multiplication of Two/Three Decimals

4.12.1.4. Word Problems on Multiplication of Decimals

4.12.2. Division of Decimals

4.12.2.1. Division of a Decimal by 10, 100, 1000 etc

4.12.2.2. Division of a Decimal by a Multiple of 10, 100, 1000 etc

4.12.2.3. Division of a Decimal by a Whole Number

4.12.2.4. Division of a Decimal by a Decimal

4.12.2.5. Division of a Whole Number by a Decimal

4.12.2.6. Word Problems on Division of a Decimal

4.12.2.7. Mixed Operations on Decimals

5. Ratio and Proportion

5.1. Ratio

5.1.1. Terms of a Ratio

5.1.2. Equivalent Ratio

5.1.3. Ratio in the Simplest Form

5.1.4. Ratio of Two Quantities by Converting Them in Same Units

5.1.5. Comparison of Ratios

5.1.6. Miscellaneous on Ratio

5.2. Proportion

5.2.1. Terms of a Proportion

5.2.2. Condition for the given Numbers/Ratios to be in Proportion

5.2.3. Find the unknown variable when four numbers are in Proportion

5.2.4. Continued proportion

6. Unitary Method

6.1. Problems on Direct Variation

6.2. Problems on Inverse Variation

7. Percentage

7.1. Conversions

7.1.1. Convert a Fraction into Percentage

7.1.2. Convert a Percentage into Fraction

7.1.3. Convert Percentage into a Ratio

7.1.4. Convert a Ratio into Percentage

7.1.5. Convert Percentage into Decimal form

7.1.6. Convert Decimal into Percentage

7.2. Percentage of a Quantity

7.3. Solving Expressions involving Percentages

7.4. Word Problems on Percentage

8. Profit and Loss

8.1. Terms Related to Profit and Loss

8.2. Problems on Finding the Gain/Loss and Gain%/Loss%

8.3. Problems on Finding the SP of the Article

8.4. Problems on Finding the CP of the Article

8.5. Problems on Finding the Number of Articles

9. Simple Interest

9.1. Problems on Calculating the Simple Interest

9.2. Problems on Calculating the Rate Percent

9.3. Problems on Calculating Time Period

9.4. Problems on Calculating the Principal

10. Exponents

10.1. Introduction to Exponents

10.2. Exponent of a Rational Number

10.3. Express Rational Numbers in Exponential Form

10.4. Solving Expressions Involving Exponents

10.5. Laws of Exponents

10.6. Word Problems on Exponents

10.7. Finding the Unknown from the Given Exponential Equation

10.8. Standard Form of Large Numbers

10.9. Standard Form of Small Numbers

10.10. Expanded Form of Large Numbers

11. Algebraic Expressions

11.1. Variables and Constants

11.2. Types of Algebraic Expressions

11.3. Operations on Algebraic Expressions

11.3.1. Addition of Algebraic Expressions

11.3.2. Subtraction of Algebraic Expressions

11.3.3. Addition and Subtraction of Algebraic Expressions

11.3.4. Multiplication of Algebraic Expressions

11.3.4.1. Multiplication of Monomials

11.3.4.2. Multiplication of a Monomial and a Binomial

11.3.4.3. Multiplication of two Binomials

12. Linear Equations in One Variable

12.1. Solving Linear Equations by the Method of Transposition

12.2. Word Problems Based on Linear Equations

13. Mensuration

13.1. Standard Units of Area

13.2. Area and Perimeter of a Square

13.3. Area and Perimeter of a Rectangle

13.4. Area of 4 Walls of a Room

13.5. Area between Two Rectangles

13.6. Area and Perimeter of Triangles

13.7. Area and Perimeter of Parallelogram and Rhombus

13.8. Circumference and Area of a Circle

13.9. Area Enclosed Between Two Different Shapes

14. Geometry

14.1. Lines and Angles

14.1.1. Types of Angles

14.1.1.1. Complementary and Supplementary Angles

14.1.1.2. Linear Pair of Angles

14.1.1.3. Vertically Opposite Angles

14.1.1.4. Angles Around a Point

14.1.2. Angles Formed when a Transversal Cuts Two Parallel Lines

14.2. Triangles

14.2.1. Classification of Triangles by the Length of the Sides

14.2.2. Classification of Triangles by the Angles

14.2.3. Properties of a Triangle

14.2.3.1. Angle Sum Property of a Triangle

14.2.3.2. Exterior Angle Property of a Triangle

14.2.3.3. Triangle Inequality

14.2.3.4. Pythagoras' Theorem

14.3. Congruence

14.3.1. Understanding the Meaning

14.3.2. Congruence of Triangles

15. Reflection and Rotational Symmetry

15.1. Linear Symmetry

15.1.1. Linear Symmetry Around Us

15.1.2. Linear Symmetry in Geometric Figures

15.1.3. Linear Symmetry in Alphabets

15.2. Rotational Symmetry

15.2.1. Rotational Symmetry in Figures

15.2.2. Rotational Symmetry in Geometric Figures

15.2.3. Rotational Symmetry in Alphabets

16. Three-Dimensional Shapes

16.1. Identifying 3-D Shapes

16.2. Faces, Edges and Vertices of 3-D Shapes (Cuboid, Cube, Cone, Cylinder, and Sphere)

16.3. Net of a 3-D Shape

17. Probability

18. Data Handling

18.1. Tabular Representation of Data

18.2. Mean, Median, and Mode

18.2.1. Mean

18.2.1.1. Mean of Ungrouped Data

18.2.1.2. Mean of Tabulated Data

18.2.2. Median

18.2.2.1. Median of Ungrouped Data

18.2.2.2. Median of Discrete Series

18.2.3. Mode

18.2.3.1. Mode of Ungrouped Data

18.2.3.2. Empirical Formula for Calculating Mode

18.3. Bar Graphs

18.3.1. Drawing Bar Graphs

18.3.2. Interpreting Bar Graphs

Grade 7 Europe School Math Comparison of Ratios

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