Integers

• Definition

  • Whole numbers, both positive and negative, including zero

• Examples

  • Positive integers: 1, 2, 3, ...

  • Negative integers: -1, -2, -3, ...

  • Zero: 0

• Operations

  • Addition

  • Subtraction

  • Multiplication

  • Division

• Number line

  • Representation of integers on a line

• Comparing integers

  • Greater than (>), less than (<), equal to (=)

• Absolute value

  • Distance of a number from zero

• Applications

  • Temperature scales

  • Bank account balances

• Integers in real life

  • Counting objects

  • Representing opposite directions

Fractions

• Definition

  • Numerator

  • Denominator

• Types of Fractions

  • Proper Fractions

  • Improper Fractions

  • Mixed Numbers

• Equivalent Fractions

• Simplifying Fractions

• Adding and Subtracting Fractions

• Multiplying and Dividing Fractions

• Converting Fractions to Decimals

• Real-life Applications of Fractions

Percentages

• Definition

  • Representation of a fraction out of 100

  • Symbol: %

• Calculation

  • Formula: (Part / Whole) * 100

  • Example: 20 out of 50 = (20 / 50) * 100 = 40%

• Applications

  • Discounts and sales

  • Interest rates

  • Grades and scores

• Converting

  • Fractions to percentages

  • Decimals to percentages

• Common Mistakes

  • Confusing percentage increase and decrease

  • Misplacing the decimal point

• Practice

  • Solving percentage problems

  • Real-life scenarios

• Summary

Decimals

• Definition

  • Numbers that include a decimal point to represent parts of a whole

• Place Value

  • Each digit's position represents a power of 10

  • The decimal point separates whole numbers from decimal fractions

• Reading and Writing Decimals

  • Read the whole number part, say "and," then read the decimal part digit by digit

  • Write the whole number, add a decimal point, then write the decimal part

• Comparing Decimals

  • Compare digit by digit from left to right

  • If necessary, add zeros to the right to make the numbers have the same length

• Operations with Decimals

  • Addition and subtraction

    • Line up the decimal points

    • Add or subtract as usual

    • Place the decimal point in the answer directly below the other decimal points

  • Multiplication

    • Ignore the decimal points and multiply as if they were whole numbers

    • Count the total number of decimal places in the factors

    • Place the decimal point in the product so that the total number of decimal places is the same

  • Division

    • Move the decimal point to the right in both the dividend and divisor until the divisor is a whole number

    • Divide as usual

    • Place the decimal point in the quotient directly above the decimal point in the dividend

Angles

• Definition

  • Angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle

• Types of angles

  • Acute angle: measures less than 90 degrees

  • Right angle: measures exactly 90 degrees

  • Obtuse angle: measures more than 90 degrees but less than 180 degrees

  • Straight angle: measures exactly 180 degrees

  • Reflex angle: measures more than 180 degrees but less than 360 degrees

• Angle relationships

  • Complementary angles: two angles that add up to 90 degrees

  • Supplementary angles: two angles that add up to 180 degrees

  • Vertical angles: two non-adjacent angles formed by intersecting lines

• Angle measurement

  • Degrees: unit of measurement for angles

  • Protractor: tool used to measure and draw angles

• Angle properties

  • Angles in a triangle add up to 180 degrees

  • Angles on a straight line add up to 180 degrees

  • Angles around a point add up to 360 degrees