Fraction, Decimal, and Percentage Basics

Fractions

• A fraction represents a part of a whole
• Consists of a numerator (top number) and a denominator (bottom number)
• Example: 1/2, 3/4
• Equivalent fractions: fractions that have the same value, but different numbers (e.g., 1/2 = 2/4)

Decimals

• A decimal is a way to represent a fraction as a number with a fractional part
• Example: 0.5, 0.25
• Decimals can be converted to fractions and vice versa
• Compare decimals by comparing their fractional parts

Percentages

• A percentage is a way to represent a fraction as a number out of 100
• Example: 25%, 50%
• Percentages can be converted to decimals and fractions, and vice versa
• Calculate percentages by dividing by 100 (e.g., 25/100 = 0.25 = 25%)

Geometry

• Basic shapes: square, rectangle, triangle, circle, hexagon
• Properties of shapes:
  • Number of sides
  • Number of vertices (corners)
  • Type of angles (acute, obtuse, right)
• Identify and classify shapes based on their properties

Multi-digit Multiplication

• Multiply multi-digit numbers using the standard algorithm
• Multiply each digit of the multiplier by the multiplicand, then add up the products
• Example: 43 × 17 = ?

Multiple Digit Addition and Subtraction

• Add or subtract multi-digit numbers using the standard algorithm
• Add or subtract each column of digits, carrying or borrowing as necessary
• Example: 456 + 279 = ?, 945 - 357 = ?

2-digit Multiplication

• Multiply 2-digit numbers using the standard algorithm
• Multiply each digit of the multiplier by the multiplicand, then add up the products
• Example: 24 × 17 = ?

Division

• Divide multi-digit numbers using the standard algorithm
• Divide each digit of the dividend by the divisor, then write the quotient
• Example: 432 ÷ 12 = ?
• Remainders: the amount left over after dividing
• Example: 17 ÷ 5 = 3 with a remainder of 2

Fractions

• A fraction is a way to represent a part of a whole
• It consists of a numerator (top number) and a denominator (bottom number)
• Examples of fractions include 1/2, 3/4, and 2/3
• Equivalent fractions are fractions that have the same value, but different numbers (e.g., 1/2 = 2/4)

Decimals

• A decimal is a way to represent a fraction as a number with a fractional part
• Examples of decimals include 0.5, 0.25, and 3.14
• Decimals can be converted to fractions and vice versa
• Decimals can be compared by comparing their fractional parts

Percentages

• A percentage is a way to represent a fraction as a number out of 100
• Examples of percentages include 25%, 50%, and 75%
• Percentages can be converted to decimals and fractions, and vice versa
• Percentages can be calculated by dividing by 100 (e.g., 25/100 = 0.25 = 25%)

Geometry

• Basic shapes include squares, rectangles, triangles, circles, and hexagons
• Properties of shapes include:
  • Number of sides
  • Number of vertices (corners)
  • Type of angles (acute, obtuse, right)
• Shapes can be identified and classified based on their properties

Multiplication

• Multi-digit multiplication involves multiplying multi-digit numbers using the standard algorithm
• The standard algorithm involves multiplying each digit of the multiplier by the multiplicand, then adding up the products
• Examples of multi-digit multiplication include 43 × 17 = ?, 24 × 17 = ?
• 2-digit multiplication involves multiplying 2-digit numbers using the standard algorithm

Addition and Subtraction

• Multi-digit addition and subtraction involve adding or subtracting multi-digit numbers using the standard algorithm
• The standard algorithm involves adding or subtracting each column of digits, carrying or borrowing as necessary
• Examples of multi-digit addition and subtraction include 456 + 279 = ?, 945 - 357 = ?

Division

• Division involves dividing multi-digit numbers using the standard algorithm
• The standard algorithm involves dividing each digit of the dividend by the divisor, then writing the quotient
• Examples of division include 432 ÷ 12 = ?
• Remainders are the amount left over after dividing
• Examples of remainders include 17 ÷ 5 = 3 with a remainder of 2

Decimals

• Decimals represent fractions with a denominator of 10, 100, 1000, etc., and can be written in expanded form (e.g., 0.5 = 5/10) or word form (e.g., five tenths)
• Comparing and ordering decimals can be done using a number line or by comparing digits
• Decimals can be added and subtracted by aligning the decimal points

Fractions

• Fractions represent a part of a whole and can be written in simplest form (e.g., 2/4 = 1/2)
• Equivalent fractions have the same value but different numerators and denominators (e.g., 1/2 = 2/4 = 3/6)
• Comparing and ordering fractions can be done using a number line or by comparing numerators and denominators
• Fractions can be added and subtracted by finding a common denominator

Percentages

• Percentages are fractions with a denominator of 100 and can be written as decimals (e.g., 25% = 0.25) or fractions (e.g., 25% = 1/4)
• Percentages can be used to show increase or decrease (e.g., 25% increase = 1.25 times the original amount)
• The formula for calculating percentages is (part/whole) x 100

Geometry

• Basic geometric concepts include points, lines, and planes
• Angles can be classified as acute (less than 90°), right (90°), obtuse (greater than 90°), or straight (180°)
• Shapes can be classified as 2D (e.g., triangles, quadrilaterals) or 3D (e.g., cubes, rectangular prisms)
• Perimeter is the distance around a shape, while area is the amount of space inside a shape

Multi-digit Multiplication

• Multiplication can be represented using arrays or the standard algorithm
• The standard algorithm involves multiplying each digit of the multiplier with the multiplicand and adding the products
• Multiplication can be used to solve real-world problems (e.g., finding the area of a rectangle)

Multiple Digit Addition and Subtraction

• Addition and subtraction can be represented using number lines or the standard algorithm
• The standard algorithm involves lining up the digits and adding or subtracting each column
• Regrouping is necessary when adding or subtracting numbers with different numbers of digits
• Addition and subtraction can be used to solve real-world problems (e.g., finding the total cost of items)

2-digit Multiplication

• 2-digit multiplication involves multiplying a 2-digit number by a 1-digit number
• The standard algorithm involves multiplying each digit of the 2-digit number with the 1-digit number and adding the products
• 2-digit multiplication can be used to solve real-world problems (e.g., finding the cost of multiple items)

Division

• Division is the inverse operation of multiplication
• Division can be represented using arrays or the standard algorithm
• The standard algorithm involves dividing the dividend by the divisor and finding the quotient and remainder
• Division can be used to solve real-world problems (e.g., sharing a certain number of items among a group of people)