Basic Arithmetic, Fractions, and Decimals

Basic Arithmetic

• Addition involves combining numbers to find a total. Example: 2 + 3 = 5
• Subtraction finds the difference between two numbers. Example: 5 - 2 = 3
• Multiplication involves repeated addition. Example: 3 x 4 = 12 (3 + 3 + 3 + 3)
• Division splits a number into equal parts. Example: 12 / 3 = 4

Fractions

• Fractions represent parts of a whole. A fraction is written as a/b, where 'a' is the numerator and 'b' is the denominator. For example, 2/5.
• Equivalent fractions represent the same part of a whole. Example 2/4 equals 1/2.
• Adding/subtracting fractions requires a common denominator.
• Multiplying fractions involves multiplying the numerators and denominators.

Decimals

• Decimals represent fractional values using a decimal point. Example: 0.5 is equivalent to 1/2.
• Adding/subtracting decimals align the decimal points.
• Multiplying decimals: multiply as if they were whole numbers, then count the total number of decimal places in the factors and put the decimal point in the product accordingly.
• Dividing decimals: move the decimal point to the right in both the dividend and divisor until the divisor is a whole number, and carry out the division.

Percentages

• Percentages are ratios expressed as parts of 100. Example: 50% is equivalent to 50/100.

Geometry

• Basic shapes include squares, rectangles, circles and triangles.
• Area is the space inside a two-dimensional shape.
• Perimeter is the distance around the outside of a two-dimensional shape.
• Volume is the space occupied by a three-dimensional object.

Algebra

• Variables (like 'x' or 'y') represent unknown quantities.
• Equations state that two expressions are equal. Example: 2x + 5 = 11
• Solving equations involves isolating the variable to find its value.
• Functions relate an input to an output. Example: f(x)=2x

Measurement

• Units of measurement include meters, centimeters, kilograms, grams, liters, and seconds.
• Conversions between units are essential.
• Understanding different measurement systems (metric, imperial).

Data Analysis and Probability

• Data analysis involves collecting, organizing, and interpreting data. Describing data in appropriate visual representations (charts, graphs).
• Probability deals with the likelihood of events.

Number System

• Natural numbers are counting numbers.
• Whole numbers are counting numbers plus zero.
• Integers include zero, positive, and negative counting numbers.