Addition, Subtraction, MULTIPLICATION

• Four-digit numbers consist of thousands, hundreds, tens, and ones.
• Example: 1,234 (1 thousand, 2 hundreds, 3 tens, 4 ones).
• Place value determines the value of each digit in the number.

Addition

• Addition is the process of combining two or more numbers to find their total, or sum.
• Start by adding the digits in the ones place, then the tens, hundreds, and thousands, moving from right to left.
• If the sum of digits in any place value column is greater than 9, carry over the tens digit to the next higher place value column.
• Example: 1,234 + 567 = 1,801

Subtraction

• Subtraction is the process of finding the difference between two numbers.
• Start by subtracting the digits in the ones place, then the tens, hundreds, and thousands, moving from right to left.
• If the digit being subtracted is larger than the digit it is being subtracted from, borrowing from the next higher place value column is required.
• Example: 1,234 - 567 = 667

Multiplication

• Multiplication is a mathematical operation that involves combining groups of equal sizes.
• Multiplication is repeated addition.
• Multiply each digit of one number by each digit of the other number, paying attention to place value.
• Use multiplication tables to help with basic multiplication facts.
• Example: 123 x 4 = 492

Division

• Division is the process of splitting a number into equal groups.
• The number being divided is the dividend, the number dividing is the divisor, the result is the quotient, and any remaining amount is the remainder.
• Use long division to divide larger numbers.
• Example: 123 ÷ 4 = 30 remainder 3

Fractions

• A fraction represents a part of a whole.
• It's written as one number over another, a numerator over a denominator.
• Numerator: The top number, indicating how many parts considered.
• Denominator: The bottom number, indicating the total number of equal parts.
• Example: 1/2 (one-half)
• Understand that the bigger the denominator, the smaller the fraction, assuming the numerator is constant.

Addition of Fractions

• Fractions can only be added if they have the same denominator (common denominator).
• If the denominators are different, find a common denominator before adding.
• Once the denominators are the same, add the numerators and keep the common denominator.
• Simplify the fraction if possible.
• Example: 1/4 + 2/4 = 3/4

Subtraction of Fractions

• Fractions can only be subtracted if they have the same denominator (common denominator).
• If the denominators are different, find a common denominator before subtracting.
• Once the denominators are the same, subtract the numerators and keep the common denominator.
• Simplify the fraction if possible.
• Example: 3/4 - 1/4 = 2/4 = 1/2

Equivalent Fractions

• Equivalent fractions are fractions that represent the same value but have different numerators and denominators.
• Multiply or divide both the numerator and the denominator by the same non-zero number to find equivalent fractions.
• Example: 1/2 = 2/4 = 4/8

Comparing Fractions

• To compare fractions, they must have the same denominator.
• Find a common denominator, convert the fractions, and then compare the numerators.
• The fraction with the larger numerator is the larger fraction.
• Example: Comparing 1/3 and 1/4, convert to 4/12 and 3/12. 4/12 > 3/12, so 1/3 > 1/4.