Operations with Whole Numbers

Addition is the process of combining two or more numbers to find their total. When we add, we join together \(\textcolor{colordef}{\text{part 1}}\) and \(\textcolor{colorprop}{\text{part 2}}\) to get the \(\textcolor{olive}{\text{total}}\).$$\textcolor{colordef}{\text{part 1}} + \textcolor{colorprop}{\text{part 2}} = \textcolor{olive}{\text{total}}$$

• The \(+\) symbol is called the plus sign. It tells us to add the numbers together.
• The \(=\) symbol is the equals sign. It shows that the numbers on both sides are the same.

Addition can be represented in different ways:

• Numbers: $$\textcolor{colordef}{7} + \textcolor{colorprop}{5} = \textcolor{olive}{12}$$
• Items: \(+\) \(=\)
• Word form:\(\textcolor{colordef}{\text{seven}}\) plus \(\textcolor{colorprop}{\text{five}}\) equals \(\textcolor{olive}{\text{twelve}}\)

When we add larger numbers, we write them in columns with their place values aligned. Then, we add each column from right to left.

Calculate \(189+784\)

Subtraction is the process of taking away one number from another to find the difference. The \(-\) symbol is called the minus sign. It tells us to take one number away from another.
Subtraction can be shown in several ways:

• Numbers: $$\textcolor{olive}{32} - \textcolor{colordef}{14} = \textcolor{colorprop}{18}$$
• Visual (Items): \(-\) \(=\)
• Words:thirty-two minus fourteen equals eighteen

When subtracting larger numbers, write them in columns with the digits aligned by place value. Then subtract each column from right to left.

Calculate \(784 - 189\)

Multiplication is the process of repeated addition. When we multiply, we add a number to itself a certain number of times. The \(\times\) symbol (or "times sign") tells us to multiply the numbers.
Multiplication can be represented in several ways:

• Numbers: $$\textcolor{colordef}{4} \times \textcolor{colorprop}{3} = \textcolor{olive}{12}$$
• Groups: \(\textcolor{colordef}{4}\) groups of \(\textcolor{colorprop}{3}\) equals \(\textcolor{olive}{12}\)
• Repeated addition: $$\textcolor{colorprop}{3}+\textcolor{colorprop}{3}+\textcolor{colorprop}{3}+\textcolor{colorprop}{3} = \textcolor{olive}{12}$$
• Words: \(\textcolor{colordef}{\text{four}}\) times \(\textcolor{colorprop}{\text{three}}\) equals \(\textcolor{olive}{\text{twelve}}\)
• Visual (Items):
• Part-whole model:

When multiplying larger numbers, write the numbers in columns so the digits align. Multiply the first number by each digit of the second number (starting from the right), then add the results.

Calculate \(123 \times 21\)

Division is the process of splitting a number into equal parts. In a division expression, the number being divided is called the dividend, and the number you divide by is the divisor. The result is the quotient. The \(\div\) symbol is the division sign.$$\textcolor{olive}{\text{Dividend}} \div \textcolor{colordef}{\text{Divisor}} = \textcolor{colorprop}{\text{Quotient}}$$Division can be represented in several ways:

• Numbers: $$\textcolor{olive}{6}\div \textcolor{colordef}{3}=\textcolor{colorprop}{2}$$
• Words: six divided by three equals two
• Items:

Sometimes a number does not divide evenly. The number left over is called the \(\textcolor{orange}{\text{remainder}}\).$$\textcolor{olive}{13} \div \textcolor{colordef}{3} = \divionRemainder{\textcolor{colorprop}{4}}{\textcolor{orange}{1}}$$This relationship can also be written as:$$\textcolor{olive}{13} = \textcolor{colordef}{3} \times \textcolor{colorprop}{4} + \textcolor{orange}{1}$$where \(\textcolor{olive}{13}\) is the dividend, \(\textcolor{colordef}{3}\) is the divisor, \(\textcolor{colorprop}{4}\) is the quotient, and \(\textcolor{orange}{1}\) is the \(\textcolor{orange}{\text{remainder}}\).
The long division algorithm shows how we can compute division step by step.

When dividing larger numbers, we work digit by digit, starting from the left. If a digit (or group of digits) is too small to be divided by the divisor, we bring down the next digit.

Calculate \(125 \div 4\)

The order of operations tells us the sequence in which to perform different operations in a calculation:

1. Parentheses (or brackets)
2. Multiplication and Division (from left to right)
3. Addition and Subtraction (from left to right)

Calculate \(4 + 2 \times 3\)

To solve a word problem:

1. Read and understand the problem.
2. Identify the steps needed to solve it.
3. Write the mathematical expression.
4. Evaluate the expression.
5. Conclude and check your answer.

If you have 5 apples, buy 4 more, then give away 2, how many apples do you have left?