\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)

Addition

Definition


Louis has two boxes of cubes. One box contains \(1\,218\) cubes, and the other box contains \(1\,123\) cubes.
\(+\)
How many cubes does Louis have in total?

To find the total number of cubes Louis has, we add the cubes in the two boxes:$$\textcolor{colordef}{1\,218} + \textcolor{colorprop}{1\,123}$$Using cubes, we can visualize the addition:
\(+\) \(=\)
This shows a total of \(\textcolor{colordef}{1\,218} + \textcolor{colorprop}{1\,123} = \textcolor{olive}{2\,341}\) cubes.
Counting each cube one by one would be tedious. Instead, we use column addition to calculate:


Definition Addition
Addition means combining quantities to find a total.
  • The \(+\) symbol means "add."
  • The \(=\) symbol shows equality on both sides.
Addition can be represented as:
  • Numbers: $$\textcolor{colordef}{1\,218} + \textcolor{colorprop}{1\,123} = \textcolor{olive}{2\,341}$$
  • Cubes:
    \(+\) \(=\)
  • Words:
    one thousand two hundred eighteen plus one thousand one hundred twenty-three equals two thousand three hundred forty-one
  • Column Addition:
  • Part-whole model:

Adding Using Columns

Method Column Addition with Carrying
To calculate:$$\textcolor{colordef}{288} + \textcolor{colorprop}{545}$$
  • Step 1: Set up the addition
    Write the numbers in a vertical column, making sure the digits line up by place value (ones under ones, tens under tens, hundreds under hundreds).
  • Step 2: Add the ones $$\textcolor{colordef}{8} \text{ ones} + \textcolor{colorprop}{5} \text{ ones} = 13 \text{ ones} = 1 \text{ ten} + \textcolor{olive}{3} \text{ ones}$$ Write the 3 in the ones place of the result and carry the 1 ten to the top of the tens column.
  • Step 3: Add the tens $$1 \text{ ten (carried)} + \textcolor{colordef}{8} \text{ tens} + \textcolor{colorprop}{4} \text{ tens} = 13 \text{ tens} = 1 \text{ hundred} + \textcolor{olive}{3} \text{ tens}$$ Write the 3 in the tens place of the result and carry the 1 hundred to the top of the hundreds column.
  • Step 4: Add the hundreds $$1 \text{ hundred (carried)} + \textcolor{colordef}{2} \text{ hundreds} + \textcolor{colorprop}{5} \text{ hundreds} = \textcolor{olive}{8} \text{ hundreds}$$ Write the 8 in the hundreds place of the result.
  • Result: $$\textcolor{colordef}{288} + \textcolor{colorprop}{545} = \textcolor{olive}{833}$$
    \(+\) \(=\)