Addition and Subtraction
Addition and Subtraction
Addition and subtraction are basic mathematical operations that are often needed to answer questions in all kinds of topics. They are important skills that underpin a lot of questions that your child may be expected to answer in their exam. The most common and easy method for addition and subtraction is the column method which we will explore in more depth.
Addition Column Method
Example of adding using the column method:
Calculate 3491 + 5234
Start with the units column on the right and work your way along the columns to the left.
1 +4 = 5
So a 5 is placed underneath lining up with the units column.
Now add the numbers in the tens column.
9 + 3 = 12
This number is greater than 10 so place the 2 underneath and carry the \textcolor{red}{1}. The \textcolor{red}{1} will be added on in the addition of the next column.
The hundreds column is next.
4 + 2 =6
Don’t forget the \textcolor{red}{1} that has been carried over.
6+\textcolor{red}{1} = 7
So the number written underneath the hundreds column is 7.
The thousands column is done in the same way.
3+5 = 8
So,
3491 + 5234 = 8725
Subtraction Column Method
Example of subtracting using the column method:
Calculate 524 - 82
Similar to addition using the column method, start with the units column.
4 - 2 = 2
So, 2 is placed in the units column of the answer.
Then move left onto the tens column. The top number is less than the bottom number so we will need to “borrow” a \textcolor{blue}{1} from the number in the hundreds column. In this case, the 5 in the hundreds column becomes a \textcolor{orange}{4} and the \textcolor{blue}{1} is given to the tens column to make \textcolor{blue}{1}2.
Now we can continue as the top number is greater than the bottom number.
\textcolor{blue}{1}2 - 8 = 4
So, 4 goes in the tens column.
For the hundreds column we now have a \textcolor{orange}{4} instead of a 5. There isn’t a number in the hundreds column for the bottom number, so the calculation becomes:
\textcolor{orange}{4} - 0 = 4
So,
524 - 82 = 442
Example 1: Decimals
Calculate 2.41 + 17.2
The important thing for your child to remember when adding decimals is to correctly line up the decimal points. In this example there are a different number of decimal places after the decimal points, so it’s easy to get confused!
It is also helpful to add a decimal point to the answer line underneath the other decimal points so it’s not forgotten later on.
In this example 17.2 only has 1 number after the decimal point but 2.41 has 2 numbers after the decimal point. To ensure everything is lined up correctly a \textcolor{red}{0} can be added to make 17.2\textcolor{red}{0} which doesn’t change the value of the number but makes it easier to line up.
So,
2.41 + 17.2 = 19.61
Example 2: Addition and Subtraction
Harvey received some money for his birthday. He received \textcolor{red}{\pounds 35} from his auntie and \textcolor{blue}{\pounds 25} from his grandma.
Harvey spent \textcolor{green}{\pounds 24} on a new jumper.
How much of his birthday money does Harvey have leftover?
[2 marks]
First, addition is needed to find the total amount of birthday money Harvey received.
\textcolor{red}{\pounds 35} + \textcolor{blue}{\pounds 25} = \pounds 60
Then use subtraction to work out how much money he has left after buying the jumper.
\pounds 60 - \textcolor{green}{\pounds 24} = \pounds 36
Addition and Subtraction Example Questions
Question 1: Calculate 3293 - 2453
[1 mark]
The units and the tens columns can be subtracted without problem. The hundreds column “borrows” a \textcolor{blue}{1} from the thousands column.
The number in the thousands column becomes a \textcolor{orange}{2} and can be subtracted as normal.
3293 - 2453 = 840
Question 2: Maureen went to the bakery and bought some cakes for her tea party. She bought 2 lemon drizzle cakes and 1 chocolate cake.
How much did she spend in total at the bakery?
[1 mark]
Lemon drizzle cake costs \pounds 1.20 and chocolate cake costs \pounds 1.85
Add these values using column method.
Remember to include \pounds 1.20 twice as Maureen is buying 2 lemon drizzle cakes!
So,
\pounds 1.20 + \pounds 1.20 + \pounds 1.85 = \pounds 4.25
Question 3: Martin has \pounds 64.
He buys a jumper for \pounds 25 and sells a scarf he owns for \pounds 19.
How much money does he now have?
This question combines addition and subtraction.
The full calculation is:
\pounds 64 - \pounds 25 + \pounds 19 =
It is easier to split the question up into two steps, one for the subtraction and one for the addition.
Step 1: \pounds 64 - \pounds 25 = \pounds 39
Step 2: \pounds 39 + \pounds 19 = \pounds 58
Martin now has \pounds 58