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Addition and Subtraction

Addition

The symbol used to represent addition is +. Other words used to describe addition include ‘plus’, ‘add’, ‘more’, ‘sum of’, ‘and’, ‘increase by’, ‘total’, and ‘together’. When you add, we count the second number from the first one. For example, if we are to add 6 and 5, we will count 6 from 5 to get a total of 11. When adding two, three or higher digit numbers, set out the addition with units underneath each other, i.e. all units/ones under each other, all the tens under each other and so on vertically. Then add the vertical columns, starting from the units/ones (the smallest) to tens and so on (the largest).

For example: 12 + 15 can be represented as follows:

Tens Units
1 2 +
1 5
2 7

When adding two, three or higher digit numbers, we’d follow the same procedure. When the sum of numbers in a column add to more than 10, we then ‘carry over’ the tens digit to the adjacent column. For example: 24 + 79 can be represented as follows:

Hundreds Tens Units
1 1
2 4 +
7 9
1 0 3

 

Finally, let’s take the example of adding a three digit and a four digit number: 155 + 2884

Thousands Hundreds Tens Units
1 1
1 5 5 +
2 8 8 4
3 0 3 9

A few further examples:

1. There are 457 boys and 519 girls in Appletree High School. How many students attend the school?

In this question, we are required to add the two numbers to get the total number of students attending Appletree High School (457 boys + 519 girls = 976 students).

Hundreds Tens Units
4 5 7 +
5 1 9
9 7 6

2. Bob is making a long distance car journey. He drives 422 kilometres on the first day, 326 kms on the second day, 212 kms on the third and 60 kms on the final day. What is the total distance Bob has driven over the four days?

Here, we should add the distances travelled on each day to get the total distance driven by Bob, i.e. 426 + 326 + 212 + 60 = 1020 kilometres

Thousands Hundreds Tens Units
1 1
4 2 2 +
3 2 6
2 1 2
6 0
1 0 2 0

 

Subtraction

Subtraction is the opposite of addition. When you subtract two numbers, we count down the second number from the first. In other words, we ‘take away’ or find out what is left of the first number after ‘taking away’ the second number.

The symbol used for representing subtraction is −. Some other words and expressions used to describe it are – minus, subtract, less than, from, difference between, decrease by, take away, reduce, how much more than, etc.

When subtracting two numbers, put them vertically in columns of units, tens, hundreds, and so on, and subtract along each column, starting with the units column first, then the tens column, and hundreds column, and so on. For example: 869 – 236 can be represented as follows:

Hundreds Tens Units
8 6 9
2 3 6
6 3 3

When you have to subtract a larger digit from a smaller digit (i.e. the top digit is smaller than the bottom digit), then we must trade, that is, take one ‘ten’ from the column to the left and add it to the column in question, while reducing the digit in the left column by 1. For example: 53 – 26 can be represented as:

Tens Units
4 13
5 3
2 6
2 7

Finally, let’s look at the subtraction of 2 three digit numbers (624 – 196)

Hundreds Tens Units
5 11 14
6 2 4
1 9 6
4 2 8

A few further examples:

1. Tom had $232 with him, and he gave $50 to Ben. How much money is now left with Tom?

Here we need to take away 50 from 232 to get the amount of money left with Tom ($232 – $50 = 182)

Hundreds Tens Units
1 13
2 3 2
5 0
1 8 2

 

2. Sally has 550 beads in a box. She takes away 177 beads to make a necklace. How many beads are left in the box?

Here we need to take away 177 from 550 to get the number of beads left in the box (550 – 177 = 373)

 

Hundreds Tens Units
4 14 10
5 5 0
1 7 7
3 7 3