## Subtraction

Addition and subtraction are said to be inverse operations. This means that if you add some number b to a quantity a then subtract the same number b, the result is the original quantity a. In the language of variables, a + b − b = a This fact can be used to model subtraction.

You can use subtraction when:

- you want to take away, or remove, one quantity from another;
- you know one quantity and the sum, and need to find out the other quantity;
- you want to compare one quantity to another.

The first use of subtraction can be modeled using the set model or the number line model. The second use of subtraction can be modeled by the missing addend. The third use of subtraction can be modeled by matching sets.

The general form of a subtraction equation, using variables, is a − b = c. The a stands for the minuend, the b stands for the subtrahend, and the c stands for the difference. In primary grades, children focus on the take-away type of subtraction problems. Children are encouraged to use manipulatives first and then use pictures to solve such subtraction problems. Some children may naturally use the count-back strategy, such as for 7 − 2, where they start with 7 and then count back 6, 5 to get 7 − 2 = 5.

Finally, children are introduced to the vertical form of writing subtraction facts as a readiness activity for future subtractions involving multidigit numbers. In general, a − b = c where a, b, and c are whole numbers and a ≥ b can also be written as

a | |

− | b |

c |

**Teaching Model 3.7:** Subtract in Vertical Form