Are you able to add $10$10 , $100$100 or even $1000$1000 to a number very quickly? It would be nice if all addition problems were like this!

Sometimes, you can use the rules of mathematics to make hard problems easier to do. Read the rules of addition below. Then, watch a video to see how you can use the rules.

Regrouping with Addition

You can add in any order. (Addition is commutative.)

You can trade a number for another equal amount. (This is called substitution.)

Did you see how the number $170$170 was replaced by the numbers $100$100 and $70$70? That's because we can trade a number with an equal amount!

Did you see how the numbers $70$70 and $200$200 switched places? That's because you can add in any order!

Regroup to Subtract

Subtracting is tricky because the order is important. Unlike addition, subtraction has to be done in a particular order, so you can't switch the numbers in a subtraction problem.

However, you can still trade numbers with equal amounts. Watch how this is helpful in this video.

Worked Examples

Question 1

Evaluate $605+305$605+305 by doing the following.

Fill in the box with the missing number.

$605=600+\editable{}$605=600+

Fill in the box with the missing number.

$305=\editable{}+5$305=+5

Using the answers from the previous parts, solve $605+305$605+305.

Question 2

Using the fact that $250=200+50$250=200+50 and $350=300+50$350=300+50, evaluate $250+350$250+350.