Properties of operations
How to not solve problems
Imagine if you had a chance to not solve a problem, because you could things you already knew! When you look at two sides of an equation, you can use some important rules to save time, such as the commutative property of multiplication (it works for addition too!), to work out if the equation is true or not. In fact, you can also use the fact that these rules don't hold true for division and subtraction to solve equations as well.
Let's look at how this rule helps us, in Video 1.
other rules
In Video 2, we'll look at some other rules that help us work out if one side of an equation equals the other side. The order of operations is useful, as well as the distributive property of multiplication. In fact, sometimes you might just notice something that just couldn't be true, so let's see how these things help us.
Often, you don't actually need to solve each side of your equation, to see if it is true or not. By thinking about rules you know, and different operations we use to solve problems, you can make a decision without solving the problems!
Worked Examples
Question 1
True or False?
$20\div2\times2=20\div20$20÷2×2=20÷20.
True
AFalse
B
Question 2
True or False?
$104-39=89-24$104−39=89−24.
True
AFalse
BHence fill in the missing blank.
$136-49$136−49 = $103$103 - $\editable{}$
Question 3
True or False?
$6875\div55=6875\div275\times5$6875÷55=6875÷275×5.
True
AFalse
BHence fill in the missing blank.
$2000\div25$2000÷25 = $2000$2000 ÷ $\editable{}$ × $5$5