Video: Using Arithmetic Operations to Complete Mathematical Problems

Use +, −, or × to fill in the blank: 9 × 2 = 22 _ 4.

03:02

Video Transcript

Use the symbol for add, subtract, or multiply to fill in the blank. Nine times two equals 22 what four.

We can think of a number sentence like this as a set of weighing scales or balances. On one side, we have the calculation nine times two. On the other side, we have the numbers 22 and four. But we don’t quite know what the symbol in between them is. And in the middle, we have an equal sign. And this equal sign is important. It tells us that both sides of the number sentence are worth the same. So imagine our set of weighing scales. It means that both sides are balanced. So whatever symbol we use in between 22 and 4, it has to give an answer that’s worth the same value as nine times two.

So a good place to start is to ask ourselves what is nine times two? We know that 10 times two equals 20. We also know that nine lots of two are two less than this. 20 take away two leaves us with 18. So nine times two must be worth 18. This means that the left-hand side of our statement is worth 18 too. Now, which symbol can we use in between 22 and four to give an answer of 18? One way of finding the answer could be to put each symbol in between the two numbers and to workout what it’s worth. But we can find the answer just by using reasoning.

For example, if we start with 22 and then we add any number at all to it, the number is going to become larger. We want to make 18. So adding four to 22 is not going to give us an answer of 18. And for exactly the same reason, the multiplication symbol is not the right one to use, either. If we start with 22 and we multiply it four times, this is also going to give us an answer that’s nowhere near an 18, it’s going to give us an answer much bigger than 22.

And so, just by crossing off the wrong answers, we found the correct symbol. But it’s always worth a check. We’ll start with 22. And we’ll count back four. One, two, three, and four. 22 take away four does equal 18. And so, if we use a subtract sign in between 22 and four, both sides of our number statement are the same. They’re both worth 18. Nine times two is equal to 22 take away four. The correct symbol to fill in the blank is the minus sign.

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