Find the missing number in this input-output table.
We’re missing the output if the input is 17. But to go from the input to the output, we need to know the rule. We need to know what’s happening to the input value to produce the output value. Let’s make a number line and graph what’s happening with some of our input-output pairs.
Our first input value is two. If you input two, you get out 39. How do we get from two to 39 on a number line? We add some amount. And to find out what we add, we can use subtraction. If we take 39 and subtract two, we’ll find out what we were adding: nine minus two is seven, bring down the three.
To get from two to 39 you need to add 37. Let’s check our rule with some of the other pairs to make sure we’ve calculated it correctly. If we start with five, the output is 42. Five plus 37 equals 42. Our missing value starts with 17. We input 17, and we know that our rule is plus 37.
We have to calculate 17 plus 37 to find out the output. Starting with the units place, seven plus seven equals 14. Write down the four, carry the one. In the tens place, one plus one plus three equals five.
17 plus 37 equals 54. If we input 17 and use this rule, plus 37, then the output value is going to be 54. The missing number in our table is 54.