Substitution into an algebraic expression
The question told us what the letter stands for, so we wrote that number in its place, kept the whole expression, and only then worked it out. Same three steps, every time.
Questions in this lesson
Transcript
A hall is set up with identical tables. Each table has n chairs around it. There are 4 tables, and 5 more chairs against the wall, which is 4 n plus 5 chairs. Find how many chairs there are when n is 6. 4 n plus 5 doesn't say how many chairs there are yet. Nobody has told us how many go round 1 table. The question tells us there are 6 chairs at each table. So every n stands for 6, and all 4 of the n change at the same time. Initially, blue meant a number we hadn't been given. Purple means a number we know, so they're all purple now. There's no blue left. We don't swap the first n and leave the other n. Putting a number in place of a letter is called substitution. We now substitute n to be 6. Before we work anything out, we write the whole expression again. 4 n plus 5 becomes 4 times 6, plus 5. And the 5 comes across untouched. 4 times 6 is 24. Nothing gets left behind, so 24 plus 5 is 29. So 4 n plus 5 equals 29, when n is 6. So there are 29 chairs in the hall.
Your turn. No hall this time, and no blocks. Sometimes a question arrives on its own, with no story around it. Find the value of 5 n minus 4 when n is 7. Try it first. Pause if you like. Same as before. We substitute n to be 7. 5 n minus 4 becomes 5 times 7, minus 4 — the 7 goes exactly where the n was. 5 times 7 is 35. 35 minus 4 is 31. That one started with a letter and ended with a number. The question told us what the letter stands for, so we wrote that number in its place, kept the whole expression, and only then worked it out. Same three steps, every time.