Welcome to the lab! The last digit of a number is a clue. Work through the five parts to discover how it tells you whether a number is a multiple of 2, 5, or 10.
Your mission
The last digit of a number is a secret code. By the end of this lab you will read it at a glance to tell whether a number is a multiple of 2, 5, or 10.
Count on, and watch the ones place
Count on in each list, then look only at the last digit of every number.
What do you notice about the last digit of each list?
Why is the last digit enough?
Is 10 a multiple of 2? of 5? of 10? (10 = 2 × 5)
Is every whole ten — 20, 30, 70 — a multiple of 2, 5 and 10?
Split off the last digit: 47 = 40 + . The 40 is whole tens, so it is already a multiple of 2, 5, and 10 — only the last digit () is left to decide.
Write the rule you discovered
Look back at what you noticed in Part 1, and complete each rule with the last digit(s):
A number is a multiple of 2 when its last digit is .
A number is a multiple of 5 when its last digit is .
A number is a multiple of 10 when its last digit is .
Try it — just the last digit: 68 → multiple of 2? 95 → multiple of 5? 240 → multiple of 10? 73 → multiple of 2?
Money ends in the right digit
A dime is 10¢, a nickel is 5¢. Stacks of dimes give 10, 20, 30 — ending in 0. Stacks of nickels give 5, 10, 15, 20 — ending in 0 or 5. The last digit does the checking for you.
A number that is a multiple of 10 ends in 0, so it is automatically a multiple of both 2 and 5. True?
What makes a multiple of BOTH 2 and 5?
A number that is a multiple of both 2 and 5 must end in a digit that is even AND (0 or 5). The only digit that is both is .
And "ends in 0" is exactly the rule for 10 — because 2 × 5 = 10.