Probability, Adding Complements and Divisibility Rules

What do the following things have in common: probability, adding complements and divisibility rules? These are all new math worksheets at Math-Drills.com!

Probability

Probability is actually a new section on the Data Management and Probability Worksheets page even though it has had "probability" in its name for quite some time. We decided to start with some probabilities with dice and spinners and included several options for both. For the sum of two dice probabilities worksheets, you can choose between a version without a helpful table or with a helpful table. For the spinners, we've included worksheets with between 4 and 12 sections. Instead of using colors, we used numbers on the spinner as we know many people have black and white printers and it also helps to distinguish between the sections, especially if there are 12 sections on a spinner.

Since it is Halloween season, we thought a Halloween probability math worksheet would be a good idea, so we made a set of them asking students what the probabilities are of getting certain candies while trick-or-treating. We also added a slightly more difficult version where students have to predict how many candies of each type they would get based on how many houses they visited.

Adding Complements

Adding Complements is an interesting skill as it challenges students to find or know what numbers add together to make certain complements. The most common ones are powers of ten (e.g. 10, 100, 1000) and powers of ten minus one (e.g. 9, 99, 999). This has all sorts of wonderful benefits in a student's repertoire of math skills. For example, in subtraction, using a counting up strategy is so much easier if students are familiar with complements of powers of ten. In the question, 1532 - 437, a student can find the 1000 complement of 437 and add it to 532 to find the answer. They could find the difference in other ways too, but knowing the 1000 complements makes this a two-step problem and can be done mentally. In money management, giving change for, say a 10 dollar bill, is made much easier knowing complements because it is simply a matter of finding the 1000 complement for the money amount without the decimal. For example, what change would you get from a 10 Pound note if the total bill was £4.54? Since the 1000 complement of 454 is 546, the change would be £5.46.

Divisibility Rules

Divisibility rules are sometimes overlooked as some people don't see much value in them, but they certainly do help students to understand numbers and patterns much better. Is there not some little joy or fascination in being able to tell whether a 10 digit number is divisible by 4 just by looking at the last two digits? In practice, divisibility rules are quite useful in things like prime factorization, finding factors of a number, long division, and fractions (e.g. simplifying fractions).

To help you break up this skill a little, we've grouped the divisibility rules into several sets. First, we put 2, 5 and 10 together. For the uninitiated, we've included the divisibility rules below where you will see that 2, 5 and 10 are quite straight-forward and only require looking at the last digit of the number. 3, 6 and 9 is our second group where you have to do a little more work to figure out whether a number is divisible by one of these.... but not too much work. The final group is 4, 7 and 8. We included 4 here only because it needed a place to go and we thought we would keep each set with three numbers. The 7 and 8 are normally the difficult ones, and these can be assessed with a calculator too if your students have great difficulty with the rules.

You might also notice we made some versions with random divisibility rules from 2 to 10 on each page. Just find the ones that work for your lesson.

Divisibility of 2, 5 and 10

A number is divisible by 2 if the final digit (the digit in the ones place) is even. Numbers ending in 0, 2, 4, 6, or 8 therefore are divisible by 2.

A number is divisible by 5 if the final digit is a 0 or a 5.

A number is divisible by 10 if the final digit is a 0.

Divisibility of 3, 6 and 9

A number is divisible by 3 if the sum of its digits is divisible by 3. For example, 285 is divisible by 3 because 2 + 8 + 5 = 15 is divisible by 3.

A number is divisible by 6 if it is divisible by both 3 and 2 (see above rules).

A number is divisible by 9 if the sum of its digits is divisible by 9. For examples, 285 is not divisible by 9 because 2 + 8 + 5 = 15 is not divisible by 9.

Divisibility of 4, 7 and 8

A number is divisible by 4 if the last two digits of the number is divisible by 4. For larger two digit numbers, you can also take the 100 complement to make it a little easier. For example 694 is not divisible by 4 since the 100 complement of 94 is 6 and 6 is not divisible by 4. (Look at that, we found a great use for 100 complements!)

For 7, there are a couple of strategies to use, but since we don't know one off the top of our heads, we're going to send you to Divisibility Math Tricks to Learn the Facts instead of just copying someone else's work.

A number is divisible by 8 if the last three digits are divisible by 8. This is the standard rule which can be a little sketchy for larger numbers, like who knows if 680 is divisible by 8? Because of this, we offer our Math-Drills.com solution which requires a little arithmetic, but can be accomplished quite easily with a little practice. As you know 8 is 2 to the third power, so we thought if you could divide the last three digits of a number by 2 three times, it would be divisible by 8. 680 ÷ 2 ÷ 2 ÷ 2 = 340 ÷ 2 ÷ 2 = 170 ÷ 2 = 85. We have a winner! 680 is indeed divisible by 8.

We hope you enjoy our latest math worksheets and encourage you to send us a request if there is something that you would like to see on the website.