Example 3-1 Section
- 1 5 Multiplication Test
- Leaf 5 1 5 Multiplication Worksheet
- Multiplication 5 Grade
- Base 5 Multiplication
- Leaf 5 1 5 Multiplication Sheets
Dr. Roll Toss wants to calculate the probability that he will get:
a 6 and a head
Fawn Finds Fall (Grade 1) Jay's Perfect Pumpkin (Grade 1) Leaf Me Alone! (Grades 1-2) The Red Maple Spreads Its Wings (Grades 2-3) The Pumpkin Race (Grades 2-3) Henry Hardy's Rampaging Pumpkin (Grades 2-3) Let's Make a List (Grades 3-4) Autumn Preparation (Grades 3-4) Colors of Autumn (Grades 5-7) Crandall Farm Hay Rides, Part 1 (Hi/Lo Grades 4-5). 2 x 5 10 www.multiplication.com 1 x 5 5 www.multiplication.com 6 x 5 30 www.multiplication.com 5 x 5 25 www.multiplication.com 4 x 5 20 www.multiplication.com 9 x 5 45 www.multiplication.com 8 x 5 40 www.multiplication.com 7 x 5 35 www.multiplication.com.
when he rolls a fair six-sided die and tosses a fair coin. Because his die is fair, he has an equally likely chance of getting any of the numbers 1, 2, 3, 4, 5, or 6. Similarly, because his coin is fair, he has an equally likely chance of getting a head or a tail. Therefore, he can use the classical approach of assigning probability to his event of interest. The probability of his event (A), say, is:
(P(A)=dfrac{N(A)}{N(S)})
where (N(A)) is the number of ways that he can get a 6 and a head, and (N(mathbf{S})) is the number of all of the possible outcomes of his rolls and tosses. There is of course only one possible way of getting a 6 and a head. Therefore, (N(A)) is simply 1. To determine (N(mathbf{S})), he could enumerate all of the possible outcomes:
(mathbf{S}={1H, 1T, 2H, 2T, ldots})
and then count them up. Alternatively, he could use what is called the Multiplication Principle and recognize that for each of the 2 possible outcomes of a tossing a coin, there are exactly 6 possible outcomes of rolling a die. Therefore, there must be (6(2)=12) possible outcomes in the sample space. The following animation illustrates the Multiplication Principle in action for Dr. Roll Toss' problem:
In summary, then the probability of interest here is (P(A)=frac{1}{12}=0.083). Of course, this example in itself is not particularly motivating. The main takeaway point should be that the Multiplication Principle exists and can be extremely useful for determining the number of outcomes of an experiment (or procedure), especially in situations when enumerating all of the possible outcomes of an experiment (procedure) is time- and/or cost-prohibitive. Let's generalize the principle.
If there are:
(n_1) outcomes of a random experiment (E_1)The hardest part of using the Multiplication Principle is determining, (n_i), the number of possible outcomes for each random experiment (procedure) performed. You'll want to pay particular attention to:
- whether replication is permitted
- whether other restrictions exist
Let's take a look at another example.
Example 3-2 Section
How many possible license plates could be stamped if each license plate were required to have exactly 3 letters and 4 numbers?
Solution
Imagine trying to solve this problem by enumerating each of the possible license plates: AAA1111, AAA1112, AAA1113, .. you get the idea! The Multiplication Principle makes the solution straightforward. If you think of stamping the license plate as filling the first three positions with one of 26 possible letters and the last four positions with one of 10 possible digits:
the Multiplication Principle tells us that there are:
Again, that is:
((26times 26times 26)times (10times 10times 10times 10))
or 175,760,000 possible license plates. That's a lot of license plates! If you're hoping for one particular license plate, your chance (1 divided by 175,760,000) of getting it are practically nil.
Now, how many possible license plates could be stamped if each license plate were required to have 3 unique letters and 4 unique numbers?
Solution
In this case, the key is to recognize that the replication of numbers is not permitted. There are still 26 possibilities for the first letter position. Suppose the first letter is an A. Then, since the second letter can't also be an A, there are only 25 possibilities for the second letter position. Now suppose the second letter is, oh let's say, a B. Then, since the third letter can't be either an A or a B, there are only 24 possibilities for the third letter position. Similar logic applies for the number positions. There are 10 possibilities for the first number position. Then, supposing the first number is a zero, there are only 9 possibilities for the second number position, because the second number can't also be a zero. Similarly, supposing the second number is a one, there are only 8 possibilities for the third number position. And, supposing the third number is a two, there are 7 possibilities for the last number position:
Therefore, the Multiplication Principle tells us that in this case there are 78,624,000 possible license plates:
That's still a lot of license plates!
Example 3-3 Section
Let's take a look at one last example. How many subsets are possible out of a set of 10 elements?
Solution
Let's suppose that the ten elements are the letters A through J:A, B , C, D, E, F, G, H, I, J
Well, there are 10 subsets consisting of only one element: {A}, {B}, .., and {J}. If you're patient, you can determine that there are 45 subsets consisting of two elements: {AB}, {AC}, {AD}, .., {IJ}. If you're nuts and don't mind tedious work, you can determine.. oh, never mind! Let's use the Multiplication Principle to tackle this problem a different way. Rather than laboriously working through and counting all of the possible subsets, we could think of each element as something that could either get chosen or not get chosen to be in a subset. That is, A is either chosen or not.. that's two possibilities. B is either chosen or not.. that's two possibilities. C is either chosen or not.. that's two possibilities. And so on. Thinking of the problem in this way, the Multiplication Principle then readily tells us that there are:
(2times 2times 2times 2times 2times 2times 2times 2times 2times 2 )
or (2^{10}=1024) possible subsets. I personally would not have wanted to solve this problem by having to enumerate and count each of the possible subsets. Incidentally, we'll see many more problems similar to this one here when we investigate the binomial distribution later in the course.
Welcome to the multiplication facts worksheets page at Math-Drills.com! On this page, you will find Multiplication worksheets for practicing multiplication facts at various levels and in a variety of formats. This is our most popular page due to the wide variety of worksheets for multiplication available. Or it could be that learning multiplication facts and multiplication strategies are essential to many topics in mathematics beyond third grade math.
Learning multiplication facts to the point of quick recall should be a goal for all students and will serve them well in their math studies. Multiplication facts are actually easier to learn than you might think. First of all, it is only essential to learn the facts from 1 to 9. Somewhere along the way students can learn that anything multiplied by zero is zero. Hopefully, that is an easy one. Students also need to learn to multiply by ten as a precursor to learning how to multiply other powers of ten. After those three skills are learned, everything else is long multiplication. Multiplying by 11 is actually two-digit multiplication. Now, learning fact tables of 11 and beyond will do no harm to those students who are keen and able to learn these things quickly, and it might help them figure out how many eggs are in a gross faster than anyone else, but keep it simple for those students who struggle a bit more.
Most Popular Multiplication Facts Worksheets this Week
Multiplication Tables
Multiplication Facts Tables With Individual Questions
The multiplication tables with individual questions include a separate box for each number. In each box, the single number is multiplied by every other number with each question on one line. The tables may be used for various purposes such as introducing the multiplication tables, skip counting, as a lookup table, patterning activities, and memorizing.
The compact multiplication tables are basically lookup charts. To look up a multiplication fact, find the first factor in the column header and the second factor in the row headers; then use straight edges, your fingers or your eyes to find where the column and row intersect to get the product. These tables are better than the previous tables for finding patterns, but they can be used in similar ways. Each PDF includes a filled out table page and a blank table page. The blank tables can be used for practice or assessment. You might also make a game out of it, such as 'Pin the Fact on the Table' (a play on Pin the Tail on the Donkey). Students are given a product (answer) and they pin it on an enlarged version or the table (photocopier enlargement, interactive whiteboard, overhead projector, etc.). Paper-saving versions with multiple tables per page are included. There are also left-handed versions (students who use their left hands might block the row headings on the right-handed versions).
The left-handed versions of the multiplication tables recognize that students who use their left hands might block the row headings on the right-handed versions.
Five Minute Frenzy Charts
Five minute frenzy charts are 10 by 10 grids that are used for multiplication fact practice (up to 12 x 12) and improving recall speed. They are very much like compact multiplication tables, but all the numbers are mixed up, so students are unable to use skip counting to fill them out. In each square, students write the product of the column number and the row number. They try to complete the chart in a set time with an accuracy goal (such as less than five minutes and score 98 percent or better).
It is important to note here that you should NOT have students complete five minute frenzies if they don't already know all of the multiplication facts that appear on them. If you want them to participate with the rest of the class, cross off the rows and columns that they don't know and have them complete a modified version. Remember, these charts are for practice and improving recall, not a teaching tool by itself.
Students who write with their left hands may cover the row headings on the right-handed versions, so these versions have the row headings on the other side.
Multiplication Facts to 7 × 7 = 49
Multiplication facts to 49 refer to any facts using the digits 0 to 7. On the worksheets below, we've included just enough questions to cover each fact once. Using the digits from 1 to 7 means there are 49 facts all together, so we've put 49 questions on the page. Using the digits from 0 to 7 means there are 64 facts all together, so the worksheets with a range of 0 to 7 include 64 questions on the page. The large print pages have fewer questions on them, but all the questions are unique and in the given range.
When a student first learns multiplication facts, try not to overwhelm them with the entire multiplication table. The (A) version of each worksheet below includes one row of the facts in order with the target digit on the bottom and one row with the target digit on the top. The remaining rows include each of the facts once, but the target digit is randomly placed on the top or the bottom and the facts are randomly mixed on each row. The other versions (accessed from the A version page) do not have the first two rows organized.
Multiplication Facts to 9 × 9 = 81
The multiplication facts to 81 worksheets include versions with 81, 100 and 35 questions. The reason for the 81 question versions is because there are exactly 81 facts from 1 × 1 to 9 × 9, so each worksheet has each fact exactly once. The worksheet with zeros included also has 81 per page only to reduce the number of questions that include zero. The 100 questions versions include some repetition, but this has been controlled, so each question will appear no more than twice on each worksheet. On the multiplication facts to 81 with zeros worksheet with 100 questions, each fact appears exactly once, but you will note quite a few questions that include 0. The 35 questions worksheets are meant for any students who require fewer questions or a larger font.
When learning multiplication facts, it is useful to have each fact isolated on a set of practice questions to help reinforce the individual fact. The following worksheets isolate each fact. These worksheets can be used as practice sheets, assessment sheets, or in conjunction with another teaching strategy such as manipulative use. If you are looking for different versions, you will find them once you load the first worksheet.
Multiplication Facts to 10 × 10 = 100
Multiplication facts worksheets with facts to 10 × 10 = 100 including individual facts worksheets.
Multiplying by 10 is often a lesson itself, but here we have included it with the other facts. Students usually learn how to multiply by 10 fairly quickly, so this section really is not a whole lot more difficult than the multiplication facts to 81 section.
Some students find it easier to focus on one multiplication fact at a time. These multiplication worksheets include some repetition, of course, as there is only one thing to multiply by. Once students practice a few times, these facts will probably get stuck in their heads for life. Some of the later versions include a range of focus numbers. In those cases, each question will randomly have one of the focus numbers in question. For example, if the range is 6 to 8, the question might include a 6, 7 or 8 or more than one depending on which other factor was chosen for the second factor.
Multiplication facts (1 to 10) with increasing ranges for the second factor
If a student is learning their times tables one at a time, these worksheets will help with practice and assessment along the way. Each one increases the range for the second factor.
1 5 Multiplication Test
Multiplication Facts to 12 × 12 = 144
Multiplication facts worksheets with facts to 12 × 12 = 144 including individual facts worksheets.
The following worksheets are intended for multiplication fact practice or assessment after students have learned all of the multiplication facts. They might also be used as a set of questions for manipulative practice. For example, students could model multiplication questions using arrays of counters. They could check their answers using the answer key.
With one, two or three target numbers at a time, students are able to practice just the multiplication facts they need.
In these multiplication worksheets, the facts are grouped into anchor groups.
Multiplication facts (1 to 12) with increasing ranges for the second factor
On these multiplication worksheets, the questions are in order and might be useful for students to remember their times tables or to help them with skip counting.
Multiplication Facts Greater Than 144
Multiplication facts from 13 × 13 = 169 and up worksheets.
Horizontal Multiplication Facts
Multiplication worksheets with questions arranged horizontally.
A horizontal orientation is sometimes just a matter of preference. If students have mastered their multiplication facts, see if these offer any challenge. Jixipix premium pack 1 1 123. Seeing questions arranged in different ways builds flexibility and adaptability in students.
These multiplication worksheets do not include any zeros.
Multiplication Strategies
The halving and doubling strategy is accomplished very much in the same way as its name. Simply halve one number and double the other then multiply. Book collector 19 0 3 download free. In many cases, this makes the multiplication of two numbers easier to accomplish mentally. This strategy is not for every multiplication problem, but it certainly works well if certain numbers are involved. For example, doubling a 5 results in a 10 which most people would have an easier time multiplying. Of course, this would rely on the other factor being easily halved. 5 × 72, using the halving and doubling strategy (doubling the first number and halving the second in this case) results in 10 × 36 = 360. Practicing with the worksheets in this section will help students become more familiar with cases in which this strategy would be used.
Multiplication Games
Leaf 5 1 5 Multiplication Worksheet
Some students are a little more motivated when learning is turned into a game. Multiplication bingo encourages students to recall multiplication facts in an environment of competition.
NewsMultiplication 5 Grade
More Information
Base 5 Multiplication
HomeAddition WorksheetsSubtraction WorksheetsMultiplication Facts WorksheetsLong Multiplication WorksheetsDivision WorksheetsMixed Operations WorksheetsLarge Print Math WorksheetsAlgebra WorksheetsBase Ten Blocks WorksheetsDecimals WorksheetsFact Families WorksheetsFractions WorksheetsGeometry WorksheetsGraph PaperIntegers WorksheetsMeasurement WorksheetsMoney Math WorksheetsNumber Lines WorksheetsNumber Sense WorksheetsOrder of Operations WorksheetsPatterning WorksheetsPercents WorksheetsPlace Value WorksheetsPowers of Ten WorksheetsStatistics WorksheetsTime Math WorksheetsMath Word Problems WorksheetsHalloween Math WorksheetsThanksgiving Math WorksheetsChristmas Math WorksheetsValentine's Day Math WorksheetsSaint Patrick's Day Math WorksheetsEaster Math WorksheetsSeasonal Math WorksheetsUnit ConverterMath Flash CardsDots Math GameSudoku Math Game
Leaf 5 1 5 Multiplication Sheets
Help and FAQ Tour Terms of Use Privacy and Cookie Policy Feedback Teachers Parents Support Math-Drills Math-Drills on Facebook Math-Drills on Twitter