Multiplication is a simpler way to do repeated addition. For example: 4 x 6 is easier than 4 + 4 + 4 + 4 + 4 + 4. You are also less likely to make a careless error using multiplication than if you use repeated addition.
An array is a way of ordering objects in rows and columns to make a rectangular shape. In an array, all the rows are equal to each other and all the columns are equal to each other and that makes a rectangular shape. For example:
The zero property of multiplication is that any factor multiplied by 0 equals 0. For example: 5 x 0 = 0
The identity property of multiplication is that any factor multiplied by 1 equals the original factor. For example: 3 x 1 = 3
The commutative property of multiplication is that two factors can be multiplied in either order and give the same answer. For example: 7 x 2 = 2 x 7
The associative property of multiplication is that three or more factors can be multiplied in different groups and still give the same answer. For example: (4 x 5) x 6 = 4 x (5 x 6)
A number is a factor of another number if it divides into it evenly without a remainder. To find factors of a number you can make a factor rainbow. See the example below: The factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24.
1 2 3 4 6 8 12 24
Prime numbers are numbers that can only be divided evenly by 1 and themselves. For example: 7 is a prime number because it only has 2 factors. These factors and 1 and 7.
Composite numbers are numbers that have more than 2 factors. For example: 4 is a composite number because its factors are 1, 2, and 4.
Since 0 has no factors it is not prime or composite.
Since 1 has only 1 factor it is not prime or composite.
A multiple can be made by multiplying a number. For examples: some multiples of 6 are 6, 12, 18, 24, 30, 36 etc because 1 x 6 = 6, 2 x 6 = 12, 3 x 6 = 18, 4 x 6 = 24, 5 x 6 = 30, 6 x 6 = 36, etc.
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To practice multiplying.
To practice factors and multiples.
To practice multiplication facts.
To practice multiples.
To practice using a multiplication grid.
To practice multiplication facts.
When one number is divided by another, the result is called a quotient. The dividend is the number being divided and the divisor is the number used to divide another number.
You can use basic facts and patterns to divide by multiples of 10.
Divisibility Rules:
| Number | Divisibility Rules |
| 2 | All even numbers or all numbers with 0, 2, 4, 6, or 8 in the ones place. |
| 3 | Any whole number whose digits add up to a multiple of 3. For example: 204 is divisible by 3 because 2 + 0 + 4 = 6 and 6 is a multiple of 3 because 2 x 3 = 6. |
| 5 | All whole numbers with 5 or 0 in the ones place. |
| 6 | Any whole number that is divisible by BOTH 2 and 3. |
| 9 | Any whole number whose digits add up to a multiple of 9. For example: 9,954 is divisible by 9 because 9 + 9 + 5 + 4 = 27 and 27 is a multiple of 9 because 3 x 9 = 27. |
| 10 | All whole numbers with a 0 in the ones place. |
Dividing by 1 Digit
Dividing by 2 Digits
When we know how many groups there are and how many things are to be shared, but we don't know how many are in each group, we divide to share equally.
Division is the inverse of multiplication. Inverse operations undo each other. For example: 5 x 20 = 100 and 100 divided by 20 = 5.
Division is a simpler way to do repeated subtraction.
Any number, except 0, is divisible by 1 and itself. For example: 30 divided by 1 = 30 and 30 divided by 30 = 1. Division of 0 is a special case of divisibility because any number, except 0, will divide into 0. Zero divided by any number, except 0, is zero. For example: 0 divided by 3 = 0.
Division by 0 cannot be done.
When we divide we can use the expanded division algorithm. Go to the Click Me button below for expanded algorithm power point to see how to use the division algorithm.
To estimate a quotient, you can use compatible numbers, or numbers that are easy to divide mentally. Look for numbers that are part of fact families:
Expanded Algorithm Power Point
To practice division facts.
To practice division facts.
To practice completing division equations.
