Multiplication and division properties

Multiplication properties

The commutation property of multiplication

From the permutation of the multipliers the product does not change.

a • b = b • a

The combinational property of multiplication

To multiply a number by the product of two numbers, you can first multiply it by the first factor, and then multiply the resulting product by the second factor.

a • (b • c) = (a • b) • c

The transfer and combination properties of multiplication allow us to formulate a rule for the transformation of products.

When multiplying several numbers, you can rearrange them as you like and merge them into groups.

Zero property when multiplied

If at least one factor in a product is zero, then the product itself will be zero.

a • 0 = 0

0 • a • b • c = 0

Distribution property of multiplication with respect to addition

To multiply the sum by a number, you can multiply each term by this number and add the results.

(a + b) • c = a • c + b • c

This property holds for any number of terms.

(a + b + c + d) • k = a • k + b • k + c • k + d • k

Distribution property of multiplication with respect to subtraction

To multiply the difference by a number, you can multiply by this number, first decremented and then subtracted, and subtract the second from the first work.

In literal form, the property is written as:

(a - b) • c = a • c - b • c

To multiply a number by the product of two numbers, you can first multiply it by the first factor, and then multiply the resulting product by the second factor.

Division properties

• No number can be divided by zero.
• Dividing zero by number produces zero.
  0: a = 0
• Dividing any number by 1 yields the same number.
  b: 1 = b

If the dividend and the divisor are multiplied or divided by the same natural number, then their quotient will not change.

a: b = (a • k): (b • k), where k is any natural number.

Please note that the property of division above allows us to reduce fractions.

Using all the above properties allows us to simplify expressions.