Name: Understanding the Distributive Property
Uploaded: 2019-07-19
Duration: 11 min 54 s
Description: We know about the commutative and the associative property, but there is more to learn! This next one, the distributive property, is very important in algebra.

Question

Using the properties of multiplication, find the product of the following.

(- 111) \times (- 89) + 111

Accepted Answer

The distributive property of multiplication of integers over addition of integers states that if $a, b$ and $c$ are three integers, then $a \times (b + c) = a \times b + a \times c$ is true. This means multiplication of integers is distributive over the addition.

The commutative property of multiplication of integers states that if $a$ and $b$ are two integers, then $a \times b = b \times c$ is true. This means the multiplication of integers can be done in any order.

We shall use both these properties to find the product of the given mathematical expression.

Steps to find the product of integers:

(i) First, we find the product of the integers like the product of whole numbers, without considering the signs of the integers.

(ii) Then, we attach positive or negative signs before the product according as:

The product of two integers of unlike signs is always negative.

The product of two integers of like signs is always positive.

Thus, we get, $(- 111) \times (- 89) + 111$

$= 111 \times (- 1) \times (- 89) + 111 \times 1$

$= 111 \times 89 + 111 \times 1$

$= 111 \times (89 + 1)$

$= 111 \times 90$

$= 9990$

Therefore, the required answer is $9990$ .

Using the properties of multiplication, find the product of the following.
$(- 111) \times (- 89) + 111$

Important Questions on Integers

Learn and Prepare for any exam you want !

Using the properties of multiplication, find the product of the following. (-111)×(-89)+111

Important Questions on Integers

Learn and Prepare for any exam you want !

Using the properties of multiplication, find the product of the following.
$(- 111) \times (- 89) + 111$