In this lesson, we will apply the distributive property to find the product of two numbers.
We can also use the distributive property of multiplication over addition and subtraction to find the product of two given numbers.
In Mathematics, we say that multiplication is distributive over addition and subtraction because given \(a, b\) and \(c\) belonging to the set of Real numbers \((\mathbb{R})\), the relations below are true.
Addition
\(a (b + c) = ab + ac\)
Subtraction
\(a (b - c) = ab - ac\)
Using the two properties above, we can say that when finding the product of two numbers, we can express one of the numbers as a sum or difference of two other numbers, and apply the distributive property to find the product of our initial numbers.
Consider the examples below:
Example 1
Using the distributive property, find the product of 10 and 14.
Solution
Product of 10 and 14
\(\Rightarrow 10 \times 14\)
\(\Rightarrow 10 \times (4 + 10)\)
\(\Rightarrow 10(4) + 10(10)\)
\(\Rightarrow 40 + 100\)
\(\Rightarrow 140\)
We expressed 14 as the sum of 4 and 10, that is, \(14 = 4 + 10\)
Steps for using the distributive property
1. Identify the two numbers to be multiplied.
2. Choose one number to express as the sum or difference of two other numbers.
3. Apply the distributive property of multiplication over addition and/or subtraction as shown above.
4. Simplify further to get the product.
Example 2
Using the distributive property, find the product of 7 and 15.
Solution
Example 3
Using the distributive property, find the product of 18 and 6.
Solution
Example 4
Using the distributive property, find the product of 25 and 9.
Solution
Example 5
Using the distributive property, find the product of 17 and 7.
Solution
Use the distributive property to find the product of the following pairs of numbers.
-
17 and 18
-
29 and 12
-
16 and 7
-
15 and 11
-
9 and 16
Test yourself on what you have learnt so far. Click on the link below when you are ready.
Kindly contact the administrator on 0208711375 for the link to the test.
To advertise on our website kindly call on 0208711375 or 0249969740.