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More About Multiplication |
Perfect Squares - Mathematically, a perfect square is when you multiply a two numbers that are the same. The result of the multiplication is the perfect square. For example,
4 x 4 = 16
Therefore, 16 is a perfect square.
To use the integer bars to find a perfect square, you can follow the methods described in Activity 1 and you will end up with an image that is a perfect square. Here is an example of using the integer bars to show the square of the number 4:
The perfect square on the left is made of 4 bars of size 4. The one on the right is made by overlapping two size 4 bars then filling out the empty space to complete the perfect square. In bothe cases the answer is 16.
Exercise - Find all of the numbers that are perfect squares between 1 and 100. You can use the Multiplication Table that you filled out in the exercise above.
When you are done, check your answers.
Prime Numbers and Composites
Prime Numbers - A prime number is a whole number that only has two factors which are itself and one. For example the number 7 has only two factors which are 1 x 7 = 7. There are no other factors that you can multiply to get the answer 7. Another example would be the number 13. The only two factors that you can multiply to get 13 are 1 x 13 = 13. Here is a list of all the prime numbers between 2 and 100:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97
Would you like to learn more about prime numbers?
Composites - A composite is the product of two or more prime numbers. For example the number 10 is the product of 2 x 5 = 10. Another example is the number 20 which is the product of 2 x 2 x 5 = 20 where 2 and 5 are both prime numbers. The list of all the composites consists of all of the numbers that are not prime numbers. If you combine all of the prime and composite numbers you get a list of all the numbers. Here is a list of all the composite numbers between 2 and 100:
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 25, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 98, 99, and 100.
0 and 1 - Both numbers, zero and one, are neither prime nor composite.
Distributive Property - When you have an equation such as 5 x (2 + 3) it implies that the 5 multiplies both the 2 and the 3. Another way of writing this same equation is:
(5 x 2) + (5 x 3)
Let's solve both of these equations to show that we get the same result.
5 x (2 + 3) Original equation (5 x 2) + (5 x 3) The 5 distributes among the 2 and the 3 5 x 5 First we add the 2 and 3 in the parenthesis which results in 5 10 + 15 First we multiply each of the sections in parenthesis. The 5 x 2 results in 10 and the 5 x 3 results in 15 25 Now we multiply 5 x 5 which results in 25 25 Now we add 10 + 15 which results in 25 We can demonstrate the distributive property using the integer bars.
First let's solve the original equation:
5 x (2 + 3)
First the 2 and 3 add up to 5:
Now multiply that result by 5:
And the result is 25.
Now we will use the integer bars to solve the distributive equation:
(5 x 2) + (5 x 3)
We need to add 5 red bars to 5 green bars:
Again, the result is 25.
Exercises - Here are three exercises for you to practice the distributive property. For each exercise solve the original equation, then write the equivalent distributive equation and solve it too.
- 4 x (2 + 6)
- 7 x (3 + 4)
- 8 x (5 + 4)
Once you have solved these equations, you can check your answers.
Learning to Multiply Using Integer Bars
Table of Contents
Learning to Divide Using Integer Bars
Last Updated: Friday, 25-Jul-2003 17:34:36 GMT
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