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|| PRE-ALGEBRA ||
|| MULTIPLICATION AND DIVISION IN EQUATIONS ||
FOR AGES 10 AND 11
POINTS TO REMEMBER :
* Order of operation..
Parentheses Exponents Multiplication Division Addition Subtraction
(P E M D A S)
1. The operations inside parentheses "( )" and brackets "[ ]" are done first.
2. Then any operations involving exponents are done.
3. Next do all multiplication and division in the equation starting from left to right.
4. Finally, do all the addition and subtraction in the equation from left to right.
For Example:
[5 + 4] x [4 - 2] + [9(4 x 5) - 2 - 3² + (6 - 3) x 5 + 2²+ 20 / 2 - 4] + [3 - 2 x 4 + 8 - 6(7 - 2)].
= [9] x [2] + [9(20) - 2 - 3² + (3) x 5 + 2² + 20/2 - 4] + [3 - 2 x 4 + 8 - 6(5)].
= [9] x [2] + [180 - 2 - 9 + 3 x 5 + 4 + 20/2 - 4] + [3 - 8 + 8 - 30].
= 18 + 180 -2 - 9 + 15 + 4 + 10 - 4 + [-27].
= 18 + 180 - 2 - 9 + 15 + 4 + 10 - 4 - 27.
= 198 - 11 + 29 - 31.
= 187 - 2.
= 185.
* * Changing the order of numbers you are multiplying together doesn't change their total.
For Example:
a x b = b x a. or ab = ba.
*** Zero times any number is zero and 1 times any number is the same number or in other words any number multiplied by zero is zero and any number multiplied by one is the same number.
For Example:
a x 0 = 0.
0 x a = 0.
a x 1 = a.
1 x a = a.
**** If two sides of an equation are equal, you can multiply or divide each sides by the same number or quantity and it will still be equal.
For Example:
a = b.
a x c = b x c. or ac = bc. Where c is not zero. (If c is zero, everything will be zero.)
(a/c) = (b/c).
Exercise:
Problem:
6a = 42.
Solution:
6a = 42.
6a / 6 = 42 / 6.
a= 7.
Problem:
a / 5 = 10.
Solution:
a / 5 = 10.
(a / 5) x 5 = 10 x 5.
a = 50.
Combined operations:
Problem:
7a - 7 = 49.
Solution:
7a - 7 = 42.
7a - 7 + 7 = 42 + 7 = 49.
7a = 49.
7a / 7 = 49 / 7.
a = 7.
Problem:
5(a + 2) = 25.
Solution:
5(a + 2) = 25.
5a + 10 = 25.
5a + 10 - 10 = 25 - 10.
5a = 15.
5a / 5 = 15 / 5.
a = 3.
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