Download Fundamentals of Math A.45 Name Solving One

Fundamentals of Math
A.45
Name
Solving One-step Equations (w/fractions)
Using Multiplication and Division
Date
Period
To solve algebraic equations we do the opposite of what the problem says.
If we SEE a multiplication sign ( either  or  ), then we need to divide by that number on both sides
of the equation; OR we could multiply by the ________________ .
We want to “be fair” to both sides, so do the same thing to both sides!
Review using integers:
1. 6x  54
What is another way of solving this equation using multiplication instead of division? Instead of
dividing by ____ we could multiply by _____ . Notice the two numbers you filled in the blanks are
__________________ .
Solve these using your choice of methods:
2. 3x  36
3. 2x  38
If we SEE a division sign ( which might look like  or / or any fraction bar ), then we need to
multiply by that number on both sides of the equation.
4. What is another way of writing this equation using multiplication instead of division?
x 10

means the same thing as
3 7
5.
x 3

4 5
   x  10
7

To solve, multiply both sides by ___ .
6. x  (4)  7 (rewrite this equation as a fraction before solving)
We handle equations involving fractions in the same way, and now you have some options for
solving equations (remember when you divide you can also multiply by the reciprocal):
If possible, rewrite the problem given using the “opposite” operation; then solve.
x
2

7
9
Example:
1
2
 x
7
9
This division problem could be rewritten as a multiplication problem:
To solve, multiply both sides by 7  x 
14
9
7.
x 16

4 3
This problem is dividing by _____. To solve multiply by ______ .
x  ____
8.
x
 22 This problem is dividing by _____. To solve multiply by ______ .
3
x  ____
9.
x
 21 This problem is dividing by _____. To solve multiply by ______ .
5
x  ____
3x  12
Example:
To solve this problem we need to divide by _____ OR multiply by _____:
x  ____
1
 x  13
6
To solve this problem we need to divide by _____ OR multiply by _____:
x  ____
Note: it’s far better to multiply by an integer than to divide by a fraction but you’ll get the same
answer.
10. 11x  55 To solve this problem we need to divide by _____ OR multiply by _____:
x  ____
11. 8 x 
72
To solve this problem we need to divide by _____ OR multiply by _____:
5
x  ____
12. 10 x 
1
To solve this problem we need to divide by _____ OR multiply by _____:
3
x  ____
A.45 Homework
Due Wed, 12/18/13
Solve for x .
1. 2 x 
8
11
2.
5
3
x
2
16
4.
4
2
x
3
5
5. 3x 
7.
x 3

5 14
8.
3
10
2x 3

3 8
3. 3 x 
6. 4 x 
9.
5
8
5x 5

12 6
9
23