Carson Elementary And Intermediate Algebra 3e Page 2
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Carson Elementary and Intermediate Algebra 3e
Section 2.3.3
Example 2:
1
3
2
y
3
y
5
y
There are 3 terms and the LCD is 10.
5
10
5
1
3
2
10
y
3
10
y
5
10
y
Multiply each term by 10.
5
10
5
2(y – 3) = 3(y + 5) – 2(2)y
Reduce each fraction to eliminate the denominators.
2y – 6 = 3y + 15 – 4y
Distributive property to remove parentheses.
2y – 6 = -y + 15
Combine like terms.
3y – 6 = 15
Add y to both sides.
3y = 21
Add 6 to both sides.
y = 7
Divide both sides by 3.
2. Clearing Decimals
Decimal numbers are just another way to write a fraction. .3 is 3/10, .05 is 5/100. We can clear
decimals from an equation in the same way that we clear fractions – by multiplying each term by the
LCD. The nice things about decimals is the LCD is always a power of 10 and to multiply by a power of
10, we just move the decimal point to the right the same number of places as there are zeros in the
number. If the LCD is 100, we move the decimal point 2 places to the right. If the LCD is 1000, we
move the decimal point 3 places to the right.
Example 3:
0.06(25) + 0.27x = 0.3(4 + x)
There are 3 terms and the LCD is 100.
100(0.06)(25) + 100(0.27)x = 100(0.3)(4 + x)
Multiply each term by 100.
6(25) + 27x = 30(4 + x)
Move decimal 2 places.
150 + 27x = 120 + 30x
Distributive property to remove parentheses.
150 - 3x = 120
Subtract 30x from both sides.
-3x = -30
Subtract 150 from both sides.
x = 10
Divide both sides by -3.
V Zabrocki 2010
page 2
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