Solving Equations with fractions
Algebra

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Algebra: Jill cut 3 1/2 ft chain into 2 pieces in order to hang 2 bird feeders. The longer piece of chain was 1 5/6 ft long. Tell how to write and solve an equation to find the length of the shorter piece.
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Let's write down what we know.
the total amount of chain is 3 1/2 ft
There are two piece of chains, let's call x=chain 1 and y=chain 2
we know that the longer chain was 1 5/6 long. For the sake of the argument, let's call x the longer chain. In otherwords x=1 5/6
We know that the sum of the two chains must be 3 1/2 ft, to solve for y, we set up an equation as follows
x+y= 3 1/2
1 5/6 +y= 3 1/2
Lets change the mixed fractions into simple fractions.
1 5/6= 1 x 6+5=11/6
3 1/2= 3 x 2+1=7/2
11/6 +y=7/2 (subtract 11/6 from both sides)
y=7/211/6 (get a common denominator, in this case it is 6. So we just have to multiply the first fraction by 3/3)
y=21/611/6=10/6=5/3
y= 1 2/3 back in mixed franction
Check your work.
1 5/6+1 2/3 (put into simple fractions)
11/6+5/3 (multiply the second equation by 2/2 to get a common denominator)
11/6+10/6=21/6=7/2
Which is exactly what 3 1/2 is! Thus our answer is correct.
thus chain 1= 1 5/6 ft and chain 2 = 1 2/3ft
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