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Chapter 9 · Questions · page 65 of 68

Can the answer to an equation be a fraction?

Short answerYes. Many equations have fraction answers, and that does not mean you made a mistake. Leave it as a fraction in simplest form.

levelAlgebra 1
standard8.EE.C.7b
practiceMulti-step equations

Textbook problems are often built to land on whole numbers, which makes a fraction feel wrong. It is not. The last step is a division, and divisions do not have to come out even. Check it the same way as any answer.

How to use it

  1. Solve as usual until the last division.
  2. If it does not divide evenly, write it as a fraction.
  3. Simplify the fraction and keep the sign in front.
  4. Check by substituting, fractions and all.

Example

3(x−2)=5(x+4)⇒3x−6=5x+20⇒−2x=26⇒x=−133(x - 2) = 5(x + 4) \Rightarrow 3x - 6 = 5x + 20 \Rightarrow -2x = 26 \Rightarrow x = -13
2x+1=6⇒2x=5⇒x=522x + 1 = 6 \Rightarrow 2x = 5 \Rightarrow x = \frac{5}{2}

Where it goes wrong

  • Rounding to a decimal like 2.5 when a fraction was asked for, or the reverse.
  • Going back to look for a mistake that is not there.

Related

Simplify each side firstCheck by substitutionEquivalent fractions and simplest form
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