Equivalent fractions review

Review equivalent fractions with multiplication, and try some practice problems.

Equivalent fractions

Fractions are equivalent if they are equal or represent the same amount.
Want to learn about visualizing equivalent fractions? Check out this article.

Finding equivalent fractions using multiplication

Let's look at an example.
What number could replace aa below?
23=a12\dfrac23=\dfrac{a}{12}
First, we need to figure out what to multiply 33 by to get 1212:
23×4=12\dfrac23\times\dfrac{}{4}=\dfrac{}{{12}}
Next, we multiply the numerator by the same number as the denominator:
23×44=812\dfrac23\times\dfrac{4}{4}=\dfrac{8}{{12}}
23=812\dfrac23=\dfrac{8}{{12}}, so we can replace the aa with an 88.
Want to learn more about equivalent fractions? Check out this video.

Practice

Problem 1
What number could replace rr below?
24=r8\dfrac{2}{4} = \dfrac{r}{8}
  • Your answer should be
  • an integer, like 66
  • a simplified proper fraction, like 3/53/5
  • a simplified improper fraction, like 7/47/4
  • a mixed number, like 1 3/41\ 3/4
  • an exact decimal, like 0.750.75
  • a multiple of pi, like 12 pi12\ \text{pi} or 2/3 pi2/3\ \text{pi}

Want to try more problems like this? Check out this exercise.