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Dividing fractions review

Review the basics of dividing fractions, and try some practice problems.

Dividing fractions

Dividing fractions is the same as multiplying by the reciprocal (inverse).
For example:
start fraction, 3, divided by, 4, end fraction, start color #e07d10, divided by, end color #e07d10, start fraction, start color #11accd, 2, end color #11accd, divided by, start color #1fab54, 3, end color #1fab54, end fractionequals, start fraction, 3, divided by, 4, end fraction, start color #e07d10, times, end color #e07d10, start fraction, start color #1fab54, 3, end color #1fab54, divided by, start color #11accd, 2, end color #11accd, end fraction
Once we have a multiplication problem, we multiply the numerators then multiply the denominators.
Example 1: Fractions
start fraction, 3, divided by, 2, end fraction, divided by, start fraction, 8, divided by, 3, end fraction, equals, question mark
The reciprocal of start fraction, 8, divided by, 3, end fraction is start fraction, 3, divided by, 8, end fraction.
Therefore:
start fraction, 3, divided by, 2, end fraction, divided by, start fraction, 8, divided by, 3, end fraction, equals, start fraction, 3, divided by, 2, end fraction, times, start fraction, 3, divided by, 8, end fraction
empty space, equals, start fraction, 3, times, 3, divided by, 2, times, 8, end fraction
empty space, equals, start fraction, 9, divided by, 16, end fraction
Example 2: Mixed numbers
3, start fraction, 1, divided by, 2, end fraction, divided by, 1, start fraction, 1, divided by, 4, end fraction, equals
Let's start by converting the mixed numbers to fractions.
empty space, 3, start fraction, 1, divided by, 2, end fraction, divided by, 1, start fraction, 1, divided by, 4, end fraction
equals, start fraction, 7, divided by, 2, end fraction, divided by, start fraction, 5, divided by, 4, end fraction
equals, start fraction, 7, divided by, 2, end fraction, dot, start fraction, 4, divided by, 5, end fraction, space, space, space, space, space, space, space, start text, M, u, l, t, i, p, l, y, space, b, y, space, t, h, e, space, r, e, c, i, p, r, o, c, a, l, point, end text
equals, start fraction, 7, divided by, start color #11accd, 1, end color #11accd, start cancel, 2, end cancel, end fraction, dot, start fraction, start color #11accd, 2, end color #11accd, start cancel, 4, end cancel, divided by, 5, end fraction, space, space, space, space, space, space, space, start text, S, i, m, p, l, i, f, y, point, end text
equals, start fraction, 7, divided by, start color #11accd, 1, end color #11accd, end fraction, dot, start fraction, start color #11accd, 2, end color #11accd, divided by, 5, end fraction
equals, start fraction, 14, divided by, 5, end fraction, start text, space, o, r, space, end text, 2, start fraction, 4, divided by, 5, end fraction
Want to learn more about dividing fractions? Check out this video.
Want to review multiplying fractions? Check out this article.

Practice

Problem 1
  • Current
start fraction, 3, divided by, 5, end fraction, divided by, start fraction, 1, divided by, 9, end fraction, equals, question mark
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3, slash, 5
  • a simplified improper fraction, like 7, slash, 4
  • a mixed number, like 1, space, 3, slash, 4
  • an exact decimal, like 0, point, 75
  • a multiple of pi, like 12, space, start text, p, i, end text or 2, slash, 3, space, start text, p, i, end text

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

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