Module 4 · Fractions · Lesson 14 of 39

Simplifying and equivalent fractions

Reduce to lowest terms, build equivalent fractions, and why 0 can't be on the bottom.

In this lesson · about 16 minutes

  • Reduce a fraction to lowest terms by canceling common factors
  • Rewrite a fraction with a new denominator
  • Explain why a fraction with 0 in the denominator is undefined

If you've driven 50 of 100 miles, you're halfway: 50100 = 12. Writing a fraction with the smallest possible numbers is called reducing to lowest terms. 630945 looks complicated, but it is just 23.

How: find the prime factors of the top and bottom. A factor that appears in both cancels. If everything cancels, the fraction is 1: 33 = 1.

Worked example

Simplify 630/945

Factor the numerator and denominator into primes.

    Step 0 of 4

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    Equivalent fractions

    Fractions that are equal, like 3045 and 23, are equivalent. To go the other way, multiply the top and bottom by the same number. That's multiplying by a form of 1, so the value doesn't change: 35 = 3 · 25 · 2 = 610.

    Try it · interactive

    Fraction bars: see equivalent fractions

    Change the multiplier and watch the shaded amount stay exactly the same.

    2/3
    4/6

    Both bars are shaded the same amount, so 2/3 = 4/6. They are equivalent fractions. 2/3 is already in lowest terms.

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    Practice sets mastered: 0 of 3

    Tip: master each practice set first (get 5 right in a row).

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