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Math
Equivalent Fractions
Same Size Different Names
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Equivalent fractions are different fraction names that represent the same amount. They matter because the same size can be described in more than one way, such as 1/2, 2/4, and 3/6. Learning equivalent fractions helps students compare, add, subtract, and simplify fractions with confidence. A visual model, like a shaded circle or fraction bar, makes it clear that the amount has not changed.
Key Facts
- Equivalent fractions have the same value, even if their numerators and denominators are different.
- Multiplying the numerator and denominator by the same nonzero number creates an equivalent fraction: a/b = (a × n)/(b × n).
- Dividing the numerator and denominator by the same common factor creates an equivalent fraction: a/b = (a ÷ n)/(b ÷ n).
- Examples: 1/2 = 2/4 = 3/6 = 4/8.
- To test equivalence, use cross products: a/b = c/d if a × d = b × c.
- A fraction is simplified when the numerator and denominator have no common factor greater than 1.
Vocabulary
- Equivalent fractions
- Fractions that have different numerators or denominators but represent the same value.
- Numerator
- The top number of a fraction that tells how many equal parts are being counted.
- Denominator
- The bottom number of a fraction that tells how many equal parts make one whole.
- Simplify
- To write a fraction in an equivalent form with the smallest possible whole-number numerator and denominator.
- Common factor
- A number that divides evenly into two or more numbers.
Common Mistakes to Avoid
- Multiplying only the numerator is wrong because it changes the size of the fraction instead of making an equivalent fraction. You must multiply both the numerator and denominator by the same nonzero number.
- Adding the same number to the numerator and denominator is wrong because addition does not keep the same fraction value. For example, 1/2 is not equal to 2/3.
- Assuming a larger denominator always means a larger fraction is wrong because the denominator tells how many pieces the whole is split into. For the same whole, eighths are smaller pieces than fourths.
- Comparing shaded pictures with different-sized wholes is wrong because equivalent fractions must refer to the same-size whole. Always check that the models use equal wholes before comparing.
Practice Questions
- 1 Fill in the missing number: 3/5 = ?/20.
- 2 Simplify the fraction 18/24, and show the common factor you used.
- 3 A circle shaded 2/4 and a same-size circle shaded 3/6 show the same amount. Explain why these fractions are equivalent using equal parts.