Vocabulary
Mixed Number - a combination of a whole number and a fraction.
Proper Fraction - a fraction that is less than one, with the numerator less than the denominator.
Improper Fraction - a fraction that is greater than one, with the numerator greater than the denominator.
Concept
Convert improper fractions to mixed numbers or vice versa and simplify.
Rules
1. Convert a mixed number to an improper fraction:
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Multiply the whole number by the denominator.
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Add the answer from Step 1 to the numerator.
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Write the answer from Step 2 over the denominator.
2. Convert an improper fraction to mixed number:
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Divide the numerator by the denominator.
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Write down the whole number result.
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Use the remainder as the new numerator over the denominator. This is the fraction part of the mixed number.
3. In order to simplify a fraction, there must be:
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A number that will divide evenly into both the numerator and denominator so it can be reduced, or
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The numerator must be greater than the denominator, (an improper fraction), so it can be converted to a mixed number.
Example 1 Convert mixed number to improper fraction
Change the mixed number to an improper fraction.
Solution
(2 × 5) + 35
Answer: 135
Example 2 Convert improper fraction to a mixed number
Change the improper fraction to a mixed number.
Solution
23 ÷ 4 = 5 with remainder of 3
Answer: 534
Example 3 Simplify improper fraction
Simplify.
Solution
21 ÷ 749 ÷ 7= 37
Answer: 37
Pre-requisite Skills
Convert Between Mixed Numbers and Improper Fractions (4.14.11)
Write improper fraction as mixed number (5.7.1)
Write mixed number as improper fraction. (5.7.2)
Error