Mixed numbers and improper fractions
Recognise mixed numbers and improper fractions; convert from one form to the other (e.g. 2/5 + 4/5 = 6/5 = 1 1/5)
What a learner can do afterwards
- Convert improper fractions to mixed numbers, identify their whole and fraction parts, and check that the fraction part is proper, including 11/4 = 2 3/4
- Count fractional parts in given wholes and convert mixed numbers to improper fractions, including 3 2/5 = 17/5
- Add fractions or mixed numbers with matching denominators and express the sum as an improper fraction, mixed number or whole number, including 6/5 + 4/5 = 10/5 = 2
1 · Read
An improper fraction has a numerator equal to or greater than its denominator. It names one whole or more. A mixed number has a whole number beside a proper fraction. The whole number counts complete wholes, and the fraction counts the extra part.
To change an improper fraction to a mixed number, divide the numerator by the denominator. The quotient counts wholes. Write the remainder over the same denominator. For 14/5, 2 × 5 = 10 and 3 × 5 = 15 is too much. There are 2 wholes and 4 fifths left: 2 4/5. The remainder must be smaller than the denominator.
To change a mixed number to an improper fraction, count every part in the same units. Multiply the whole number by the denominator, add the numerator, and keep the denominator. For 1 2/7, the whole contains 7 sevenths. Add 2 more: 7 + 2 = 9. So 1 2/7 = 9/7.
When denominators match, add the numerators and keep the denominator. The parts keep their size. For 4/3 + 5/3, add 4 + 5 = 9 thirds. Group them in threes: 9/3 = 3. If parts remain after making wholes, write those parts over the same denominator.
To add mixed numbers with matching denominators, add their whole numbers and then their fraction parts. For 1 1/6 + 2 3/6, the wholes make 3 and the sixths make 4/6. The total is 3 4/6. If the fraction parts fill another whole, include it in the whole-number part.
You can check a conversion by rebuilding the original numerator. Multiply the mixed number's whole part by its denominator, then add its fraction's numerator. Also check that its fraction part is proper. To find a missing whole part, remove the extra fraction's numerator first, then group the remaining parts into wholes.
An improper fraction and a mixed number can name the same amount, so you can convert between them by dividing or by multiplying and adding.
Questions written for this learning dataset. Readings adapted from Khan Academy reviews of mixed numbers and equivalent fractions. Linked videos are by Khan Academy. The six fraction flashcards are imported.
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