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 11/4 to 2 3/4
- Convert 3 2/5 to 17/5
- Write 6/5 + 4/5 = 10/5 = 2 as both improper fraction and whole number
The lesson
An improper fraction has a top number equal to or bigger than the bottom number, like 7/4. It is worth one whole amount or more. A mixed number shows the same amount a different way: a whole number sitting next to a fraction, like 1 3/4.
Take 11/4. Split 11 blocks into groups of 4, since 4 is the denominator. Two full groups of 4 make 8, with 3 blocks left over. Two full groups mean 2 wholes, and the 3 leftover blocks mean 3/4. So 11/4 equals 2 3/4.
To go the other way, multiply the whole number by the denominator, then add the numerator. For 3 2/5: 3 x 5 = 15, plus 2 makes 17. Keep the same denominator: 17/5.
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.
Watch it
Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.