Grade 5

Fractions

A full pass through fractions, from what the denominator actually counts to adding and subtracting fractions whose denominators do not match.

6 lessons

  1. 1What do the numerator and the denominator of a fraction mean?The denominator, the number underneath, says how many equal parts the whole was divided into. The numerator, on top, says how many of those parts we took. Three quarters means the whole was cut into four equal parts and we took three of them — and the word equal is the condition without which there is no fraction at all.25m
  2. 2What are equivalent fractions and how do you reduce one?Multiplying or dividing the numerator and the denominator by the same number changes how a fraction looks but not what it is worth: a half, two quarters and four eighths are the same amount. Expanding multiplies both, reducing divides both, and a fraction is fully reduced when no common factor is left.30m
  3. 3What is an improper fraction and how do you convert it to a mixed number?An improper fraction has a numerator larger than its denominator, so it holds more than one whole. The same amount can be written as a mixed number: a whole with a fraction beside it. You convert by dividing — how many times the denominator fits into the numerator — and back again by multiplying and adding.30m
  4. 4How do you compare two fractions and put them in order?If the denominators match, the larger fraction is the one with the larger numerator. If the numerators match, the larger one is the fraction with the smaller denominator, because the whole was cut into fewer pieces. In any other case, expand both to a common denominator and then compare numerators.25m
  5. 5How do you add and subtract fractions with the same denominator?Add the numerators and leave the denominator as it is. When the parts are the same size you simply count them, so two fifths plus two fifths is four fifths. The denominator does not get added, because it names the size of the part rather than counting how many there are.30m
  6. 6How do you add fractions with different denominators?Expand both fractions to the same denominator, and only then add the numerators. Parts of different sizes cannot be counted together, so expanding is not a technical step but the condition for adding at all. You find the common denominator among the multiples of the larger one.40m