Fractions and Ratio: The Unitary Method

Methods in this video

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1. 1

   Find one part first, then scale up

   ▶ 1:06

   When to use it: The question gives a fixed mix that repeats ('for every 2 in the first pile, 5 go in the second and 3 in the third', '2 eggs for every 5 pancakes') plus the total of one item or the amount to make, and asks for the total, the amount of another item, or how many more are needed.

   • When things come in a fixed mix (a round of 2, 5 and 3 cherries; a batch of 2 eggs for 5 pancakes), treat one mix as one part and work out how much is in one part.
   • Divide the known total by how many of that item are in one part to find the number of parts, then scale up the whole part: every item is multiplied by the same number.
   • Check what the question asks: for 'altogether', give the total; for 'how many more', take away what is already there.
2. 2

   Working together: add what each does in a day

   ▶ 3:18

   When to use it: Two (or more) people or animals share one job (painting a wall, eating a feeder of seeds). The question only says how long each takes alone and asks how long they take together or when they finish; sometimes one starts alone and the other joins later.

   • When you only know how many days or minutes each takes, cut the whole job into equal small parts: use a common multiple of the two times, the smallest one, found by going up in multiples of the bigger number.
   • Work out how many parts each does per day or per minute. Working together, add those amounts (the rates); never average or add the days.
   • If one starts alone, take away what they finish alone first, then work out the rest together.