Problem
What fraction is left after the first step
Using 2/7 leaves 7/7 - 2/7 = 5/7 of the original water.
Taking a part away from a whole is just subtracting fractions with the same denominator, a fifth-grade idea.
5.NF.B.4Identify SubproblemsWhat fraction is left after the second step
Pouring out 4/5 of that leaves one fifth of 5/7, which is 1/7 of the original.
A fraction of a fraction is found by multiplying them; here it collapses neatly to 1/7 of the start.
5.NF.B.4Identify SubproblemsThe 12 litres left over is one seventh of the water the tank started with.
Why?
After 2/7 is used the tank still holds 5/7 of what it began with, because the part used and the part left make up the whole.
Why?
Pouring out four fifths of that leaves one fifth of it, and one fifth of five sevenths is one seventh.
Why?
Cutting each of the five sevenths into five equal slivers and keeping one sliver from each gathers back exactly one seventh's worth.
Match the leftover to 12 liters and work backwards
If one seventh is 12 L, the whole tank held 12 x 7 = 84 L.
Knowing the value of one equal part lets you rebuild the whole by multiplying back up.
5.NF.B.6Work BackwardsIf you know the value of just one equal part, multiply back up to find the whole.
- What fraction is left after the first step
- What fraction is left after the second step
- Match the leftover to 12 liters and work backwards