KA-0137Multi-step arithmetic word problems
5 points, difficulty 3 of 3Level 3–4about 90sA jug holds 900 ml of juice. A third is poured out, then 150 ml is added. How many millilitres are in the jug?
Hints
Take them one at a time. The first gives nothing away.
1A nudge
Do the two steps in order.
2The strategy
Work out how much is poured out, subtract it, and only then add the 150 ml. Doing the addition first changes the size of the third that gets poured away.
3The full solution
A third of 900 is 300, so 600 is left. Adding 150 gives 750 ml.
Solution
The reliable way
A third of 900 ml is 300 ml, so pouring that out leaves 900 - 300 = 600 ml. Adding 150 ml gives 600 + 150 = 750 ml. Note that the third is a third of the original 900, not of anything later - the order in the sentence is the order of the arithmetic. The transferable idea: fractions are always a fraction of something specific, so name that something before you compute.
The elegant way
Pouring away a third leaves two thirds, which is 600, and 600 + 150 = 750.
Why this is on the test: Multi-step problems are lost by reordering the steps, and the fraction here is of the starting amount rather than of what is left at the end.