Relationships between Unknowns: Sum and Difference Problems

Methods in this video

Tap a time to jump to where the video teaches that method.

1. 1

   Take away the extra first

   ▶ 1:16

   When to use it: There are just two amounts: you are given their total and told that one is some number more, less, longer or older than the other (adding and taking away only, no 'times'). You are asked for one of them, or which statement cannot be right. The total may be hidden in a perimeter or an average.

   • Line up two bars from the left; the extra piece on the longer bar is the difference.
   • Take the extra away first: total − difference = two equal bars; halve it for the smaller one, then add the difference back for the larger one.
   • If what is left after taking the difference away won't split into two whole numbers, the statement cannot be right; a sum and a difference are both odd or both even.
2. 2

   Pick a base and line them up

   ▶ 5:16

   When to use it: Three or more amounts are linked sentence by sentence only by 'more / less / heavier / lighter / older / further than' (adding and taking away, no 'times'); you are given their total, or asked how far apart two of them are, or the difference between the heaviest and the lightest.

   • Put one amount at 0 as the base, write each amount as 'base + something' and line them up; check which is bigger in each sentence before you mark it.
   • Asked how far apart two are: read it straight off the line; you don't need anyone's actual value.
   • With a total: take the extras away, fill in what is short, then share equally; once you have the base, don't stop — add back for the one you are asked about.