## Working Backwards with Fractions

The heuristics concept of working backwards can come in different variations and forms for upper primary school. One way to solve it is to use a table. Another way to solve it is to use a model. In the questions below, we are using the branch method to solve these questions as it involves several stages. Video solutions on the “how to” have already been added to our database of questions.

Example 1:

A train left station A with some passengers in it.
At station B, 3/4 of the passengers in the train alighted and 20 passengers boarded it.
At station C, 2/5 of the passengers in the train alighted and 60 passengers boarded it.
Finally, at station D, 1/2 of the passengers in the train alighted and 20 passengers boarded it.
How many passengers were there on the train as it left station A if there were 80 passengers on the train as it left station D?

Example 2:

A bus left an interchange carrying some passengers with it.
At the first stop, 1/4 of the people in it alighted and 5 people boarded it.
At the 2nd stop,1/2 of the people in it alighted and 20 people boarded the bus.
When it left the 2nd stop, there were 60 passengers in it.
How many passengers were there in the bus when it left the interchange?