Singapore Math Guru

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?

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Example 2:

bus-30603_1280editA 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?

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So how do we teach our children to identify such questions.Typically, in a “working backwards” question, the end result is given. And, when a student reads on, he eventually has to find the beginning input. So there is no way a student can solve a question like that unless he uses algebra(not advocated) or find a way to work backwards from the end result.

To really understand what we are talking about, do try the questions above and watch the video explanations to them. You can also find out the answers after you attempt them.

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