05 Ratio Word Problem (Involving 3 persons)

In my humble opinion, students usually have difficulty with mathematical word problems is  that they do not have strong basic mathematical concepts. For example, in teaching of ratio, the students must know clearly that “all parts are equal”. This fundamental principle can help them solving involving even the most difficult problem. For this word problem, I will try solving a ratio word problem

The ratio of the number of Alex`s marbles to Raju`s is 2:1 and the ratio of the number of Raju`s marbles to Jim`s is 4:5. Find the ratio of the number of Alex`s marbles to Raju`s to Jim`s.

The ratio of the number of Alex`s marbles to Raju`s is 2:1 and the ratio of the number of Raju`s marbles to Jim`s is 4:5.
Let’s “attack” the first part of the statement (The ratio of the number of Alex`s marbles to Raju`s is 2:1). Possible Questions to ask: Who has more ? What does it mean by 2:1? How do you show it on the model?

The ratio of the number of Alex`s marbles to Raju`s is 2:1 and the ratio of the number of Raju`s marbles to Jim`s is 4:5.
Now for the 2nd part (the ratio of the number of Raju`s marbles to Jim`s is 4:5). Possible Questions to ask: Who has more ? What does it mean by 4:5?

Instead of building on the model for the first part, I will just draw the 2nd part “separately” before trying to make the association with the first statement.

 Find the ratio of the number of Alex`s marbles to Raju`s to Jim`s.

Get the students to look at the models drawn and get them to see why there is a need to break the bars to “common or same parts”. After all, ratio is all about “same parts”.

Possible Questions to ask: Can I find the ratio by looking at the model ? Are the parts equal? What does it mean by ratio? If Raju has 4 parts, how many parts does Alex have?

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