Word problems involving "four times as many as"

Someone asked for help to explain the concepts of multiplicative word problems involving "as many as", like the ones below:

1) Haley had four times as many dollars as her sister. Together they had $60. How much money does Haley have?


2) Rachel had 5 times as many dollars as her sister, Nora. They had a total of $90. How much money did each of them have?


The BAR MODEL is an excellent tool for helping children understand what is going on in these types of word problems.

In (1), draw a bar for Haley and another for her sister. Divide Haley's bar into four parts, and make the other bar just one such part long.

Haley |---|---|---|---|

Sister |---|


Now you will see that the TOTAL needs divided into FIVE equal parts — and from then on it is easy-peasy.




Additionally, you can use Thinking Blocks website to build such bar models INTERACTIVELY.

For problems like (1) and (2) above, choose the fourth model from the left (rightmost) in the top row that is bluish in color. Then click "Start modeling" button. Video tutorials exist also. This is not my site, but it's a very nice interactive tool for this concept!




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