Guide to Gaps & Intervals

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Gaps and Intervals word problems are very common in the Primary 4 and Primary 5 school examinations. They often appear as a “tree-planting”, “flower pots” or “lamp posts” question. 

First, let’s observe how the number of gaps is related to the number of items. 

Items = Gaps + I

Now, let’s use this idea and apply it to an example question.

Example:

Along a road, 25 trees are planted at equal distances. The distance between the first and the fourth tree is 20.4 m. What is the distance between the first and the last tree?

Solution:

 
Since number of items = number of gaps + 1, between 4 trees there will be 3 gaps, and between 25 trees, there will be 24 gaps.

Answer: The distance between the first and the last tree is 163.2 m.

Now, what happens if the items are not arranged along a straight line, but along the perimeter of a closed figure instead?

Example: 
 

Some potted plants are positioned at equal distances along the perimeter of a square field. If there are 17 potted plants along each side, how many potted plants are there altogether?

In this case, the items at the two ends of each side will overlap to form corners of the figure. Hence, when solving, we should be mindful of the overlaps and avoid double-counting them.

Answer: There are 64 potted plants altogether.

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" Guide to Gaps & Intervals "

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