Question

Saroj planted 6 mango trees in a row in her garden. The distance between two adjacent mango trees is $\dfrac{5}{4}m$. Find the distance between the first and last mango tree.

Answer 1

Hint: We will first draw a rough figure of trees planted in a row. Now, we will see how many adjacent distances come between the first and the last mango tree. Then, multiply that number by the given distance.

Complete step by step answer:
Let us refer to the figure given below:

Here, we have 6 trees in a row.
Now, let us mark the first and last tree in the same picture, we will then have the following with us:

Now, we see that we have 4 trees in between the first and last tree. And, if we look at the blank distances. One from first to second tree, two from second to third three, three from third to fourth tree, four from fourth to fifth three and five from fifth to the last tree.
Hence, we have 5 distances which are all $\dfrac{5}{4}m$ apart from each other.
Therefore, we have distance between the first and last tree as $\left( {\dfrac{5}{4} \times 5} \right)m$.
Simplifying it, we will get: distance between first and last tree as $\dfrac{{25}}{4}m$.

$\therefore $ The distance between first and last tree as $\dfrac{{25}}{4}m$.

Note:
 The students might wonder and want to use addition instead of multiplication. They may use addition as well because multiplication is repeated addition. When we need to multiply 5 and 2, this means we have to add 5 twice or add ‘2’ 5 times. Now, looking at the given question in a similar way, we see that we can add the distance all the way from first tree to last tree by jumping from one tree to next adjacent tree instead of jumping from first to last. It is just an easy way.
The students must not forget to write the units which are “meters” here. Because if we write only 5, it does not make any sense that it is length or anything. It just represents a number whereas units like m and cm specify that they are lengths.