Question

write about which method you prefer to use to divide by 5 counting up, counting back on a number line, or dividing by 10, and then doubling the quotient?

Answer 1

The preferred method for dividing by 5 is to divide by 10 and then double the quotient. This method is efficient and capitalizes on understanding reciprocals and the inverse relationship between multiplication and division. It is a quick and intuitive way to solve division problems without needing a number line.

Step-by-step explanation:

When faced with the task of dividing by 5, my preferred method is to divide by 10 and then double the quotient. This technique is straightforward because it involves working with a power of 10. For instance, dividing by powers of 10 simply means we move the decimal to the left by the number of zeros in the power of ten. Therefore, if you are dividing a number by 10, you would move the decimal point one place to the left. After this, you would double your answer. This method tends to be more efficient than counting up or counting back on a number line, especially with larger numbers.

For example, if you have the number 50, and you want to divide by 5, first, divide by 10, which gives you 5, and then double that quotient to reach the final answer of 10. This can be especially helpful because once you are familiar with the reciprocals of numbers, you can easily switch between division and multiplication to solve problems more quickly.

Moreover, understanding the relationship between multiplication and division by using their reciprocals leads to a conceptual understanding that multiplication and division are inverse operations. Thus, multiplying by the reciprocal of a number is the same as dividing by the original number. This connection is vital in grasping how to simplify and solve various mathematical problems.

Answer 2

In First method : counting up, counting back on a number line,

If we want the quotient after dividing the number by 5 then we count how many 5 we get from 0 to the dividend.

For example :
`(30)/(5)`

Since, from 0 to 30 there are six 5's obtained. ( because 5 × 6 = 30 )

Thus,
`(30)/(5)=6`

In Second Method : dividing by 10, and then doubling the quotient.

First we divide the number by 10 then multiply the quotient by 2.

For Example:
`(30)/(5)`

Since,
`(30)/(10)=3`

`2* 3 = 6`

Thus,
`(30)/(5)=6`

Now, when we compare the above methods then we conclude that for the smaller numbers first method is appropriate because for small numbers we can easily count total 5's from 0. While for large numbers Second method is appropriate because it is hard to count the total 5's for the large number.