When you divide a whole number by a decimal divisor less than 1, how does the size of the quotient relate to the divisor?
Try a couple.
10 / 0.5 = ?
25 / 0.1 = ?
When you divide a whole number by a decimal divisor less than 1, the size of the quotient will be greater than the divisor.
To understand why this is the case, let's first look at an example: dividing 6 by 0.2.
To begin, you can set up the division problem like this: 6 ÷ 0.2.
To convert the divisor to a whole number, you can multiply both the dividend (6) and the divisor (0.2) by 10. This will give you: 60 ÷ 2.
Now you can perform the division: 60 ÷ 2 = 30. The quotient, in this case, is 30.
As you can see, the quotient (30) is greater than the divisor (0.2).
This relationship between the quotient and the divisor can be explained by understanding the concept of decimals. Decimals less than 1 represent fractions or parts of a whole. When you divide a whole number by a decimal less than 1, you are essentially dividing it into smaller parts, resulting in a larger quotient.
In our example, 0.2 can be thought of as 2/10 or 1/5. Dividing 6 by 1/5 is equivalent to multiplying 6 by its reciprocal, 5/1. Hence, the quotient is 30, which is greater than the divisor (0.2).
So, when you divide a whole number by a decimal divisor less than 1, the size of the quotient will always be greater than the divisor.