What is 10.25 divided by 0.25?
The correct answer and explanation is:
The result of 10.25 divided by 0.25 is: 10.250.25=41\frac{10.25}{0.25} = 41
Explanation (300 words):
Division is the process of determining how many times one number (the divisor) fits into another number (the dividend). Here, we want to find out how many times 0.25 fits into 10.25.
To make division easier, especially when decimals are involved, one common method is to eliminate the decimal points by multiplying both the dividend and divisor by the same power of 10. This does not change the quotient (the result) because multiplying both numbers by the same factor is equivalent to multiplying the entire fraction by 1.
In this case, the divisor 0.25 has two decimal places. So, multiply both 10.25 and 0.25 by 100 to convert the divisor into a whole number: 10.25×100=102510.25 \times 100 = 1025 0.25×100=250.25 \times 100 = 25
Now the division becomes: 102525\frac{1025}{25}
This is easier to compute because both numbers are whole numbers. Next, divide 1025 by 25.
- 25 goes into 100 exactly 4 times (since 25 × 4 = 100)
- 25 goes into 1025 a total of 41 times, because 25 × 41 = 1025.
So, 102525=41\frac{1025}{25} = 41
Therefore, 10.250.25=41\frac{10.25}{0.25} = 41
Conceptual understanding:
Dividing by 0.25 is equivalent to multiplying by 4 because 0.25 is one-quarter (¼). So, dividing a number by 0.25 asks: “How many quarter units are in this number?” For example:
- 1 divided by 0.25 = 4 (because one contains four quarters)
- So, 10.25 divided by 0.25 = 10.25 × 4 = 41.
This method also confirms our result quickly without long division.