How to Divide a Smaller Number by a Bigger Number
Dividing a smaller number by a bigger number might seem challenging at first, but it's actually quite straightforward when you understand the basic principles. This article will guide you through the process using clear examples and explanations.
Setting Up the Division
The first step in dividing a smaller number by a bigger number is to set up the division properly. Write the smaller number as the dividend and the bigger number as the divisor. For example, if you want to divide 3 by 5, you would set it up as (frac{3}{5}) or 3 ÷ 5.
Performing the Division
Since the smaller number is less than the bigger number, the result will be a fraction or a decimal less than 1.
Fraction Result
The fraction (frac{3}{5}) remains as is. This indicates how many times the bigger number (5) fits into the smaller number (3).
Decimal Result
To convert this fraction to a decimal, you simply perform the division 3 ÷ 5. The result is 0.6.
Interpreting the Result
The result 0.6 tells us that the bigger number (5) fits into the smaller number (3) zero times with a remainder. This remainder is represented as a decimal (0.6).
Example
Let’s take another example: dividing 4 by 10.
Setup
Write out the division as (frac{4}{10}) or 4 ÷ 10.
Simplified Fraction
You can simplify (frac{4}{10}) to (frac{2}{5}). However, for division, we often use the whole number form.
Decimal Result
To convert to a decimal, perform 4 ÷ 10, which equals 0.4.
Summary
When the dividend is smaller than the divisor, the result will be a fraction or a decimal less than 1. You can express this answer in various forms depending on your needs, such as a fraction or a decimal.
Adapting the Long Division Method
If you need to add more decimal places, you can add a decimal point and as many zeros as you want to the end of the smaller number. This allows you to perform long division using the same principles as dividing a large number by a small number.
Example 1: 2/3
2.000 ÷ 3 0.666 (rounded to two decimal places, 0.67)
Example 2: 12/13
12.000 ÷ 13 0.923 (rounded to two decimal places, 0.92)
Example 3: 9/11
9.000 ÷ 11 0.818 (rounded to two decimal places, 0.82)
Final Tips
When performing long division, if you reach the last remainder and your answer has the correct number of decimal places, round the last digit up if the final remainder is greater than or equal to half of the quotient. Remember, when the precision of the answer isn't specified, it should usually have as many significant digits as the shorter number in the original problem.