How Much Less than 2 is the Sum of 1/5 and 3/10

Understanding the addition and subtraction of fractions, and their conversion to decimals, is a fundamental skill in mathematics. This article will walk you through the process of solving the problem: 'How much less than 2 is the sum of 1/5 and 3/10'. This common fraction problem can be easily tackled by following these steps and gaining insight into the mechanics of fractional arithmetic.

Understanding Fractions and Decimals

Fractions and decimals are two ways to represent parts of a whole. Fractions are written with a numerator (the top number) and a denominator (the bottom number), while decimals are written using a decimal point to separate the whole number part from the fractional part.

Let's start with the fractions 1/5 and 3/10. Each of these fractions represents a part of the whole, and both can be converted into decimal form for easier calculation.

Converting the Fractions to Decimals

The first step in solving this problem is to convert the fractions 1/5 and 3/10 into decimals.

1/5 as a Decimal

To convert 1/5 into a decimal:

Divide the numerator by the denominator: 1 ÷ 5 0.2

3/10 as a Decimal

For 3/10, the conversion is even simpler:

Divide the numerator by the denominator: 3 ÷ 10 0.3

Adding the Decimals

Now that both fractions have been converted into decimals, we can add them together:

0.2 0.3 0.5

Subtracting from 2

The next step is to find out how much less 0.5 is when compared to 2. This requires subtracting 0.5 from 2:

2 - 0.5 1.5

This result, 1.5, can also be expressed in a mixed number form as 1 1/2, which is equivalent to 1.5 in decimal form.

Practice and Application

Understanding and practicing problems like this can significantly improve your ability to work with fractions and decimals in various contexts. Here are a few exercises to practice further:

Add 2/5 and 4/10 and then subtract the sum from 2. Convert and add 1/3 and 2/6, and then find how much less the sum is from 2.

Conclusion

Mastering the addition and subtraction of fractions, as well as their conversion to decimals, is a valuable skill in both academic and real-world scenarios. This article has provided a detailed guide to solving the specific problem: 'How much less than 2 is the sum of 1/5 and 3/10'. By following the steps outlined, you can confidently solve similar problems and enhance your mathematical proficiency.