How to Check Your Answer When Subtracting Mixed Numbers

In this guide, we will walk through the process of solving and checking a subtraction problem involving mixed numbers. We will use the example of 2 1/3 - 1 1/4. Understanding how to check your answer not only ensures accuracy but also helps reinforce your mathematical reasoning skills.

Solving the Problem Step-by-Step

Let's break down the problem 2 1/3 - 1 1/4 into its components and solve it using both the long and quick methods.

1. Converting to Improper Fractions

To solve this problem, we first need to convert the mixed numbers into improper fractions:

2 1/3 7/3 1 1/4 5/4

Next, we find a common denominator for the fractions. The least common multiple (LCM) of 3 and 4 is 12.

Now, we convert each fraction to have a common denominator of 12:

7/3 28/12 5/4 15/12

Subtract the numerators while keeping the common denominator:

28/12 - 15/12 13/12

2. Converting Back to a Mixed Number

Since 13/12 is an improper fraction, we convert it back to a mixed number:

13/12 1 1/12 (13 divided by 12 1 with a remainder of 1)

So, the final answer is 1 1/12.

Checking Your Answer

Now that we have our answer, let's check it using two methods: the long way and the quick way.

Long Method

Add the whole numbers: 2 - 1 1 Add the fractional parts: 1/3 1/4 (4/12 3/12) 7/12

Combining these, we get 1 7/12. This checks out as the sum of the whole number and the fractional part is correct, and the resulting fraction is proper.

Quick Method

1. Check the whole numbers: 2 - 1 1

2. Check the fractional part: 1/3 1/4 7/12

3. The sum of these parts equals the answer 1 7/12, which is proper.

Since the fractional part is less than 1 and the whole number matches, the answer is correct.

Conclusion

By using both the detailed and quick methods, you can double-check your answers for subtraction involving mixed numbers. This ensures accuracy and helps build confidence in your mathematical skills.