Work Out 1 3 4 − 2 3 1 \frac{3}{4} - \frac{2}{3} 1 4 3 − 3 2 . Give Your Answer As A Mixed Number In Its Simplest Form.

Mar 9, 2025 by ADMIN 124 views

**Solving Mixed Number Subtraction: A Step-by-Step Guide**

Introduction

In mathematics, mixed numbers are a combination of a whole number and a fraction. When subtracting mixed numbers, it's essential to follow a specific order of operations to ensure accuracy. In this article, we will guide you through the process of subtracting mixed numbers, using the example $1 \frac{3}{4} - \frac{2}{3}$ .

Understanding Mixed Numbers

A mixed number is a combination of a whole number and a fraction. It's written in the form $a \frac{b}{c}$ , where $a$ is the whole number, $b$ is the numerator, and $c$ is the denominator. For example, $1 \frac{3}{4}$ is a mixed number where $1$ is the whole number, $3$ is the numerator, and $4$ is the denominator.

Subtracting Mixed Numbers: A Step-by-Step Guide

To subtract mixed numbers, follow these steps:

Step 1: Convert the Mixed Numbers to Improper Fractions

To subtract mixed numbers, it's easier to convert them to improper fractions first. An improper fraction is a fraction where the numerator is greater than or equal to the denominator.

Convert $1 \frac{3}{4}$ $1 \frac{3}{4}$ to an improper fraction:
- Multiply the whole number by the denominator: $1 \times 4 = 4$
- Add the numerator to the result: $4 + 3 = 7$
- Write the result as an improper fraction: $\frac{7}{4}$
Convert $\frac{2}{3}$ to an improper fraction (if necessary). In this case, it's already an improper fraction.

Step 2: Find a Common Denominator

To subtract fractions, they must have a common denominator. The least common multiple (LCM) of the denominators is the smallest number that both denominators can divide into evenly.

Find the LCM of 4 and 3:
- List the multiples of 4: 4, 8, 12, 16, 20, 24
- List the multiples of 3: 3, 6, 9, 12, 15, 18
- The smallest number that appears in both lists is 12, so the LCM is 12

Step 3: Convert the Fractions to Have the Common Denominator

Convert $\frac{7}{4}$ $\frac{7}{4}$ to have a denominator of 12:
- Multiply the numerator and denominator by 3: $\frac{7 \times 3}{4 \times 3} = \frac{21}{12}$
Convert $\frac{2}{3}$ $\frac{2}{3}$ to have a denominator of 12:
- Multiply the numerator and denominator by 4: $\frac{2 \times 4}{3 \times 4} = \frac{8}{12}$

Step 4: Subtract the Fractions

Now that the fractions have a common denominator, subtract them:

$\frac{21}{12} - \frac{8}{12} = \frac{21 - 8}{12} = \frac{13}{12}$

Step 5: Convert the Result to a Mixed Number

To convert the improper fraction to a mixed number, divide the numerator by the denominator:

Divide 13 by 12:
- 12 goes into 13 once, with a remainder of 1
- Write the result as a mixed number: $1 \frac{1}{12}$

Conclusion

Q: What is the first step in subtracting mixed numbers?

A: The first step in subtracting mixed numbers is to convert them to improper fractions. This involves multiplying the whole number by the denominator and adding the numerator to the result.

Q: How do I find a common denominator for two fractions?

A: To find a common denominator, list the multiples of each denominator and find the smallest number that appears in both lists. This is the least common multiple (LCM) of the two denominators.

Q: What if the denominators are not multiples of each other?

A: If the denominators are not multiples of each other, you can find the LCM by listing the multiples of each denominator and finding the smallest number that appears in both lists.

Q: Can I subtract mixed numbers without converting them to improper fractions?

A: While it's possible to subtract mixed numbers without converting them to improper fractions, it's not recommended. Converting to improper fractions makes the process easier and more accurate.

Q: How do I convert an improper fraction to a mixed number?

A: To convert an improper fraction to a mixed number, divide the numerator by the denominator. The whole number part is the result of the division, and the remainder is the new numerator.

Q: What if the result of the subtraction is an improper fraction?

A: If the result of the subtraction is an improper fraction, you can convert it to a mixed number by dividing the numerator by the denominator.

Q: Can I subtract mixed numbers with different signs?

A: Yes, you can subtract mixed numbers with different signs. To do this, follow the same steps as before, but be sure to change the sign of the second mixed number.

Q: What if I get a negative result when subtracting mixed numbers?

A: If you get a negative result when subtracting mixed numbers, it means that the second mixed number is larger than the first. To write the result as a mixed number, make sure to include the negative sign.

Q: Can I use a calculator to subtract mixed numbers?

A: Yes, you can use a calculator to subtract mixed numbers. However, it's still important to understand the steps involved in the process to ensure accuracy.

Q: What are some common mistakes to avoid when subtracting mixed numbers?

A: Some common mistakes to avoid when subtracting mixed numbers include:

Forgetting to convert the mixed numbers to improper fractions
Not finding a common denominator
Subtracting the wrong fractions
Not converting the result to a mixed number if necessary

Conclusion

Subtracting mixed numbers can be a challenging task, but with practice and patience, you can master the process. By following the steps outlined in this article and avoiding common mistakes, you can ensure accuracy and confidence when working with mixed numbers.