Calculate: ${ 1 \frac{3}{8} - 1 \frac{1}{10} = }$

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Mastering Mixed Numbers: A Step-by-Step Guide to Calculating ${ 1 \frac{3}{8} - 1 \frac{1}{10} = }$

When it comes to mathematics, mixed numbers can be a bit tricky to work with. However, with a solid understanding of the concept and some practice, you'll be able to tackle even the most complex calculations with ease. In this article, we'll delve into the world of mixed numbers and explore how to calculate ${ 1 \frac{3}{8} - 1 \frac{1}{10} = }$. Whether you're a student looking to improve your math skills or a professional seeking to refresh your knowledge, this guide is perfect for you.

What are Mixed Numbers?

A mixed number is a combination of a whole number and a fraction. It's written in the form of abca \frac{b}{c}, where aa is the whole number, bb is the numerator, and cc is the denominator. For example, 2342 \frac{3}{4} is a mixed number that represents 22 whole units and 34\frac{3}{4} of a unit.

Understanding the Problem

The problem we're trying to solve is $ 1 \frac{3}{8} - 1 \frac{1}{10} = }$. To tackle this, we need to first understand what we're dealing with. We have two mixed numbers $1 \frac{3{8}$ and 11101 \frac{1}{10}. Our goal is to subtract the second mixed number from the first.

Step 1: Convert Mixed Numbers to Improper Fractions

To make the calculation easier, let's convert the mixed numbers to improper fractions. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and add the numerator. Then, we write the result as the new numerator over the denominator.

For 1381 \frac{3}{8}, we have:

1×8=81 \times 8 = 8 8+3=118 + 3 = 11

So, 138=1181 \frac{3}{8} = \frac{11}{8}.

For 11101 \frac{1}{10}, we have:

1×10=101 \times 10 = 10 10+1=1110 + 1 = 11

So, 1110=11101 \frac{1}{10} = \frac{11}{10}.

Step 2: Find a Common Denominator

Now that we have the mixed numbers in improper fraction form, we need to find a common denominator. The common denominator is the least common multiple (LCM) of the two denominators. In this case, the denominators are 88 and 1010. The LCM of 88 and 1010 is 4040.

Step 3: Convert Improper Fractions to Have the Common Denominator

Now that we have the common denominator, we need to convert the improper fractions to have the common denominator. To do this, we multiply the numerator and denominator of each fraction by the necessary factor to get the common denominator.

For 118\frac{11}{8}, we multiply the numerator and denominator by 55 to get:

11×58×5=5540\frac{11 \times 5}{8 \times 5} = \frac{55}{40}

For 1110\frac{11}{10}, we multiply the numerator and denominator by 44 to get:

11×410×4=4440\frac{11 \times 4}{10 \times 4} = \frac{44}{40}

Step 4: Subtract the Fractions

Now that we have the improper fractions with the common denominator, we can subtract them. To do this, we subtract the numerators and keep the common denominator.

5540−4440=55−4440=1140\frac{55}{40} - \frac{44}{40} = \frac{55 - 44}{40} = \frac{11}{40}

And there you have it! We've successfully calculated ${ 1 \frac{3}{8} - 1 \frac{1}{10} = }$. By converting the mixed numbers to improper fractions, finding a common denominator, and subtracting the fractions, we arrived at the final answer of 1140\frac{11}{40}.

Tips and Tricks

  • When working with mixed numbers, it's essential to convert them to improper fractions to make calculations easier.
  • Finding a common denominator is crucial when subtracting fractions.
  • Make sure to multiply the numerator and denominator by the necessary factor to get the common denominator.
  • When subtracting fractions, subtract the numerators and keep the common denominator.

Practice Problems

Try your hand at these practice problems to reinforce your understanding of mixed numbers and fraction subtraction:

  • { 2 \frac{1}{4} - 1 \frac{3}{8} = \}

  • { 3 \frac{2}{5} - 2 \frac{1}{10} = \}

  • { 4 \frac{3}{4} - 3 \frac{1}{2} = \}

Mastering mixed numbers and fraction subtraction takes practice, but with this guide, you're well on your way to becoming a math whiz. Remember to convert mixed numbers to improper fractions, find a common denominator, and subtract the fractions. With these tips and tricks, you'll be able to tackle even the most complex calculations with ease. Happy calculating!
Mastering Mixed Numbers: A Q&A Guide to Calculating ${ 1 \frac{3}{8} - 1 \frac{1}{10} = }$

In our previous article, we explored the concept of mixed numbers and how to calculate ${ 1 \frac{3}{8} - 1 \frac{1}{10} = }$. However, we know that practice makes perfect, and there's no better way to reinforce your understanding than by answering common questions and practicing with real-world examples. In this article, we'll tackle some of the most frequently asked questions about mixed numbers and fraction subtraction.

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction where the numerator is greater than or equal to the denominator.

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

A: To convert a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. Then, write the result as the new numerator over the denominator.

Q: What is the common denominator, and why is it important?

A: The common denominator is the least common multiple (LCM) of the two denominators. It's essential to find a common denominator when subtracting fractions because it allows us to subtract the numerators and keep the common denominator.

Q: How do I find the common denominator?

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

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

A: If the denominators are not multiples of each other, you can use the following steps to find the common denominator:

  1. List the multiples of each denominator.
  2. Find the smallest multiple that appears in