Emma Buys ${ 3 \frac{2}{3}\$} Yards Of Blue Fabric And Some Yellow Fabric At A Store. She Buys A Total Of ${ 5 \frac{1}{3}\$} Yards Of Fabric. The Equation ${ 5 \frac{1}{3} = 3 \frac{2}{3} + Y\$} Can Be Used To Represent This
Introduction
Mixed numbers are a combination of a whole number and a fraction. They are commonly used to represent quantities that are not whole, such as measurements or amounts of fabric. In this article, we will explore how to solve equations involving mixed numbers, using the example of Emma buying fabric at a store.
Understanding Mixed Numbers
A mixed number is a combination of a whole number and a fraction. It is written in the form of a b/c, where a is the whole number and b/c is the fraction. For example, 3 2/3 is a mixed number that represents 3 whole units and 2/3 of a unit.
The Problem
Emma buys 3 2/3 yards of blue fabric and some yellow fabric at a store. She buys a total of 5 1/3 yards of fabric. The equation 5 1/3 = 3 2/3 + y can be used to represent this situation, where y is the amount of yellow fabric Emma buys.
Solving the Equation
To solve the equation, we need to isolate the variable y. We can do this by subtracting 3 2/3 from both sides of the equation.
5 1/3 - 3 2/3 = y
To subtract mixed numbers, we need to subtract the whole numbers and the fractions separately. We can do this by converting the mixed numbers to improper fractions.
(5*3 + 1)/3 - (3*3 + 2)/3 = y
Simplifying the equation, we get:
(15 + 1)/3 - (9 + 2)/3 = y
16/3 - 11/3 = y
5/3 = y
Converting the Answer to a Mixed Number
To convert the answer to a mixed number, we need to divide the numerator by the denominator.
5 ÷ 3 = 1 with a remainder of 2
So, the answer is 1 2/3.
Conclusion
In this article, we have seen how to solve an equation involving mixed numbers. We have used the example of Emma buying fabric at a store to illustrate the process. By following the steps outlined in this article, you should be able to solve similar equations involving mixed numbers.
Tips and Tricks
- When subtracting mixed numbers, make sure to subtract the whole numbers and the fractions separately.
- When converting mixed numbers to improper fractions, multiply the whole number by the denominator and add the numerator.
- When converting improper fractions to mixed numbers, divide the numerator by the denominator and write the remainder as a fraction.
Practice Problems
- Solve the equation
4 1/2 = 2 3/4 + y. - Solve the equation
6 2/3 = 3 1/3 + y. - Solve the equation
8 1/4 = 4 3/4 + y.
Answer Key
1 9/163 5/93 5/16
References
About the Author
Q: What is a mixed number?
A: A mixed number is a combination of a whole number and a fraction. It is written in the form of a b/c, where a is the whole number and b/c is the fraction.
Q: How do I add mixed numbers?
A: To add mixed numbers, you need to add the whole numbers and the fractions separately. For example, to add 3 2/3 and 2 1/3, you would add the whole numbers (3 + 2 = 5) and the fractions (2/3 + 1/3 = 3/3 = 1). The result would be 5 1.
Q: How do I subtract mixed numbers?
A: To subtract mixed numbers, you need to subtract the whole numbers and the fractions separately. For example, to subtract 3 2/3 from 2 1/3, you would subtract the whole numbers (2 - 3 = -1) and the fractions (1/3 - 2/3 = -1/3). The result would be -1 1/3.
Q: How do I multiply mixed numbers?
A: To multiply mixed numbers, you need to multiply the whole numbers and the fractions separately. For example, to multiply 3 2/3 and 2 1/3, you would multiply the whole numbers (3 * 2 = 6) and the fractions (2/3 * 1/3 = 2/9). The result would be 6 2/9.
Q: How do I divide mixed numbers?
A: To divide mixed numbers, you need to divide the whole numbers and the fractions separately. For example, to divide 3 2/3 by 2 1/3, you would divide the whole numbers (3 ÷ 2 = 1.5) and the fractions (2/3 ÷ 1/3 = 2). The result would be 1 2/3.
Q: Can I use a calculator to solve mixed number equations?
A: Yes, you can use a calculator to solve mixed number equations. However, you need to make sure that the calculator is set to the correct mode (e.g. fraction mode) and that you are entering the numbers correctly.
Q: How do I convert a mixed number to an improper fraction?
A: To convert a mixed number to an improper fraction, you need to multiply the whole number by the denominator and add the numerator. For example, to convert 3 2/3 to an improper fraction, you would multiply 3 by 3 (9) and add 2 (11). The result would be 11/3.
Q: How do I convert an improper fraction to a mixed number?
A: To convert an improper fraction to a mixed number, you need to divide the numerator by the denominator and write the remainder as a fraction. For example, to convert 11/3 to a mixed number, you would divide 11 by 3 (3 with a remainder of 2). The result would be 3 2/3.
Q: What are some common mistakes to avoid when working with mixed numbers?
A: Some common mistakes to avoid when working with mixed numbers include:
- Not converting mixed numbers to improper fractions before performing operations
- Not simplifying fractions before performing operations
- Not checking the signs of the numbers before performing operations
- Not using the correct mode on a calculator
Q: How can I practice solving mixed number equations?
A: You can practice solving mixed number equations by working through problems in a textbook or online resource, or by creating your own problems and solutions. You can also try using online tools or apps to generate mixed number equations and practice solving them.
Q: What are some real-world applications of mixed number equations?
A: Mixed number equations have many real-world applications, including:
- Measuring lengths and widths of objects
- Calculating areas and volumes of objects
- Determining quantities of materials needed for a project
- Solving problems involving time and speed
Q: Can I use mixed number equations to solve problems involving money?
A: Yes, you can use mixed number equations to solve problems involving money. For example, you can use mixed number equations to calculate the cost of items that are sold in fractions of a dollar.