Write the steps for converting an improper fraction to a mixed number. Include a numeric example along with your written steps. Also, show how you would check your answer to see if it is correct.Explain whether it is possible to have a percentage value that is greater than 100%? Why or why not? Give an example.Which of the following improper fractions are equivalent to “9”? Show the mathematical verification for each one that you feel is equal to “9.”

Introduction:

Converting an improper fraction to a mixed number can seem daunting, but it is a straightforward process that anyone can do with practice. It is an important skill to have, especially when dealing with fractions in real-world situations. In this article, we will provide step-by-step instructions for converting improper fractions to mixed numbers, along with an example and how to check if your answer is correct. Additionally, we will discuss whether it is possible to have a percentage value that is greater than 100% and provide an example. Finally, we will explore which of the following improper fractions are equivalent to “9” and provide the mathematical verification for each.

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Description:

Converting an improper fraction to a mixed number is important when you need to represent fractions in a more readable and understandable form. An improper fraction is when the numerator is greater than or equal to the denominator, while a mixed number is a number that consists of a whole number and a fraction. To convert an improper fraction to a mixed number, you need to follow a few steps.

Steps for converting an improper fraction to a mixed number:

Step 1: Divide the numerator by the denominator.

Step 2: Write down the whole number result, which is the integer portion of the mixed number.

Step 3: Write the remainder over the original denominator to get the fractional portion of the mixed number.

For example, let’s convert the improper fraction 7/4 to a mixed number:

Step 1: 7 ÷ 4 = 1 with a remainder of 3

Step 2: The whole number portion is 1

Step 3: The fractional portion is 3/4

Therefore, 7/4 as a mixed number is 1 3/4.

To check if your answer is correct, you can convert the mixed number back to an improper fraction and see if it matches the original improper fraction. In this case, 1 3/4 as an improper fraction is (4 x 1) + 3/4 = 7/4, which matches the original improper fraction.

It is not possible to have a percentage value that is greater than 100%, as 100% represents the whole value of something. Any value greater than 100% implies that there is more than the whole, making it impossible. For example, if you say a cake is 120% delicious, it implies that there is an additional 20% of cake deliciousness beyond the whole cake, which makes no sense.

Now, let’s explore which of the following improper fractions are equivalent to “9” and provide the mathematical verification for each.

5/9, 27/3, 81/9, 90/10, 45/5

The improper fraction 81/9 is equivalent to “9,” as 81 ÷ 9 = 9. To verify mathematically, you can convert 9 to an improper fraction by multiplying it by the denominator of 9/1. The resulting improper fraction is 81/9, which matches the original improper fraction.

Objectives:

– To understand the steps for converting an improper fraction to a mixed number

– To be able to identify and solve equivalent improper fractions

– To know whether it is possible to have a percentage value greater than 100%

Learning Outcomes:

At the end of this lesson, students will be able to:

– Convert improper fractions to mixed numbers

– Determine if a percentage value is greater than 100%

– Identify equivalent improper fractions

Steps for Converting an Improper Fraction to a Mixed Number:

1. Divide the numerator (top number) by the denominator (bottom number)

2. Write down the whole number quotient

3. Write down the remainder as the numerator

4. Place the denominator underneath the numerator to form the mixed number

Example: Convert 7/4 to a mixed number

1. 7 ÷ 4 = 1 with a remainder of 3

2. Write down 1 as the whole number

3. Write down 3 as the numerator

4. Place 4 underneath the 3 to get 1 3/4

To check if the answer is correct, convert the mixed number back to an improper fraction and simplify. In this case, 1 3/4 would be 7/4, which is the same as the original fraction.

Explanation of Percentage Value greater than 100%:

No, it is not possible to have a percentage value that is greater than 100%. A percentage is a fraction or decimal multiplied by 100. Therefore, 100% represents the whole amount or 1 whole unit. Anything greater than 100% would mean exceeding the whole amount, which is not possible.

Example: If a student scores 95 out of 90 on a test, the percentage score would be 105.55%. However, this is not possible as the maximum score a student can get is 100%.

Equivalent Improper Fractions to “9”:

– 27/3 = 9

– 81/9 = 9

– 63/7 = 9

To verify mathematical equivalence, simplify each fraction to its lowest terms. In this case, 27/3 and 81/9 are already in their simplest form. To simplify 63/7, divide both the numerator and denominator by their greatest common factor, which is 7. This gives us 9/1, which is equal to 9.

Suggested Resources/Books:

1) “The Complete Idiot’s Guide to Fractions” by Monica Martinez and Don Sevcik

2) “Mathematics for the Nonmathematician” by Morris Kline

3) “Math Refresher for Adults: The Perfect Solution” by Jonathan Tullis

4) “Basic Math and Pre-Algebra For Dummies” by Mark Zegarelli

5) “Fractions in Real-Life Situations” by Lisa M. Bolt Simons

Similar asked questions:

1) How do you convert a mixed number to an improper fraction?

2) How do you add or subtract fractions with different denominators?

3) How can you simplify a fraction that cannot be reduced?

4) How do you convert a decimal to a fraction?

5) How do you find the least common multiple of two or more numbers?

Steps for converting an improper fraction to a mixed number:

1) Divide the numerator by the denominator.

2) The quotient represents the whole number portion of the mixed number.

3) The remainder represents the numerator of the fraction.

4) Write the whole number and the fraction with the same denominator.

5) Simplify the resulting fraction, if possible.

Example: Converting 17/5 to a mixed number

1) 17 ÷ 5 = 3 with a remainder of 2

2) 3 is the whole number portion of the mixed number.

3) 2 is the numerator of the fraction portion of the mixed number.

4) Write 3 2/5 as the mixed number.

5) In this example, the fraction cannot be simplified further.

Checking the answer: To check if the answer is correct, multiply the denominator of the fraction portion by the whole number and add the numerator. The result should equal the original numerator. In this case, (5 x 3) + 2 = 17, so the answer is correct.

Explanation of whether it is possible to have a percentage value that is greater than 100%:

It is possible to have a percentage value that is greater than 100%. A percentage is a fraction of 100, so any value greater than 100 represents a value that is more than the whole. For example, 200% represents a value that is double the whole amount. However, it is important to note that percentages greater than 100% are typically used in specific contexts, such as when calculating changes in value or growth rates.

The following improper fractions are equivalent to “9”:

1) 81/9

Mathematical verification: Divide the numerator by the denominator. 81 ÷ 9 = 9

2) 45/5

Mathematical verification: Divide the numerator by the denominator. 45 ÷ 5 = 9

3) 72/8

Mathematical verification: Divide the numerator by the denominator. 72 ÷ 8 = 9

4) 90/10

Mathematical verification: Divide the numerator by the denominator. 90 ÷ 10 = 9

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