Understanding 7.5 as a Fraction: A Comprehensive Guide
Introduction
Fractions are an essential part of our daily lives, representing parts of a whole. 7.5 is a common fraction that often arises in various contexts. This article aims to provide a thorough understanding of 7.5 as a fraction, covering its conversion methods, applications, and practical examples.
Converting 7.5 to a Fraction
Step 1: Multiply by 100%
To convert a decimal to a fraction, we multiply it by 100%.
7.5 * 100% = 750%
Step 2: Interpret as a Fraction
The result represents the numerator of the fraction. Adding 100 as the denominator gives us:
7.5 = 750% / 100% = **750/100**
Step 3: Simplify (Optional)
We can simplify the fraction by dividing both the numerator and denominator by their greatest common factor (GCF), which is 5.
750/100 = (750 ÷ 5) / (100 ÷ 5) = **150/20**
Therefore, 7.5 is equivalent to the fraction 150/20.
Applications of 7.5 as a Fraction
Percentages and Proportions
7.5 as a fraction represents 750%. This concept is widely used in various fields, such as:
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Sales discounts: A 7.5% discount on an item
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Interest rates: 7.5% annual percentage yield (APY)
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Recipe measurements: 750 grams out of every 100 grams
Probability and Statistics
In probability and statistics, 7.5 as a fraction is expressed as 0.075 or 7.5%. It represents a probability or proportion of 7.5 out of 100.
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Probability of flipping a coin and getting tails: 0.075 or 7.5%
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Percentage of students who scored above 90%: 7.5%
Practical Examples
Example 1: Calculating a Bill with 7.5% Tax
Suppose you purchased items worth $100 at a store with a 7.5% sales tax.
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Convert 7.5% to a fraction: 7.5% = 750/10000
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Multiply the fraction by the amount: 7.5% x $100 = (750/10000) x $100 = $7.50
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Add the tax to the original amount: $100 + $7.50 = $107.50
Example 2: Determining the Probability of Drawing a Blue Card
A deck of cards contains 10 blue cards and 40 cards in total.
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Convert the probability to a fraction: 7.5% = 10/40 = 1/4
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The probability of drawing a blue card: It is 1 out of every 4 draws.
Example 3: Dividing a Pizza Equally
Suppose you want to divide a pizza equally between 12 friends.
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Convert 1/12 to a fraction: 1/12 = 25/300
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The fraction of pizza each friend gets: 25/300 or approximately 8.33% of the whole pizza
Effective Strategies for Understanding 7.5 as a Fraction
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Visualize the fraction: Draw a rectangle divided into 100 equal parts. Shade 75 of them to represent 750%.
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Use manipulatives: Use fraction tiles or counters to represent 7.5 and visually understand its relationship to 100%.
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Practice conversion: Regularly convert 7.5 between decimals, percentages, and fractions.
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Relate to real-life situations: Connect the concept of 7.5 as a fraction to situations you encounter daily, such as discounts, probabilities, and measurements.
Step-by-Step Approach to Converting 7.5 to a Fraction
- Multiply 7.5 by 100%.
- Simplify the resulting fraction, if necessary.
- Divide both the numerator and denominator by their GCF to obtain the simplest form of the fraction.
Frequently Asked Questions (FAQs)
Q: What is the simplest form of 7.5 as a fraction?
A: 150/20 or 3/4
Q: How do I convert 0.075 to a fraction?
A: Multiply by 100% and simplify: 0.075 x 100% = 75/100 = 3/4
Q: What percentage is represented by the fraction 750/10000?
A: 7.5%
Q: How do I find the fraction of a whole number?
A: Divide the part by the whole, for example: 5/12 represents 5 parts out of a total of 12 parts.
Q: What is the probability of rolling a number greater than 4 on a standard six-sided die?
A: 1/2 or 50%
