What is the value of $\left(\frac{3}{4}-\frac{1}{2}\right)+5.25$ expressed as a fraction?
Answer (2)
Simplify the expression inside the parenthesis: 4 3 − 2 1 = 4 1 .
Convert the decimal 5.25 to a fraction: 5.25 = 4 21 .
Add the two fractions: 4 1 + 4 21 = 4 22 .
Simplify the resulting fraction: 4 22 = 2 11 .
The value of the expression is 2 11 .
Explanation
Understanding the problem We are asked to find the value of the expression ( 4 3 − 2 1 ) + 5.25 expressed as a fraction. This involves subtracting and adding fractions and converting a decimal to a fraction.
Simplifying the parenthesis First, let's simplify the expression inside the parenthesis: 4 3 − 2 1 . To subtract these fractions, we need a common denominator, which is 4. So we rewrite 2 1 as 4 2 . Therefore, 4 3 − 2 1 = 4 3 − 4 2 = 4 3 − 2 = 4 1 .
Converting decimal to a fraction Next, we need to convert the decimal 5.25 into a fraction. We can write 5.25 as 5 100 25 . Simplifying the fraction 100 25 , we get 4 1 . So, 5.25 = 5 4 1 . Converting this mixed number to an improper fraction, we have 5 4 1 = 4 5 × 4 + 1 = 4 20 + 1 = 4 21 .
Adding the fractions Now, we add the result from the parenthesis to the fraction we obtained from the decimal: 4 1 + 4 21 = 4 1 + 21 = 4 22 .
Simplifying the final fraction Finally, we simplify the fraction 4 22 by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, 4 22 = 4 ÷ 2 22 ÷ 2 = 2 11 . Therefore, the value of the expression ( 4 3 − 2 1 ) + 5.25 expressed as a fraction is 2 11 .
Examples
Understanding fractions and decimals is essential in everyday life. For example, when you're cooking and need to measure ingredients, you often encounter fractions and decimals. If a recipe calls for 4 3 cup of flour and you only have a 2 1 cup measure, you need to know how much more to add. Similarly, if you're calculating the cost of items on sale, you might need to add a decimal discount to a fraction of the original price. Knowing how to convert between fractions and decimals and perform basic arithmetic operations with them is crucial for accurate measurements and calculations in various real-life situations.
The value of the expression ( 4 3 − 2 1 ) + 5.25 is 2 11 when expressed as a fraction. This involves simplifying the fractions and converting the decimal to a fraction. The calculations involved include finding a common denominator and simplifying the final result.
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