Find the sum.
[tex]\frac{3}{2}+\frac{3}{5}+\frac{3}{7}=[/tex]
A. 1
B. 1
C. 4
D. 1
Answer (2)
Simplify the nested fraction: 2 − 2 3 3 = 6 .
Find a common denominator for the remaining fractions: 5 3 + 7 3 = 35 21 + 35 15 .
Add the fractions: 35 21 + 35 15 = 35 36 .
Add the whole number and the fraction: 6 + 35 36 = 7 35 1 .
7 35 1
Explanation
Understanding the Problem We are asked to find the sum of three terms: 2 − 2 3 3 , 5 3 , and 7 3 . The first term involves a fraction within a fraction, which we'll need to simplify first.
Simplifying the First Denominator Let's simplify the denominator of the first term: 2 − 2 3 . To do this, we need to find a common denominator, which is 2. So, we have 2 − 2 3 = 2 4 − 2 3 = 2 1 .
Simplifying the First Term Now we can simplify the first term: 2 − 2 3 3 = 2 1 3 . Dividing by a fraction is the same as multiplying by its reciprocal, so 2 1 3 = 3 × 2 = 6 .
Finding a Common Denominator Now we can rewrite the original expression as: 6 + 5 3 + 7 3 . To add the fractions, we need to find a common denominator for 5 and 7, which is 5 × 7 = 35 .
Converting the Fractions Convert the fractions to have the common denominator: 5 3 = 5 × 7 3 × 7 = 35 21 and 7 3 = 7 × 5 3 × 5 = 35 15 .
Adding the Fractions Now we can add the fractions: 35 21 + 35 15 = 35 21 + 15 = 35 36 .
Final Calculation So the expression becomes 6 + 35 36 . Since 35 36 = 1 35 1 , the final result is 6 + 1 35 1 = 7 35 1 .
Comparing with Options Comparing our result 7 35 1 with the given options, we see that none of the options match exactly. However, let's re-examine the options to see if there's a typo or if we can manipulate our answer to match one of them. The closest option seems to be B, which is 1 35 4 . It seems there was a mistake in the original problem or options. However, based on our calculations, the correct answer is 7 35 1 .
Examples
Fractions are used in everyday life, such as when you're cooking and need to measure ingredients. For example, if a recipe calls for 3 2 cup of flour and you want to double the recipe, you need to multiply the fraction by 2. Understanding how to add, subtract, multiply, and divide fractions is essential for accurate measurements and successful cooking. This also applies to other areas like calculating discounts while shopping or understanding proportions in various fields.
The sum of the fractions 2 3 + 5 3 + 7 3 is calculated to be 2 70 37 . None of the provided answer options match this result. The calculations include finding a common denominator and summing the fractions step by step.
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