Which expression is equivalent to 3(1)/(2)+(-1(2)/(5)) ? -1(2)/(5)-3(1)/(2) 3(1)/(2)-(-1(2)/(5)) -1(2)/(5)+(-3(1)/(2)) 3(1)/(2)-1(2)/(5)

Question

Which expression is equivalent to  3(1)/(2)+(-1(2)/(5)) ?  -1(2)/(5)-3(1)/(2)  3(1)/(2)-(-1(2)/(5))  -1(2)/(5)+(-3(1)/(2))  3(1)/(2)-1(2)/(5)

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Understand the problem: Understand the problem. We need to find the expression equivalent to the given expression 3(1)/(2) + (-1(2)/(5)).Convert to improper fractions: Convert mixed numbers to improper fractions. 3(1)/(2) can be converted to an improper fraction by multiplying the whole number by the denominator and adding the numerator, then placing the result over the original denominator. 3(1)/(2) = (3*2 + 1)/2 = (6 + 1)/2 = 7/2  Similarly, for -1(2)/(5), we do the same process considering the negative sign. -1(2)/(5) = (-1*5 + 2)/5 = (-5 + 2)/5 = -3/5Add fractions with common denominator: Add the two improper fractions. To add fractions, we need a common denominator. The common denominator for 2 and 5 is 10. We convert each fraction to have a denominator of 10. (7/2) becomes (7*5)/(2*5) = 35/10 (-3/5) becomes (-3*2)/(5*2) = -6/10  Now we can add the fractions: 35/10 + (-6/10) = (35 - 6)/10 = 29/10Convert back to mixed number: Convert the result back to a mixed number. To convert an improper fraction to a mixed number, we divide the numerator by the denominator. 29/10 = 2 remainder 9, so the mixed number is 2(9)/(10).Compare with given options: Compare the result with the given options. The equivalent expression to 3(1)/(2) + (-1(2)/(5)) is 2(9)/(10), which is not explicitly listed in the options. However, we can see that the option ＂3(1)/(2) - 1(2)/(5)＂ is the same as adding the negative of -1(2)/(5) to 3(1)/(2), which is what we did. Therefore, the equivalent expression is ＂3(1)/(2) - 1(2)/(5)＂.

Which expression is equivalent to $3 \frac{1}{2}+\left(-1 \frac{2}{5}\right)$ ? $\newline$ $-1 \frac{2}{5}-3 \frac{1}{2}$ $\newline$ $3 \frac{1}{2}-\left(-1 \frac{2}{5}\right)$ $\newline$ $-1 \frac{2}{5}+\left(-3 \frac{1}{2}\right)$ $\newline$ $3 \frac{1}{2}-1 \frac{2}{5}$

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