Respuesta :
The addition of the mass given as fractions can be simplified when the two
masses have the same denominator.
- The expression that makes the sum of the numbers easy is option C; [tex]\underline{C) \ (3\ 1/2 + 8\ 1/2) + (5\ 3/4 + 2\ 1/4) + 7 \ 2/3}[/tex]
Reasons:
The given masses are;
3 1/2 g, 5 3/4 g, 8 1/2 g, 2 1/4g, 7 2/3g
Expressing the given masses as proper fractions give;
[tex]\displaystyle 3 \ 1/2 = \mathbf{\frac{7}{2}}[/tex]
[tex]\displaystyle 5 \ 3/4 = \mathbf{\frac{23}{4}}[/tex]
[tex]\displaystyle 8 \ 1/2 = \mathbf{\frac{17}{2}}[/tex]
[tex]\displaystyle 2 \ 1/4 = \mathbf{\frac{9}{4}}[/tex]
[tex]\displaystyle 7 \ 2/3 = \mathbf{\frac{23}{3}}[/tex]
The process of summing two or more fractions, is simplified if the
denominators of the fractions are equal, therefore, we have;
[tex]\displaystyle 3 \ 1/2 + 5 \ 3/4 + 8 \ 1/2 + 2 \ 1/4 + 7 \ 2/3 = \frac{7}{2} +\frac{23}{4} +\frac{17}{2} +\frac{9}{4} +\frac{23}{3}[/tex]
Collecting terms having the same denominator gives;
[tex]\displaystyle \mathbf{\frac{7}{2}+\frac{17}{2} +\frac{23}{4} +\frac{9}{4} +\frac{23}{3} }= \frac{7 + 17}{2} + \frac{23 + 9}{4} + \frac{23}{3} = 12 + 8 + \frac{23}{3} = 20+\frac{23}{3}[/tex]
Therefore, finding the sum of the numbers is made easy when the numbers are arranged as follows;
[tex]\displaystyle \frac{7}{2}+\frac{17}{2} +\frac{23}{4} +\frac{9}{4} +\frac{23}{3} = \mathbf{\displaystyle 3 \ 1/2+ 8 \ 1/2) + 5 \ 3/4 + 2 \ 1/4) + 7 \ 2/3}[/tex]
[tex]\displaystyle 3 \ 1/2+ 8 \ 1/2 + 5 \ 3/4 + 2 \ 1/4 + 7 \ 2/3 = \mathbf{(3 \ 1/2+ 8 \ 1/2) + (5 \ 3/4 + 2 \ 1/4) + 7 \ 2/3}[/tex]
Therefore;
The expression that would make finding the sum of the five numbers easy is [tex]\underline{C) \ (3\ 1/2 + 8\ 1/2) + (5\ 3/4 + 2\ 1/4) + 7 \ 2/3}[/tex]
Learn more about the addition and subtraction of fractions here:
https://brainly.com/question/24378782
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