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2. What is the difference between [tex]\( \frac{1261}{4} \)[/tex] and [tex]\( 78 \frac{2}{3} \)[/tex]?

A. [tex]\( 47 \frac{7}{12} \)[/tex]

B. [tex]\( \frac{481}{3} \)[/tex]

C. [tex]\( 58 \frac{5}{12} \)[/tex]

D. [tex]\( \frac{577}{12} \)[/tex]


Sagot :

To determine the difference between [tex]\( \frac{1261}{4} \)[/tex] and [tex]\( 78 \frac{2}{3} \)[/tex], we can follow these steps:

1. Calculate the value of [tex]\( \frac{1261}{4} \)[/tex]:

[tex]\[ \frac{1261}{4} = 315.25 \][/tex]

2. Convert the mixed number [tex]\( 78 \frac{2}{3} \)[/tex] to an improper fraction and then to a decimal:

[tex]\[ 78 \frac{2}{3} = 78 + \frac{2}{3} = 78 + 0.66666666666667 \approx 78.66666666666667 \][/tex]

3. Subtract [tex]\( 78 \frac{2}{3} \)[/tex] from [tex]\( 315.25 \)[/tex]:

[tex]\[ 315.25 - 78.66666666666667 = 236.58333333333331 \][/tex]

The difference between [tex]\( \frac{1261}{4} \)[/tex] and [tex]\( 78 \frac{2}{3} \)[/tex] is approximately [tex]\( 236.58333333333331 \)[/tex].

Now, compare this result with the provided options:

A. [tex]\( 47 \frac{7}{12} \approx 47.58333333333333 \)[/tex]
B. [tex]\( \frac{481}{3} \approx 160.33333333333334 \)[/tex]
C. [tex]\( 58 \frac{5}{12} \approx 58.41666666666667 \)[/tex]
D. [tex]\( \frac{577}{12} \approx 48.083333333333336 \)[/tex]

Based on the calculated difference, none of the given options match [tex]\( 236.58333333333331 \)[/tex]. Therefore, none of the provided answer choices (A, B, C, D) are correct.