Clarke Whittaker
03/27/2024 · High School
\( 7\frac{3}{4}-....=3\frac{2}{5} \)
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Tutor-Verified Answer
Step-by-step Solution
To solve the equation \( 7\frac{3}{4} - x = 3\frac{2}{5} \), we first convert the mixed numbers into improper fractions.
1. Convert \( 7\frac{3}{4} \):
\[
7\frac{3}{4} = 7 \times 4 + 3 = 28 + 3 = 31 \quad \text{(improper fraction: } \frac{31}{4}\text{)}
\]
2. Convert \( 3\frac{2}{5} \):
\[
3\frac{2}{5} = 3 \times 5 + 2 = 15 + 2 = 17 \quad \text{(improper fraction: } \frac{17}{5}\text{)}
\]
Now, we rewrite the equation:
\[
\frac{31}{4} - x = \frac{17}{5}
\]
Next, we isolate \( x \):
\[
x = \frac{31}{4} - \frac{17}{5}
\]
To perform the subtraction, we need a common denominator. The least common multiple of 4 and 5 is 20.
Convert both fractions:
\[
\frac{31}{4} = \frac{31 \times 5}{4 \times 5} = \frac{155}{20}
\]
\[
\frac{17}{5} = \frac{17 \times 4}{5 \times 4} = \frac{68}{20}
\]
Now substitute back into the equation:
\[
x = \frac{155}{20} - \frac{68}{20} = \frac{155 - 68}{20} = \frac{87}{20}
\]
Finally, we can convert \( \frac{87}{20} \) back to a mixed number:
\[
87 \div 20 = 4 \quad \text{(remainder } 7\text{)}
\]
Thus,
\[
\frac{87}{20} = 4\frac{7}{20}
\]
So, the solution is:
\[
x = 4\frac{7}{20}
\]
Quick Answer
\( x = 4\frac{7}{20} \)
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