Which expression is equivalent to 3(7)/(8)-6(1)/(4)? Choose 1 answer: (A) 3(7)/(8)+(-6(1)/(4)) (B) 3(7)/(8)+(6(1)/(4)) (c) 6(1)/(4)-(3(7)/(8)) (D) -6(1)/(4)+(-3(7)/(8))

Question

Which expression is equivalent to  3(7)/(8)-6(1)/(4)? Choose 1 answer: (A)  3(7)/(8)+(-6(1)/(4)) (B)  3(7)/(8)+(6(1)/(4)) (c)  6(1)/(4)-(3(7)/(8)) (D)  -6(1)/(4)+(-3(7)/(8))

Bytelearn · Accepted Answer

Understand the problem: Understand the problem. We need to find an expression equivalent to the given expression 3(7)/(8)-6(1)/(4). This involves understanding subtraction of fractions.Convert to improper fractions: Convert mixed numbers to improper fractions. 3(7)/(8) is already an improper fraction, so it remains the same. 6(1)/(4) as an improper fraction is 6*4 + 1 = 25/4.Rewrite with improper fractions: Rewrite the original expression using the improper fraction for 6(1)/(4). The original expression 3(7)/(8)-6(1)/(4) becomes 3(7)/(8) - 25/4.Find common denominator: Find a common denominator for the fractions. The common denominator for 8 and 4 is 8.Convert to common denominator: Convert the second fraction to have the common denominator. To convert 25/4 to have a denominator of 8, we multiply both the numerator and the denominator by 2, which gives us 50/8.Rewrite with common denominator: Rewrite the expression with the common denominator. Now the expression is 3(7)/(8) - 50/8.Subtract fractions: Subtract the fractions. Subtracting the fractions with the common denominator gives us (3*7 - 50)/8, which simplifies to (21 - 50)/8.Simplify result: Simplify the result. (21 - 50)/8 simplifies to -29/8, which is an improper fraction.Convert to mixed number: Convert the improper fraction back to a mixed number. -29/8 as a mixed number is -3(5)/(8).Find equivalent expression: Look for the equivalent expression among the choices. The equivalent expression to 3(7)/(8)-6(1)/(4) is -3(5)/(8), which is not directly listed among the choices. However, we can express this as the addition of a negative, which is choice (A) 3(7)/(8)+(-6(1)/(4)).

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