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Math  /  Numbers & Operations

QuestionUse properties of rational numbers to multiply the following. −65×3.875-\frac{6}{5} \times 3.875 A. 10740\frac{107}{40} B. −245-\frac{24}{5} C. −9320-\frac{93}{20} D. −15548-\frac{155}{48}

Studdy Solution

STEP 1

1. We are multiplying a negative rational number by a positive decimal number.
2. The result should be expressed as a rational number.
3. We need to identify the correct answer from the given options.

STEP 2

1. Convert the decimal to a fraction.
2. Multiply the fractions.
3. Simplify the result.
4. Match the result with the given options.

STEP 3

Convert the decimal 3.875 3.875 to a fraction.
Since 3.875 3.875 has three decimal places, it can be expressed as:
3.875=387510003.875 = \frac{3875}{1000}
Simplify the fraction by finding the greatest common divisor (GCD) of 3875 3875 and 1000 1000 .

STEP 4

Calculate the GCD of 3875 3875 and 1000 1000 .
The GCD is 125 125 .
Simplify the fraction:
38751000=3875÷1251000÷125=318\frac{3875}{1000} = \frac{3875 \div 125}{1000 \div 125} = \frac{31}{8}

STEP 5

Multiply the fractions:
−65×318-\frac{6}{5} \times \frac{31}{8}
Multiply the numerators and the denominators:
=−6×315×8=−18640= \frac{-6 \times 31}{5 \times 8} = \frac{-186}{40}

STEP 6

Simplify the fraction −18640\frac{-186}{40}.
Find the GCD of 186 186 and 40 40 , which is 2 2 .
Simplify:
−18640=−186÷240÷2=−9320\frac{-186}{40} = \frac{-186 \div 2}{40 \div 2} = \frac{-93}{20}

STEP 7

Match the simplified result −9320\frac{-93}{20} with the given options.
The correct answer is:
C. −9320-\frac{93}{20}
The correct answer is:
−9320\boxed{-\frac{93}{20}}

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