Consider the problem.

−3/8×−1 2/3
Determine the sign of the product.

(1 point)
Responses

Positive - If the signs of the factors are the same, the product is positive.
Positive - If the signs of the factors are the same, the product is positive.

Negative - If the signs of the factors are negative, the product is negative.
Negative - If the signs of the factors are negative, the product is negative.
Question 2
Determine the product in simplest form.

−3/8×−1 2/3
(1 point)
Responses

−58
negative 5 eighths

58
5 eighths

940
9 over 40

1524
15 over 24
Skip to navigation

1 answer

To determine the sign of the product and compute \(-\frac{3}{8} \times -1 \frac{2}{3}\), we can follow these steps:

Step 1: Determine the signs of the factors

  1. The first factor is \(-\frac{3}{8}\) (negative).
  2. The second factor, \(-1 \frac{2}{3}\), is also negative because it has a negative sign in front.

Conclusion of Sign

Since both factors are negative, the product will be positive. Therefore, the response is: Positive - If the signs of the factors are the same, the product is positive.

Step 2: Compute the product in simplest form

To compute the product \(-\frac{3}{8} \times -1 \frac{2}{3}\), we first convert the mixed number \(-1 \frac{2}{3}\) to an improper fraction.

  1. Convert \(-1 \frac{2}{3}\) to an improper fraction:

    • Multiply the whole number \(1\) by the denominator \(3\) and add the numerator \(2\): \[ 1 \times 3 + 2 = 3 + 2 = 5 \]
    • Therefore, \(-1 \frac{2}{3} = -\frac{5}{3}\).
  2. Now, multiply the two fractions: \[ -\frac{3}{8} \times -\frac{5}{3} \] The negatives cancel out (because negative times negative is positive): \[ = \frac{3}{8} \times \frac{5}{3} \] When multiplying fractions, multiply the numerators and the denominators: \[ = \frac{3 \times 5}{8 \times 3} = \frac{15}{24} \]

  3. Simplify \(\frac{15}{24}\):

    • Find the greatest common divisor (GCD) of \(15\) and \(24\), which is \(3\).
    • Divide both numerator and denominator by \(3\): \[ = \frac{15 \div 3}{24 \div 3} = \frac{5}{8} \]

Final Answer

Thus, the product in simplest form is: 5 eighths (58).

So, the answers are:

  • Determining the sign: Positive
  • Determining the product in simplest form: 5 eighths (58).
Similar Questions
  1. Multiply Rational Numbers Quick Check2 of 52 of 5 Items Question Determine the sign of the product of −0.708×−6.24 .(1
    1. answers icon 1 answer
  2. Consider the problem.−38×−123 Determine the sign of the product. (1 point) Responses Positive - If the signs of the factors
    1. answers icon 1 answer
    1. answers icon 1 answer
  3. Determine the sign of the product of 1732×(−110).(1 point)Responses negative negative The product has no sign. The product
    1. answers icon 1 answer
more similar questions