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−9/10(−4/5)

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To calculate \(-\frac{9}{10} \times -\frac{4}{5}\), you can follow these steps:

  1. Multiply the numerators: \[ -9 \times -4 = 36 \]

  2. Multiply the denominators: \[ 10 \times 5 = 50 \]

  3. Combine the results: \[ -\frac{9}{10} \times -\frac{4}{5} = \frac{36}{50} \]

  4. Simplify \(\frac{36}{50}\) by finding the greatest common divisor (GCD). The GCD of 36 and 50 is 2. \[ \frac{36 \div 2}{50 \div 2} = \frac{18}{25} \]

Therefore, \(-\frac{9}{10} \times -\frac{4}{5} = \frac{18}{25}\).

−1/4(−2 1/3)

To calculate \(-\frac{1}{4} \times -2 \frac{1}{3}\), we need to first convert the mixed number into an improper fraction.

  1. Convert the mixed number \(-2 \frac{1}{3}\) to an improper fraction: \[ -2 \frac{1}{3} = -\left(2 \times 3 + 1 \right) / 3 = -\frac{7}{3} \]

  2. Now multiply: \[ -\frac{1}{4} \times -\frac{7}{3} \]

  3. Multiply the numerators and denominators: \[ \text{Numerator: } (-1) \times (-7) = 7 \] \[ \text{Denominator: } 4 \times 3 = 12 \]

  4. So we have: \[ -\frac{1}{4} \times -\frac{7}{3} = \frac{7}{12} \]

Therefore, \(-\frac{1}{4} \times -2 \frac{1}{3} = \frac{7}{12}\).

Evaluate 1/3mn
if m=−3/10
and n=−4/5

To evaluate \(\frac{1}{3}mn\) given \(m = -\frac{3}{10}\) and \(n = -\frac{4}{5}\), follow these steps:

  1. Calculate the product \(mn\): \[ mn = \left(-\frac{3}{10}\right) \times \left(-\frac{4}{5}\right) \] Since the product of two negative numbers is positive: \[ mn = \frac{3 \times 4}{10 \times 5} = \frac{12}{50} \]

  2. Simplify \(\frac{12}{50}\): The greatest common divisor of 12 and 50 is 2. \[ \frac{12 \div 2}{50 \div 2} = \frac{6}{25} \]

  3. Now substitute \(mn\) back into the expression \(\frac{1}{3}mn\): \[ \frac{1}{3}mn = \frac{1}{3} \times \frac{6}{25} \]

  4. Multiply the fractions: \[ \frac{1 \times 6}{3 \times 25} = \frac{6}{75} \]

  5. Simplify \(\frac{6}{75}\): The greatest common divisor of 6 and 75 is 3. \[ \frac{6 \div 3}{75 \div 3} = \frac{2}{25} \]

So, the value of \(\frac{1}{3}mn\) when \(m = -\frac{3}{10}\) and \(n = -\frac{4}{5}\) is \(\frac{2}{25}\).

Evaluate −2/3cd
if c=−1/5
and d=−1 1/2

To evaluate \(-\frac{2}{3}cd\) given \(c = -\frac{1}{5}\) and \(d = -1 \frac{1}{2}\), follow these steps:

  1. Convert the mixed number \(d = -1 \frac{1}{2}\) to an improper fraction: \[ -1 \frac{1}{2} = -\left(1 \times 2 + 1\right) / 2 = -\frac{3}{2} \]

  2. Now substitute \(c\) and \(d\) into the expression \(cd\): \[ cd = \left(-\frac{1}{5}\right) \times \left(-\frac{3}{2}\right) \] Since the product of two negative numbers is positive: \[ cd = \frac{1 \times 3}{5 \times 2} = \frac{3}{10} \]

  3. Next, substitute \(cd\) back into the expression \(-\frac{2}{3}cd\): \[ -\frac{2}{3}cd = -\frac{2}{3} \times \frac{3}{10} \]

  4. Multiply the fractions: \[ -\frac{2 \times 3}{3 \times 10} = -\frac{6}{30} \]

  5. Simplify \(-\frac{6}{30}\): The greatest common divisor of 6 and 30 is 6. \[ -\frac{6 \div 6}{30 \div 6} = -\frac{1}{5} \]

Thus, the value of \(-\frac{2}{3}cd\) when \(c = -\frac{1}{5}\) and \(d = -1 \frac{1}{2}\) is \(-\frac{1}{5}\).

Evaluate 12abcd
if a=−2.4
, b=−5/6
, c=−1 1/5
, and d=2/3

To evaluate \(12abcd\) given \(a = -2.4\), \(b = -\frac{5}{6}\), \(c = -1 \frac{1}{5}\), and \(d = \frac{2}{3}\), follow these steps:

  1. Convert the mixed number \(c = -1 \frac{1}{5}\) to an improper fraction: \[ -1 \frac{1}{5} = -\left(1 \times 5 + 1\right) / 5 = -\frac{6}{5} \]

  2. Now substitute the values of \(a\), \(b\), \(c\), and \(d\) back into the expression \(12abcd\): \[ 12 \cdot a \cdot b \cdot c \cdot d = 12 \cdot \left(-2.4\right) \cdot \left(-\frac{5}{6}\right) \cdot \left(-\frac{6}{5}\right) \cdot \left(\frac{2}{3}\right) \]

  3. Calculate the product step by step:

    • First, calculate \(ab\): \[ ab = (-2.4) \cdot \left(-\frac{5}{6}\right) = 2.4 \cdot \frac{5}{6} = \frac{2.4 \cdot 5}{6} = \frac{12}{6} = 2 \]

    • Next, calculate \(cd\): \[ cd = \left(-\frac{6}{5}\right) \cdot \left(\frac{2}{3}\right) = -\frac{6 \cdot 2}{5 \cdot 3} = -\frac{12}{15} = -\frac{4}{5} \quad (\text{after simplification}) \]

  4. Now multiply \(ab\) and \(cd\): \[ abcd = 2 \cdot \left(-\frac{4}{5}\right) = -\frac{8}{5} \]

  5. Multiply by 12: \[ 12abcd = 12 \cdot \left(-\frac{8}{5}\right) = -\frac{96}{5} \]

So, the value of \(12abcd\) when \(a = -2.4\), \(b = -\frac{5}{6}\), \(c = -1 \frac{1}{5}\), and \(d = \frac{2}{3}\) is \(-\frac{96}{5}\), or in decimal form, \(-19.2\).

Evaluate 1/2abcd
if a=−2.4
, b=−5/6
, c=−1 1/5
, and d=2/3

To evaluate \(\frac{1}{2} abcd\) given \(a = -2.4\), \(b = -\frac{5}{6}\), \(c = -1 \frac{1}{5}\), and \(d = \frac{2}{3}\), let's go step by step:

Step 1: Convert the Mixed Number

Convert \(c = -1 \frac{1}{5}\) to an improper fraction: \[ -1 \frac{1}{5} = -\left(1 \times 5 + 1\right) / 5 = -\frac{6}{5} \]

Step 2: Calculate \(abcd\)

Now substitute the values:

\[ abcd = a \cdot b \cdot c \cdot d = \left(-2.4\right) \cdot \left(-\frac{5}{6}\right) \cdot \left(-\frac{6}{5}\right) \cdot \left(\frac{2}{3}\right) \]

Step 3: Break it down into parts

  1. Calculate \(ab\): \[ ab = (-2.4) \cdot \left(-\frac{5}{6}\right) = 2.4 \cdot \frac{5}{6} \] To compute this: \[ ab = \frac{2.4 \cdot 5}{6} = \frac{12}{6} = 2 \]

  2. Calculate \(cd\): \[ cd = \left(-\frac{6}{5}\right) \cdot \left(\frac{2}{3}\right) = -\frac{6 \cdot 2}{5 \cdot 3} = -\frac{12}{15} = -\frac{4}{5} \quad (\text{after simplification}) \]

  3. Combine \(ab\) and \(cd\): \[ abcd = 2 \cdot \left(-\frac{4}{5}\right) = -\frac{8}{5} \]

Step 4: Calculate \(\frac{1}{2} abcd\)

Now we compute: \[ \frac{1}{2} abcd = \frac{1}{2} \cdot \left(-\frac{8}{5}\right) = -\frac{8}{10} = -\frac{4}{5} \]

Thus, the value of \(\frac{1}{2} abcd\) when \(a = -2.4\), \(b = -\frac{5}{6}\), \(c = -1 \frac{1}{5}\), and \(d = \frac{2}{3}\) is \(-\frac{4}{5}\).