Questions: Evaluate mt, for m=16 8/9 and t=-26 1/8. mt= (Simplify your answer. Type a mixed numeral, if possible.)

Transcript text: Evaluate $m t$, for $m=16 \frac{8}{9}$ and $t=-26 \frac{1}{8}$. $\mathrm{mt}=$ $\square$ (Simplify your answer. Type a mixed numeral, if possible.)

Solution

Solution Steps

To evaluate the expression $ m \times t $ where $ m = 16 \frac{8}{9} $ and $ t = -26 \frac{1}{8} $, we first convert the mixed numbers into improper fractions. Then, we multiply these fractions together. Finally, we simplify the resulting fraction and convert it back to a mixed number if necessary.

Step 1: Convert Mixed Numbers to Improper Fractions

We start by converting the mixed numbers $ m = 16 \frac{8}{9} $ and $ t = -26 \frac{1}{8} $ into improper fractions.

For $ m $: \[ m = 16 \frac{8}{9} = \frac{16 \times 9 + 8}{9} = \frac{144 + 8}{9} = \frac{152}{9} \]

For $ t $: \[ t = -26 \frac{1}{8} = -\left(26 \times 8 + 1\right)/8 = -\frac{208 + 1}{8} = -\frac{209}{8} \]

Step 2: Multiply the Improper Fractions

Next, we multiply the two improper fractions: \[ m \times t = \frac{152}{9} \times -\frac{209}{8} = -\frac{152 \times 209}{9 \times 8} = -\frac{31768}{72} \]

Step 3: Simplify the Resulting Fraction

We simplify the fraction $ -\frac{31768}{72} $. The greatest common divisor (GCD) of 31768 and 72 is 8, so we divide both the numerator and the denominator by 8: \[ -\frac{31768 \div 8}{72 \div 8} = -\frac{3971}{9} \]

Step 4: Convert to Mixed Number

To express $ -\frac{3971}{9} $ as a mixed number, we divide 3971 by 9: \[ 3971 \div 9 = 441 \quad \text{(whole number part)} \] The remainder is: \[ 3971 - (441 \times 9) = 7 \] Thus, we can express the result as: \[ -\frac{3971}{9} = -441 \frac{7}{9} \]