Solved on Dec 19, 2023

Find the value of the expression $12 \frac{2}{9} \cdot (-\frac{9}{5})$ .

STEP 1

Assumptions
1. The expression given is $12 \frac{2}{9} \cdot\left(-\frac{9}{5}\right)$ .
2. The expression involves a mixed number multiplied by a negative fraction.

STEP 2

First, we need to convert the mixed number into an improper fraction.
$12 \frac{2}{9} = 12 + \frac{2}{9}$

STEP 3

To convert the whole number part into a fraction with the same denominator as the fractional part, multiply the whole number by the denominator of the fractional part.
$12 \cdot 9 = 108$

STEP 4

Now, add the numerator of the fractional part to the result from the previous step to get the numerator of the improper fraction.
$108 + 2 = 110$

STEP 5

Write the mixed number as an improper fraction using the numerator from the previous step and the same denominator as the fractional part.
$12 \frac{2}{9} = \frac{110}{9}$

STEP 6

Now we can multiply the improper fraction by the negative fraction.
$\frac{110}{9} \cdot\left(-\frac{9}{5}\right)$

STEP 7

Before multiplying, we can simplify the expression by canceling out any common factors between the numerators and denominators.
$\frac{110}{9} \cdot\left(-\frac{9}{5}\right) = \frac{110 \cancel{9}}{\cancel{9}} \cdot\left(-\frac{\cancel{9}}{5}\right)$

STEP 8

After canceling out the common factor of 9, we have:
$\frac{110}{1} \cdot\left(-\frac{1}{5}\right)$

STEP 9

Now, multiply the numerators and the denominators separately.
$\frac{110 \cdot (-1)}{1 \cdot 5}$

STEP 10

Perform the multiplication.
$\frac{-110}{5}$

STEP 11

Finally, divide the numerator by the denominator to simplify the fraction.
$-110 \div 5 = -22$
The value of the expression is $-22$ .

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Find the value of the expression $12 \frac{2}{9} \cdot (-\frac{9}{5})$ .

STEP 1

Assumptions
1. The expression given is $12 \frac{2}{9} \cdot\left(-\frac{9}{5}\right)$ .
2. The expression involves a mixed number multiplied by a negative fraction.

STEP 2

First, we need to convert the mixed number into an improper fraction.
$12 \frac{2}{9} = 12 + \frac{2}{9}$

STEP 3

To convert the whole number part into a fraction with the same denominator as the fractional part, multiply the whole number by the denominator of the fractional part.
$12 \cdot 9 = 108$

STEP 4

Now, add the numerator of the fractional part to the result from the previous step to get the numerator of the improper fraction.
$108 + 2 = 110$

STEP 5

Write the mixed number as an improper fraction using the numerator from the previous step and the same denominator as the fractional part.
$12 \frac{2}{9} = \frac{110}{9}$

STEP 6

Now we can multiply the improper fraction by the negative fraction.
$\frac{110}{9} \cdot\left(-\frac{9}{5}\right)$

STEP 7

Before multiplying, we can simplify the expression by canceling out any common factors between the numerators and denominators.
$\frac{110}{9} \cdot\left(-\frac{9}{5}\right) = \frac{110 \cancel{9}}{\cancel{9}} \cdot\left(-\frac{\cancel{9}}{5}\right)$

STEP 8

After canceling out the common factor of 9, we have:
$\frac{110}{1} \cdot\left(-\frac{1}{5}\right)$

STEP 9

Now, multiply the numerators and the denominators separately.
$\frac{110 \cdot (-1)}{1 \cdot 5}$

STEP 10

Perform the multiplication.
$\frac{-110}{5}$

STEP 11

Finally, divide the numerator by the denominator to simplify the fraction.
$-110 \div 5 = -22$
The value of the expression is $-22$ .

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Find the value of the expression 1229⋅(−95)12 \frac{2}{9} \cdot (-\frac{9}{5})1292​⋅(−59​).

STEP 1

Assumptions1. The expression given is 1229⋅(−95)12 \frac{2}{9} \cdot\left(-\frac{9}{5}\right)1292​⋅(−59​).2. The expression involves a mixed number multiplied by a negative fraction.

STEP 2

First, we need to convert the mixed number into an improper fraction.1229=12+2912 \frac{2}{9} = 12 + \frac{2}{9}1292​=12+92​

STEP 3

To convert the whole number part into a fraction with the same denominator as the fractional part, multiply the whole number by the denominator of the fractional part.12⋅9=10812 \cdot 9 = 10812⋅9=108

STEP 4

Now, add the numerator of the fractional part to the result from the previous step to get the numerator of the improper fraction.108+2=110108 + 2 = 110108+2=110

STEP 5

Write the mixed number as an improper fraction using the numerator from the previous step and the same denominator as the fractional part.1229=110912 \frac{2}{9} = \frac{110}{9}1292​=9110​

STEP 6

Now we can multiply the improper fraction by the negative fraction.1109⋅(−95)\frac{110}{9} \cdot\left(-\frac{9}{5}\right)9110​⋅(−59​)

STEP 7

STEP 8

After canceling out the common factor of 9, we have:1101⋅(−15)\frac{110}{1} \cdot\left(-\frac{1}{5}\right)1110​⋅(−51​)

STEP 9

Now, multiply the numerators and the denominators separately.110⋅(−1)1⋅5\frac{110 \cdot (-1)}{1 \cdot 5}1⋅5110⋅(−1)​

STEP 10

Perform the multiplication.−1105\frac{-110}{5}5−110​

STEP 11

Finally, divide the numerator by the denominator to simplify the fraction.−110÷5=−22-110 \div 5 = -22−110÷5=−22The value of the expression is −22-22−22.

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Find the value of the expression $12 \frac{2}{9} \cdot (-\frac{9}{5})$ .

Assumptions
1. The expression given is $12 \frac{2}{9} \cdot\left(-\frac{9}{5}\right)$ .
2. The expression involves a mixed number multiplied by a negative fraction.

First, we need to convert the mixed number into an improper fraction.
$12 \frac{2}{9} = 12 + \frac{2}{9}$

To convert the whole number part into a fraction with the same denominator as the fractional part, multiply the whole number by the denominator of the fractional part.
$12 \cdot 9 = 108$

Now, add the numerator of the fractional part to the result from the previous step to get the numerator of the improper fraction.
$108 + 2 = 110$

Write the mixed number as an improper fraction using the numerator from the previous step and the same denominator as the fractional part.
$12 \frac{2}{9} = \frac{110}{9}$

Now we can multiply the improper fraction by the negative fraction.
$\frac{110}{9} \cdot\left(-\frac{9}{5}\right)$

After canceling out the common factor of 9, we have:
$\frac{110}{1} \cdot\left(-\frac{1}{5}\right)$

Now, multiply the numerators and the denominators separately.
$\frac{110 \cdot (-1)}{1 \cdot 5}$

Perform the multiplication.
$\frac{-110}{5}$

Finally, divide the numerator by the denominator to simplify the fraction.
$-110 \div 5 = -22$
The value of the expression is $-22$ .