Solved on Dec 21, 2023

Divide $1 \frac{4}{9}$ by $-\frac{2}{9}$ and write the quotient in simplest form.

STEP 1

Assumptions
1. We are given a mixed number $1 \frac{4}{9}$ .
2. We are given a negative fraction $-\frac{2}{9}$ .
3. We need to divide the mixed number by the negative fraction.
4. The final answer should be in simplest form.

STEP 2

First, we need to convert the mixed number into an improper fraction.
$1 \frac{4}{9} = 1 + \frac{4}{9}$

STEP 3

To convert the mixed number into an improper fraction, we multiply the whole number by the denominator of the fraction and add the numerator.
$1 \frac{4}{9} = \frac{1 \times 9}{9} + \frac{4}{9}$

STEP 4

Now, calculate the improper fraction.
$1 \frac{4}{9} = \frac{9}{9} + \frac{4}{9} = \frac{9 + 4}{9}$

STEP 5

Simplify the improper fraction.
$1 \frac{4}{9} = \frac{13}{9}$

STEP 6

Now, we need to divide the improper fraction by the negative fraction.
$\frac{13}{9} \div \left(-\frac{2}{9}\right)$

STEP 7

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
$\frac{13}{9} \div \left(-\frac{2}{9}\right) = \frac{13}{9} \times \left(-\frac{9}{2}\right)$

STEP 8

Now, multiply the numerators and the denominators of the fractions.
$\frac{13}{9} \times \left(-\frac{9}{2}\right) = \frac{13 \times (-9)}{9 \times 2}$

STEP 9

Calculate the product of the numerators and the denominators.
$\frac{13 \times (-9)}{9 \times 2} = \frac{-117}{18}$

STEP 10

Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 117 and 18 is 9.

STEP 11

Now, divide both the numerator and the denominator by the GCD to simplify the fraction.
$\frac{-117}{18} = \frac{-117 \div 9}{18 \div 9}$

STEP 12

Calculate the simplified fraction.
$\frac{-117 \div 9}{18 \div 9} = \frac{-13}{2}$
The quotient is $-\frac{13}{2}$ , which is the answer in simplest form.

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Divide $1 \frac{4}{9}$ by $-\frac{2}{9}$ and write the quotient in simplest form.

STEP 1

Assumptions
1. We are given a mixed number $1 \frac{4}{9}$ .
2. We are given a negative fraction $-\frac{2}{9}$ .
3. We need to divide the mixed number by the negative fraction.
4. The final answer should be in simplest form.

STEP 2

First, we need to convert the mixed number into an improper fraction.
$1 \frac{4}{9} = 1 + \frac{4}{9}$

STEP 3

To convert the mixed number into an improper fraction, we multiply the whole number by the denominator of the fraction and add the numerator.
$1 \frac{4}{9} = \frac{1 \times 9}{9} + \frac{4}{9}$

STEP 4

Now, calculate the improper fraction.
$1 \frac{4}{9} = \frac{9}{9} + \frac{4}{9} = \frac{9 + 4}{9}$

STEP 5

Simplify the improper fraction.
$1 \frac{4}{9} = \frac{13}{9}$

STEP 6

Now, we need to divide the improper fraction by the negative fraction.
$\frac{13}{9} \div \left(-\frac{2}{9}\right)$

STEP 7

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
$\frac{13}{9} \div \left(-\frac{2}{9}\right) = \frac{13}{9} \times \left(-\frac{9}{2}\right)$

STEP 8

Now, multiply the numerators and the denominators of the fractions.
$\frac{13}{9} \times \left(-\frac{9}{2}\right) = \frac{13 \times (-9)}{9 \times 2}$

STEP 9

Calculate the product of the numerators and the denominators.
$\frac{13 \times (-9)}{9 \times 2} = \frac{-117}{18}$

STEP 10

Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 117 and 18 is 9.

STEP 11

Now, divide both the numerator and the denominator by the GCD to simplify the fraction.
$\frac{-117}{18} = \frac{-117 \div 9}{18 \div 9}$

STEP 12

Calculate the simplified fraction.
$\frac{-117 \div 9}{18 \div 9} = \frac{-13}{2}$
The quotient is $-\frac{13}{2}$ , which is the answer in simplest form.

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Divide 1491 \frac{4}{9}194​ by −29-\frac{2}{9}−92​ and write the quotient in simplest form.

STEP 1

Assumptions1. We are given a mixed number 1491 \frac{4}{9}194​.2. We are given a negative fraction −29-\frac{2}{9}−92​.3. We need to divide the mixed number by the negative fraction.4. The final answer should be in simplest form.

STEP 2

First, we need to convert the mixed number into an improper fraction.149=1+491 \frac{4}{9} = 1 + \frac{4}{9}194​=1+94​

STEP 3

To convert the mixed number into an improper fraction, we multiply the whole number by the denominator of the fraction and add the numerator.149=1×99+491 \frac{4}{9} = \frac{1 \times 9}{9} + \frac{4}{9}194​=91×9​+94​

STEP 4

Now, calculate the improper fraction.149=99+49=9+491 \frac{4}{9} = \frac{9}{9} + \frac{4}{9} = \frac{9 + 4}{9}194​=99​+94​=99+4​

STEP 5

Simplify the improper fraction.149=1391 \frac{4}{9} = \frac{13}{9}194​=913​

STEP 6

Now, we need to divide the improper fraction by the negative fraction.139÷(−29)\frac{13}{9} \div \left(-\frac{2}{9}\right)913​÷(−92​)

STEP 7

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.139÷(−29)=139×(−92)\frac{13}{9} \div \left(-\frac{2}{9}\right) = \frac{13}{9} \times \left(-\frac{9}{2}\right)913​÷(−92​)=913​×(−29​)

STEP 8

Now, multiply the numerators and the denominators of the fractions.139×(−92)=13×(−9)9×2\frac{13}{9} \times \left(-\frac{9}{2}\right) = \frac{13 \times (-9)}{9 \times 2}913​×(−29​)=9×213×(−9)​

STEP 9

Calculate the product of the numerators and the denominators.13×(−9)9×2=−11718\frac{13 \times (-9)}{9 \times 2} = \frac{-117}{18}9×213×(−9)​=18−117​

STEP 10

Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator.The GCD of 117 and 18 is 9.

STEP 11

Now, divide both the numerator and the denominator by the GCD to simplify the fraction.−11718=−117÷918÷9\frac{-117}{18} = \frac{-117 \div 9}{18 \div 9}18−117​=18÷9−117÷9​

STEP 12

Calculate the simplified fraction.−117÷918÷9=−132\frac{-117 \div 9}{18 \div 9} = \frac{-13}{2}18÷9−117÷9​=2−13​The quotient is −132-\frac{13}{2}−213​, which is the answer in simplest form.

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Divide $1 \frac{4}{9}$ by $-\frac{2}{9}$ and write the quotient in simplest form.

Assumptions
1. We are given a mixed number $1 \frac{4}{9}$ .
2. We are given a negative fraction $-\frac{2}{9}$ .
3. We need to divide the mixed number by the negative fraction.
4. The final answer should be in simplest form.

First, we need to convert the mixed number into an improper fraction.
$1 \frac{4}{9} = 1 + \frac{4}{9}$

To convert the mixed number into an improper fraction, we multiply the whole number by the denominator of the fraction and add the numerator.
$1 \frac{4}{9} = \frac{1 \times 9}{9} + \frac{4}{9}$

Now, calculate the improper fraction.
$1 \frac{4}{9} = \frac{9}{9} + \frac{4}{9} = \frac{9 + 4}{9}$

Simplify the improper fraction.
$1 \frac{4}{9} = \frac{13}{9}$

Now, we need to divide the improper fraction by the negative fraction.
$\frac{13}{9} \div \left(-\frac{2}{9}\right)$

To divide fractions, we multiply the first fraction by the reciprocal of the second fraction.
$\frac{13}{9} \div \left(-\frac{2}{9}\right) = \frac{13}{9} \times \left(-\frac{9}{2}\right)$

Now, multiply the numerators and the denominators of the fractions.
$\frac{13}{9} \times \left(-\frac{9}{2}\right) = \frac{13 \times (-9)}{9 \times 2}$

Calculate the product of the numerators and the denominators.
$\frac{13 \times (-9)}{9 \times 2} = \frac{-117}{18}$

Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 117 and 18 is 9.

Now, divide both the numerator and the denominator by the GCD to simplify the fraction.
$\frac{-117}{18} = \frac{-117 \div 9}{18 \div 9}$

Calculate the simplified fraction.
$\frac{-117 \div 9}{18 \div 9} = \frac{-13}{2}$
The quotient is $-\frac{13}{2}$ , which is the answer in simplest form.