Solved on Jan 29, 2024

Find the quotient of 3 divided by 5/6. Determine which of the following is the correct answer: $3 \frac{2}{5}$ , $3 \frac{3}{6}$ , $3 \frac{3}{5}$ , or $3 \frac{5}{6}$ .

STEP 1

Assumptions
1. We are asked to find the quotient of $3$ divided by $\frac{5}{6}$ .
2. The result will be in the form of a mixed number.

STEP 2

To divide by a fraction, we multiply by its reciprocal. The reciprocal of $\frac{5}{6}$ is $\frac{6}{5}$ .
$3 \div \frac{5}{6} = 3 \times \frac{6}{5}$

STEP 3

Now, we multiply the whole number $3$ by the fraction $\frac{6}{5}$ .
$3 \times \frac{6}{5} = \frac{3}{1} \times \frac{6}{5}$

STEP 4

Multiply the numerators together and the denominators together.
$\frac{3}{1} \times \frac{6}{5} = \frac{3 \times 6}{1 \times 5}$

STEP 5

Calculate the product of the numerators and denominators.
$\frac{3 \times 6}{1 \times 5} = \frac{18}{5}$

STEP 6

The fraction $\frac{18}{5}$ is an improper fraction, so we will convert it to a mixed number. To do this, divide the numerator by the denominator.
$\frac{18}{5} = 3 \text{ remainder } 3$

STEP 7

The quotient of the division gives us the whole number part of the mixed number, and the remainder gives us the new numerator of the fractional part.
$3 \text{ remainder } 3 = 3 \frac{3}{5}$

STEP 8

Therefore, the quotient of $3 \div \frac{5}{6}$ is $3 \frac{3}{5}$ .
The correct answer is $3 \frac{3}{5}$ .

Was this helpful?

Find the quotient of 3 divided by 5/6. Determine which of the following is the correct answer: $3 \frac{2}{5}$ , $3 \frac{3}{6}$ , $3 \frac{3}{5}$ , or $3 \frac{5}{6}$ .

STEP 1

Assumptions
1. We are asked to find the quotient of $3$ divided by $\frac{5}{6}$ .
2. The result will be in the form of a mixed number.

STEP 2

To divide by a fraction, we multiply by its reciprocal. The reciprocal of $\frac{5}{6}$ is $\frac{6}{5}$ .
$3 \div \frac{5}{6} = 3 \times \frac{6}{5}$

STEP 3

Now, we multiply the whole number $3$ by the fraction $\frac{6}{5}$ .
$3 \times \frac{6}{5} = \frac{3}{1} \times \frac{6}{5}$

STEP 4

Multiply the numerators together and the denominators together.
$\frac{3}{1} \times \frac{6}{5} = \frac{3 \times 6}{1 \times 5}$

STEP 5

Calculate the product of the numerators and denominators.
$\frac{3 \times 6}{1 \times 5} = \frac{18}{5}$

STEP 6

The fraction $\frac{18}{5}$ is an improper fraction, so we will convert it to a mixed number. To do this, divide the numerator by the denominator.
$\frac{18}{5} = 3 \text{ remainder } 3$

STEP 7

The quotient of the division gives us the whole number part of the mixed number, and the remainder gives us the new numerator of the fractional part.
$3 \text{ remainder } 3 = 3 \frac{3}{5}$

STEP 8

Therefore, the quotient of $3 \div \frac{5}{6}$ is $3 \frac{3}{5}$ .
The correct answer is $3 \frac{3}{5}$ .

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the quotient of 3 divided by 5/6. Determine which of the following is the correct answer: 3253 \frac{2}{5}352​, 3363 \frac{3}{6}363​, 3353 \frac{3}{5}353​, or 3563 \frac{5}{6}365​.

STEP 1

Assumptions1. We are asked to find the quotient of 333 divided by 56\frac{5}{6}65​.2. The result will be in the form of a mixed number.

STEP 2

To divide by a fraction, we multiply by its reciprocal. The reciprocal of 56\frac{5}{6}65​ is 65\frac{6}{5}56​.3÷56=3×653 \div \frac{5}{6} = 3 \times \frac{6}{5}3÷65​=3×56​

STEP 3

Now, we multiply the whole number 333 by the fraction 65\frac{6}{5}56​.3×65=31×653 \times \frac{6}{5} = \frac{3}{1} \times \frac{6}{5}3×56​=13​×56​

STEP 4

Multiply the numerators together and the denominators together.31×65=3×61×5\frac{3}{1} \times \frac{6}{5} = \frac{3 \times 6}{1 \times 5}13​×56​=1×53×6​

STEP 5

Calculate the product of the numerators and denominators.3×61×5=185\frac{3 \times 6}{1 \times 5} = \frac{18}{5}1×53×6​=518​

STEP 6

The fraction 185\frac{18}{5}518​ is an improper fraction, so we will convert it to a mixed number. To do this, divide the numerator by the denominator.185=3 remainder 3\frac{18}{5} = 3 \text{ remainder } 3518​=3 remainder 3

STEP 7

The quotient of the division gives us the whole number part of the mixed number, and the remainder gives us the new numerator of the fractional part.3 remainder 3=3353 \text{ remainder } 3 = 3 \frac{3}{5}3 remainder 3=353​

STEP 8

Therefore, the quotient of 3÷563 \div \frac{5}{6}3÷65​ is 3353 \frac{3}{5}353​.The correct answer is 3353 \frac{3}{5}353​.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Find the quotient of 3 divided by 5/6. Determine which of the following is the correct answer: $3 \frac{2}{5}$ , $3 \frac{3}{6}$ , $3 \frac{3}{5}$ , or $3 \frac{5}{6}$ .

Assumptions
1. We are asked to find the quotient of $3$ divided by $\frac{5}{6}$ .
2. The result will be in the form of a mixed number.

To divide by a fraction, we multiply by its reciprocal. The reciprocal of $\frac{5}{6}$ is $\frac{6}{5}$ .
$3 \div \frac{5}{6} = 3 \times \frac{6}{5}$

Now, we multiply the whole number $3$ by the fraction $\frac{6}{5}$ .
$3 \times \frac{6}{5} = \frac{3}{1} \times \frac{6}{5}$

Multiply the numerators together and the denominators together.
$\frac{3}{1} \times \frac{6}{5} = \frac{3 \times 6}{1 \times 5}$

Calculate the product of the numerators and denominators.
$\frac{3 \times 6}{1 \times 5} = \frac{18}{5}$

The fraction $\frac{18}{5}$ is an improper fraction, so we will convert it to a mixed number. To do this, divide the numerator by the denominator.
$\frac{18}{5} = 3 \text{ remainder } 3$

The quotient of the division gives us the whole number part of the mixed number, and the remainder gives us the new numerator of the fractional part.
$3 \text{ remainder } 3 = 3 \frac{3}{5}$

Therefore, the quotient of $3 \div \frac{5}{6}$ is $3 \frac{3}{5}$ .
The correct answer is $3 \frac{3}{5}$ .