Solved on Feb 15, 2024

Solve $\frac{2}{3} \div \frac{4}{5}$ . SELECT ALL THAT APPLY: $\frac{5}{6}$ , $\frac{8}{15}$ , $\frac{12}{10}$ , $\frac{10}{12}$ , $1 \frac{5}{6}$ .

STEP 1

Assumptions
1. We are given the division problem $\frac{2}{3} \div \frac{4}{5}$ .
2. We need to determine which of the given options are correct solutions to the division problem.

STEP 2

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction.
$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$

STEP 3

Apply the rule to the given division problem.
$\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4}$

STEP 4

Multiply the numerators and the denominators of the fractions.
$\frac{2 \times 5}{3 \times 4} = \frac{10}{12}$

STEP 5

Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 10 and 12 is 2.

STEP 6

Divide both the numerator and the denominator by the GCD to simplify the fraction.
$\frac{10 \div 2}{12 \div 2} = \frac{5}{6}$

STEP 7

Now we have the simplified fraction $\frac{5}{6}$ . We check this against the given options.
$\frac{5}{6}$ is one of the given options.

STEP 8

We also need to check if any other given options are equivalent to $\frac{5}{6}$ .
The option $\frac{10}{12}$ is the unsimplified form of $\frac{5}{6}$ .

STEP 9

Check if the option $1 \frac{5}{6}$ is equivalent to $\frac{5}{6}$ .
$1 \frac{5}{6}$ is a mixed number and not equal to $\frac{5}{6}$ .

STEP 10

Check if the option $\frac{8}{15}$ is equivalent to $\frac{5}{6}$ .
$\frac{8}{15}$ cannot be simplified to $\frac{5}{6}$ , so it is not equivalent.

STEP 11

Check if the option $\frac{12}{10}$ is equivalent to $\frac{5}{6}$ .
$\frac{12}{10}$ simplifies to $\frac{6}{5}$ , which is not equivalent to $\frac{5}{6}$ .

STEP 12

The correct solutions to the division problem are the options that are equivalent to $\frac{5}{6}$ .
The correct answers are $\frac{5}{6}$ and $\frac{10}{12}$ .
$\frac{5}{6}$ and $\frac{10}{12}$ are the solutions to the division problem $\frac{2}{3} \div \frac{4}{5}$ .

Was this helpful?

Solve $\frac{2}{3} \div \frac{4}{5}$ . SELECT ALL THAT APPLY: $\frac{5}{6}$ , $\frac{8}{15}$ , $\frac{12}{10}$ , $\frac{10}{12}$ , $1 \frac{5}{6}$ .

STEP 1

Assumptions
1. We are given the division problem $\frac{2}{3} \div \frac{4}{5}$ .
2. We need to determine which of the given options are correct solutions to the division problem.

STEP 2

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction.
$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$

STEP 3

Apply the rule to the given division problem.
$\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4}$

STEP 4

Multiply the numerators and the denominators of the fractions.
$\frac{2 \times 5}{3 \times 4} = \frac{10}{12}$

STEP 5

Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 10 and 12 is 2.

STEP 6

Divide both the numerator and the denominator by the GCD to simplify the fraction.
$\frac{10 \div 2}{12 \div 2} = \frac{5}{6}$

STEP 7

Now we have the simplified fraction $\frac{5}{6}$ . We check this against the given options.
$\frac{5}{6}$ is one of the given options.

STEP 8

We also need to check if any other given options are equivalent to $\frac{5}{6}$ .
The option $\frac{10}{12}$ is the unsimplified form of $\frac{5}{6}$ .

STEP 9

Check if the option $1 \frac{5}{6}$ is equivalent to $\frac{5}{6}$ .
$1 \frac{5}{6}$ is a mixed number and not equal to $\frac{5}{6}$ .

STEP 10

Check if the option $\frac{8}{15}$ is equivalent to $\frac{5}{6}$ .
$\frac{8}{15}$ cannot be simplified to $\frac{5}{6}$ , so it is not equivalent.

STEP 11

Check if the option $\frac{12}{10}$ is equivalent to $\frac{5}{6}$ .
$\frac{12}{10}$ simplifies to $\frac{6}{5}$ , which is not equivalent to $\frac{5}{6}$ .

STEP 12

The correct solutions to the division problem are the options that are equivalent to $\frac{5}{6}$ .
The correct answers are $\frac{5}{6}$ and $\frac{10}{12}$ .
$\frac{5}{6}$ and $\frac{10}{12}$ are the solutions to the division problem $\frac{2}{3} \div \frac{4}{5}$ .

Start learning now

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

Solve 23÷45\frac{2}{3} \div \frac{4}{5}32​÷54​. SELECT ALL THAT APPLY: 56\frac{5}{6}65​, 815\frac{8}{15}158​, 1210\frac{12}{10}1012​, 1012\frac{10}{12}1210​, 1561 \frac{5}{6}165​.

STEP 1

Assumptions1. We are given the division problem 23÷45\frac{2}{3} \div \frac{4}{5}32​÷54​.2. We need to determine which of the given options are correct solutions to the division problem.

STEP 2

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction.ab÷cd=ab×dc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}ba​÷dc​=ba​×cd​

STEP 3

Apply the rule to the given division problem.23÷45=23×54\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4}32​÷54​=32​×45​

STEP 4

Multiply the numerators and the denominators of the fractions.2×53×4=1012\frac{2 \times 5}{3 \times 4} = \frac{10}{12}3×42×5​=1210​

STEP 5

Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator.The GCD of 10 and 12 is 2.

STEP 6

Divide both the numerator and the denominator by the GCD to simplify the fraction.10÷212÷2=56\frac{10 \div 2}{12 \div 2} = \frac{5}{6}12÷210÷2​=65​

STEP 7

Now we have the simplified fraction 56\frac{5}{6}65​. We check this against the given options.56\frac{5}{6}65​ is one of the given options.

STEP 8

We also need to check if any other given options are equivalent to 56\frac{5}{6}65​.The option 1012\frac{10}{12}1210​ is the unsimplified form of 56\frac{5}{6}65​.

STEP 9

Check if the option 1561 \frac{5}{6}165​ is equivalent to 56\frac{5}{6}65​.1561 \frac{5}{6}165​ is a mixed number and not equal to 56\frac{5}{6}65​.

STEP 10

Check if the option 815\frac{8}{15}158​ is equivalent to 56\frac{5}{6}65​.815\frac{8}{15}158​ cannot be simplified to 56\frac{5}{6}65​, so it is not equivalent.

STEP 11

Check if the option 1210\frac{12}{10}1012​ is equivalent to 56\frac{5}{6}65​.1210\frac{12}{10}1012​ simplifies to 65\frac{6}{5}56​, which is not equivalent to 56\frac{5}{6}65​.

STEP 12

Start learning now

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

Solve $\frac{2}{3} \div \frac{4}{5}$ . SELECT ALL THAT APPLY: $\frac{5}{6}$ , $\frac{8}{15}$ , $\frac{12}{10}$ , $\frac{10}{12}$ , $1 \frac{5}{6}$ .

Assumptions
1. We are given the division problem $\frac{2}{3} \div \frac{4}{5}$ .
2. We need to determine which of the given options are correct solutions to the division problem.

To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction.
$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$

Apply the rule to the given division problem.
$\frac{2}{3} \div \frac{4}{5} = \frac{2}{3} \times \frac{5}{4}$

Multiply the numerators and the denominators of the fractions.
$\frac{2 \times 5}{3 \times 4} = \frac{10}{12}$

Simplify the fraction by finding the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 10 and 12 is 2.

Divide both the numerator and the denominator by the GCD to simplify the fraction.
$\frac{10 \div 2}{12 \div 2} = \frac{5}{6}$

Now we have the simplified fraction $\frac{5}{6}$ . We check this against the given options.
$\frac{5}{6}$ is one of the given options.

We also need to check if any other given options are equivalent to $\frac{5}{6}$ .
The option $\frac{10}{12}$ is the unsimplified form of $\frac{5}{6}$ .

Check if the option $1 \frac{5}{6}$ is equivalent to $\frac{5}{6}$ .
$1 \frac{5}{6}$ is a mixed number and not equal to $\frac{5}{6}$ .

Check if the option $\frac{8}{15}$ is equivalent to $\frac{5}{6}$ .
$\frac{8}{15}$ cannot be simplified to $\frac{5}{6}$ , so it is not equivalent.

Check if the option $\frac{12}{10}$ is equivalent to $\frac{5}{6}$ .
$\frac{12}{10}$ simplifies to $\frac{6}{5}$ , which is not equivalent to $\frac{5}{6}$ .