Math / Numbers & Operations

QuestionDivide. Write your answer in simplest form. $\frac{7}{10} \div \frac{5}{16}$

Studdy Solution

STEP 1

1. The problem involves dividing two fractions.
2. Division of fractions can be converted into multiplication by the reciprocal of the divisor.
3. The final answer should be in its simplest form.

STEP 2

1. Convert the division of fractions into multiplication by the reciprocal.
2. Multiply the numerators and denominators of the fractions.
3. Simplify the resulting fraction to its simplest form.

STEP 3

Convert the division problem into a multiplication problem by taking the reciprocal of the divisor.
$\frac{7}{10} \div \frac{5}{16} = \frac{7}{10} \times \frac{16}{5}$

STEP 4

Multiply the numerators together and the denominators together.
$\frac{7 \times 16}{10 \times 5}$

STEP 5

Calculate the products in the numerator and the denominator.
$\frac{7 \times 16}{10 \times 5} = \frac{112}{50}$

STEP 6

Simplify the fraction $\frac{112}{50}$ by finding the greatest common divisor (GCD) of 112 and 50, which is 2.
$\frac{112 \div 2}{50 \div 2} = \frac{56}{25}$

STEP 7

Ensure the fraction $\frac{56}{25}$ is in simplest form. Since 56 and 25 have no common divisors other than 1, the fraction is already simplified.
$\frac{56}{25}$
Therefore, the answer is $\frac{56}{25}$ .

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QuestionDivide. Write your answer in simplest form. $\frac{7}{10} \div \frac{5}{16}$

Studdy Solution

STEP 1

1. The problem involves dividing two fractions.
2. Division of fractions can be converted into multiplication by the reciprocal of the divisor.
3. The final answer should be in its simplest form.

STEP 2

1. Convert the division of fractions into multiplication by the reciprocal.
2. Multiply the numerators and denominators of the fractions.
3. Simplify the resulting fraction to its simplest form.

STEP 3

Convert the division problem into a multiplication problem by taking the reciprocal of the divisor.
$\frac{7}{10} \div \frac{5}{16} = \frac{7}{10} \times \frac{16}{5}$

STEP 4

Multiply the numerators together and the denominators together.
$\frac{7 \times 16}{10 \times 5}$

STEP 5

Calculate the products in the numerator and the denominator.
$\frac{7 \times 16}{10 \times 5} = \frac{112}{50}$

STEP 6

Simplify the fraction $\frac{112}{50}$ by finding the greatest common divisor (GCD) of 112 and 50, which is 2.
$\frac{112 \div 2}{50 \div 2} = \frac{56}{25}$

STEP 7

Ensure the fraction $\frac{56}{25}$ is in simplest form. Since 56 and 25 have no common divisors other than 1, the fraction is already simplified.
$\frac{56}{25}$
Therefore, the answer is $\frac{56}{25}$ .

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QuestionDivide. Write your answer in simplest form. 710÷516\frac{7}{10} \div \frac{5}{16}107​÷165​

Studdy Solution

STEP 1

1. The problem involves dividing two fractions.2. Division of fractions can be converted into multiplication by the reciprocal of the divisor.3. The final answer should be in its simplest form.

STEP 2

1. Convert the division of fractions into multiplication by the reciprocal.2. Multiply the numerators and denominators of the fractions.3. Simplify the resulting fraction to its simplest form.

STEP 3

Convert the division problem into a multiplication problem by taking the reciprocal of the divisor.710÷516=710×165\frac{7}{10} \div \frac{5}{16} = \frac{7}{10} \times \frac{16}{5}107​÷165​=107​×516​

STEP 4

Multiply the numerators together and the denominators together.7×1610×5\frac{7 \times 16}{10 \times 5}10×57×16​

STEP 5

Calculate the products in the numerator and the denominator.7×1610×5=11250\frac{7 \times 16}{10 \times 5} = \frac{112}{50}10×57×16​=50112​

STEP 6

Simplify the fraction 11250\frac{112}{50}50112​ by finding the greatest common divisor (GCD) of 112 and 50, which is 2.112÷250÷2=5625\frac{112 \div 2}{50 \div 2} = \frac{56}{25}50÷2112÷2​=2556​

STEP 7

Ensure the fraction 5625\frac{56}{25}2556​ is in simplest form. Since 56 and 25 have no common divisors other than 1, the fraction is already simplified.5625\frac{56}{25}2556​Therefore, the answer is 5625\frac{56}{25}2556​.

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Studdy solves anything!

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

QuestionDivide. Write your answer in simplest form. $\frac{7}{10} \div \frac{5}{16}$

1. The problem involves dividing two fractions.
2. Division of fractions can be converted into multiplication by the reciprocal of the divisor.
3. The final answer should be in its simplest form.

1. Convert the division of fractions into multiplication by the reciprocal.
2. Multiply the numerators and denominators of the fractions.
3. Simplify the resulting fraction to its simplest form.

Convert the division problem into a multiplication problem by taking the reciprocal of the divisor.
$\frac{7}{10} \div \frac{5}{16} = \frac{7}{10} \times \frac{16}{5}$

Multiply the numerators together and the denominators together.
$\frac{7 \times 16}{10 \times 5}$

Calculate the products in the numerator and the denominator.
$\frac{7 \times 16}{10 \times 5} = \frac{112}{50}$

Simplify the fraction $\frac{112}{50}$ by finding the greatest common divisor (GCD) of 112 and 50, which is 2.
$\frac{112 \div 2}{50 \div 2} = \frac{56}{25}$

Ensure the fraction $\frac{56}{25}$ is in simplest form. Since 56 and 25 have no common divisors other than 1, the fraction is already simplified.
$\frac{56}{25}$
Therefore, the answer is $\frac{56}{25}$ .