Solved on Jan 26, 2024

Divide and simplify $\frac{15}{6}$ divided by $\frac{11}{3}$ .

STEP 1

Assumptions
1. We are given two fractions: $\frac{15}{6}$ and $\frac{11}{3}$ .
2. We need to divide the first fraction by the second fraction.
3. Simplification of the result, if possible, is required.

STEP 2

To divide one fraction by another, we multiply the first fraction by the reciprocal of the second fraction.
$\left(\frac{a}{b}\right) \div \left(\frac{c}{d}\right) = \left(\frac{a}{b}\right) \times \left(\frac{d}{c}\right)$

STEP 3

Identify the reciprocal of the second fraction $\frac{11}{3}$ .
$Reciprocal\, of\, \frac{11}{3} = \frac{3}{11}$

STEP 4

Now, multiply the first fraction $\frac{15}{6}$ by the reciprocal of the second fraction $\frac{3}{11}$ .
$\frac{15}{6} \div \frac{11}{3} = \frac{15}{6} \times \frac{3}{11}$

STEP 5

Multiply the numerators together and the denominators together.
$\frac{15 \times 3}{6 \times 11}$

STEP 6

Calculate the multiplication of the numerators and denominators.
$\frac{15 \times 3}{6 \times 11} = \frac{45}{66}$

STEP 7

Simplify the resulting fraction by finding the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 45 and 66 is 3.

STEP 8

Divide both the numerator and the denominator by the GCD to simplify the fraction.
$\frac{45 \div 3}{66 \div 3} = \frac{15}{22}$

STEP 9

The simplified result of the division $\frac{15}{6} \div \frac{11}{3}$ is $\frac{15}{22}$ .
The simplified answer is $\frac{15}{22}$ .

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Divide and simplify $\frac{15}{6}$ divided by $\frac{11}{3}$ .

STEP 1

Assumptions
1. We are given two fractions: $\frac{15}{6}$ and $\frac{11}{3}$ .
2. We need to divide the first fraction by the second fraction.
3. Simplification of the result, if possible, is required.

STEP 2

To divide one fraction by another, we multiply the first fraction by the reciprocal of the second fraction.
$\left(\frac{a}{b}\right) \div \left(\frac{c}{d}\right) = \left(\frac{a}{b}\right) \times \left(\frac{d}{c}\right)$

STEP 3

Identify the reciprocal of the second fraction $\frac{11}{3}$ .
$Reciprocal\, of\, \frac{11}{3} = \frac{3}{11}$

STEP 4

Now, multiply the first fraction $\frac{15}{6}$ by the reciprocal of the second fraction $\frac{3}{11}$ .
$\frac{15}{6} \div \frac{11}{3} = \frac{15}{6} \times \frac{3}{11}$

STEP 5

Multiply the numerators together and the denominators together.
$\frac{15 \times 3}{6 \times 11}$

STEP 6

Calculate the multiplication of the numerators and denominators.
$\frac{15 \times 3}{6 \times 11} = \frac{45}{66}$

STEP 7

Simplify the resulting fraction by finding the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 45 and 66 is 3.

STEP 8

Divide both the numerator and the denominator by the GCD to simplify the fraction.
$\frac{45 \div 3}{66 \div 3} = \frac{15}{22}$

STEP 9

The simplified result of the division $\frac{15}{6} \div \frac{11}{3}$ is $\frac{15}{22}$ .
The simplified answer is $\frac{15}{22}$ .

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Divide and simplify 156\frac{15}{6}615​ divided by 113\frac{11}{3}311​.

STEP 1

Assumptions1. We are given two fractions: 156\frac{15}{6}615​ and 113\frac{11}{3}311​.2. We need to divide the first fraction by the second fraction.3. Simplification of the result, if possible, is required.

STEP 2

To divide one fraction by another, we multiply the first fraction by the reciprocal of the second fraction.(ab)÷(cd)=(ab)×(dc)\left(\frac{a}{b}\right) \div \left(\frac{c}{d}\right) = \left(\frac{a}{b}\right) \times \left(\frac{d}{c}\right)(ba​)÷(dc​)=(ba​)×(cd​)

STEP 3

Identify the reciprocal of the second fraction 113\frac{11}{3}311​.Reciprocal of 113=311Reciprocal\, of\, \frac{11}{3} = \frac{3}{11}Reciprocalof311​=113​

STEP 4

Now, multiply the first fraction 156\frac{15}{6}615​ by the reciprocal of the second fraction 311\frac{3}{11}113​.156÷113=156×311\frac{15}{6} \div \frac{11}{3} = \frac{15}{6} \times \frac{3}{11}615​÷311​=615​×113​

STEP 5

Multiply the numerators together and the denominators together.15×36×11\frac{15 \times 3}{6 \times 11}6×1115×3​

STEP 6

Calculate the multiplication of the numerators and denominators.15×36×11=4566\frac{15 \times 3}{6 \times 11} = \frac{45}{66}6×1115×3​=6645​

STEP 7

Simplify the resulting fraction by finding the greatest common divisor (GCD) of the numerator and the denominator.The GCD of 45 and 66 is 3.

STEP 8

Divide both the numerator and the denominator by the GCD to simplify the fraction.45÷366÷3=1522\frac{45 \div 3}{66 \div 3} = \frac{15}{22}66÷345÷3​=2215​

STEP 9

The simplified result of the division 156÷113\frac{15}{6} \div \frac{11}{3}615​÷311​ is 1522\frac{15}{22}2215​.The simplified answer is 1522\frac{15}{22}2215​.

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Divide and simplify $\frac{15}{6}$ divided by $\frac{11}{3}$ .

Assumptions
1. We are given two fractions: $\frac{15}{6}$ and $\frac{11}{3}$ .
2. We need to divide the first fraction by the second fraction.
3. Simplification of the result, if possible, is required.

To divide one fraction by another, we multiply the first fraction by the reciprocal of the second fraction.
$\left(\frac{a}{b}\right) \div \left(\frac{c}{d}\right) = \left(\frac{a}{b}\right) \times \left(\frac{d}{c}\right)$

Identify the reciprocal of the second fraction $\frac{11}{3}$ .
$Reciprocal\, of\, \frac{11}{3} = \frac{3}{11}$

Now, multiply the first fraction $\frac{15}{6}$ by the reciprocal of the second fraction $\frac{3}{11}$ .
$\frac{15}{6} \div \frac{11}{3} = \frac{15}{6} \times \frac{3}{11}$

Multiply the numerators together and the denominators together.
$\frac{15 \times 3}{6 \times 11}$

Calculate the multiplication of the numerators and denominators.
$\frac{15 \times 3}{6 \times 11} = \frac{45}{66}$

Simplify the resulting fraction by finding the greatest common divisor (GCD) of the numerator and the denominator.
The GCD of 45 and 66 is 3.

Divide both the numerator and the denominator by the GCD to simplify the fraction.
$\frac{45 \div 3}{66 \div 3} = \frac{15}{22}$

The simplified result of the division $\frac{15}{6} \div \frac{11}{3}$ is $\frac{15}{22}$ .
The simplified answer is $\frac{15}{22}$ .