Question

complex fractions and unit rates- homewori simplify: (show all your work.) 1. \\(\frac{\frac{18}{3}}{\frac{3}{4}}\\) 2. \\(\frac{\frac{3}{6}}{4}\\) 3. \\(\frac{\frac{1}{3}}{\frac{1}{4}}\\) 4. pep club members are making spirit buttons. they make 490 spirit buttons in 3 \\(\frac{1}{2}\\) h find the number of buttons the pep club makes per hour. mary is making pillows for her life skill class. she bought 2 \\(\frac{1}{2}\\) yards of fabric. her cost was $15. what was the cost per yard?

Explanation:

Problem 1: Simplify $\boldsymbol{\frac{\frac{18}{3}}{\frac{3}{4}}}$

Step1: Recall dividing by a fraction rule

Dividing by a fraction is multiplying by its reciprocal. So $\frac{\frac{18}{3}}{\frac{3}{4}}=\frac{18}{3}\times\frac{4}{3}$.

Step2: Simplify $\frac{18}{3}$

$\frac{18}{3} = 6$.

Step3: Multiply the results

$6\times\frac{4}{3}=\frac{24}{3}=8$.

Step1: Recall dividing by a number rule

Dividing by a number is multiplying by its reciprocal. So $\frac{\frac{3}{6}}{4}=\frac{3}{6}\times\frac{1}{4}$.

Step2: Simplify $\frac{3}{6}$

$\frac{3}{6}=\frac{1}{2}$.

Step3: Multiply the results

$\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}$. (Wait, original problem might be $\frac{\frac{3}{6}}{\frac{4}{1}}$? Wait, the original is $\frac{\frac{3}{6}}{4}$? Wait, looking at the image, the second problem is $\frac{\frac{3}{6}}{4}$? Wait, no, the user's image shows the second problem as $\frac{\frac{3}{6}}{4}$? Wait, no, the numerator is $\frac{3}{6}$ and denominator is $4$? Wait, maybe I misread. Wait, the second problem is $\frac{\frac{3}{6}}{4}$? Wait, no, the original is $\frac{\frac{3}{6}}{4}$? Wait, let's re - check. The second problem is $\frac{\frac{3}{6}}{4}$. So:

Step1: Simplify $\frac{3}{6}$

$\frac{3}{6}=\frac{1}{2}$.

Step2: Divide by 4 (multiply by $\frac{1}{4}$)

$\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}$. Wait, but maybe the problem is $\frac{\frac{3}{6}}{\frac{4}{1}}$? No, the denominator is $4$, which is $\frac{4}{1}$. So the correct simplification:

Step1: $\frac{\frac{3}{6}}{4}=\frac{3}{6}\div4=\frac{3}{6}\times\frac{1}{4}$

Step2: Simplify $\frac{3}{6}$ to $\frac{1}{2}$

Step3: $\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}$

Step1: Recall dividing by a fraction rule

Dividing by a fraction is multiplying by its reciprocal. So $\frac{\frac{1}{3}}{\frac{1}{4}}=\frac{1}{3}\times\frac{4}{1}$.

Step2: Multiply the fractions

$\frac{1\times4}{3\times1}=\frac{4}{3}$.

Answer:

$8$

Problem 2: Simplify $\boldsymbol{\frac{\frac{3}{6}}{\frac{4}{1}}}$ (Note: $\frac{3}{6}$ over $4$ is $\frac{\frac{3}{6}}{4}$)