Fractional Unit Rate and Equivalent Rate Review

Problem: Movie tickets are 3 for 33.75. Roller skating costs 46 dollars for 4 students. How much will 12 students save by going to the movies?

Movies:

\( 12 \div 3 = 4 \)

\( 33.75 \times 4 = 135 \)

Skating:

\( 12 \div 4 = 3 \)

\( 46 \times 3 = 138 \)

Compare the totals:

\( 138 - 135 = 3 \)

Answer: They save 3 dollars by going to the movies.

Problem: Emma reached 4 people in 25 phone calls. Kyler reached 2 people in 10 phone calls. Who will reach more people in 50 calls? How many more?

Emma:

\( \frac{4}{25} = \frac{x}{50} \)

\( 25 \times 2 = 50 \), so \( 4 \times 2 = 8 \)

Emma reaches 8 people.

Kyler:

\( \frac{2}{10} = \frac{x}{50} \)

\( 10 \times 5 = 50 \), so \( 2 \times 5 = 10 \)

Kyler reaches 10 people.

\( 10 - 8 = 2 \)

Answer: Kyler reaches 2 more people.

Problem: Machine A pops 15.75 ounces in 3 minutes. Machine B pops 22 ounces in 4 minutes. If each runs for 10 minutes, will there be enough for twelve 9-ounce bags?

Machine A unit rate:

\( 15.75 \div 3 = 5.25 \)

In 10 minutes:

\( 5.25 \times 10 = 52.5 \)

Machine B unit rate:

\( 22 \div 4 = 5.5 \)

In 10 minutes:

\( 5.5 \times 10 = 55 \)

Total popcorn:

\( 52.5 + 55 = 107.5 \)

Needed:

\( 12 \times 9 = 108 \)

Answer: No. They are \(0.5\) ounce short.

Problem: Daniel typed a 32-word paragraph in \( \frac{2}{3} \) of a minute. What is his typing speed in words per minute?

Words per minute means words for 1 minute.

Set up the rate:

\( \frac{32\text{ words}}{\frac{2}{3}\text{ minute}} \)

Divide by \( \frac{2}{3} \):

\( 32 \div \frac{2}{3} \)

Multiply by the reciprocal:

\( 32 \times \frac{3}{2} \)

\( 16 \times 3 = 48 \)

Answer: 48 words per minute

Problem: Isela took \( \frac{1}{4} \) hour to knit \( \frac{2}{5} \) of a foot of scarf. What is her speed in feet per hour?

Feet per hour means feet for 1 hour.

Set up the rate:

\( \frac{\frac{2}{5}\text{ ft}}{\frac{1}{4}\text{ hour}} \)

Divide:

\( \frac{2}{5} \div \frac{1}{4} \)

Multiply by the reciprocal:

\( \frac{2}{5} \times \frac{4}{1} = \frac{8}{5} \)

\( \frac{8}{5} = 1\frac{3}{5} \)

Answer: \(1\frac{3}{5}\) feet per hour

Problem: Reid completed 60 jumping jacks in \( \frac{2}{3} \) of a minute. Saif completed 40 jumping jacks in \( \frac{1}{2} \) of a minute. Who had more jumps per minute and by how much?

Reid:

\( 60 \div \frac{2}{3} = 60 \times \frac{3}{2} = 90 \)

Reid did 90 jumps per minute.

Saif:

\( 40 \div \frac{1}{2} = 40 \times 2 = 80 \)

Saif did 80 jumps per minute.

Compare:

\( 90 - 80 = 10 \)

Answer: Reid had 10 more jumps per minute.