3.4 Rational Numbers

Which of the following are perfect squares?

1. 45
2. 144

Determine which of the following are rational numbers:

1. $\sqrt{73}$
2. $4.556$
3. $3 \frac{1}{5}$
4. $\frac{41}{17}$
5. $5 . \bar{64}$

Determine if $\frac{12}{30}$ and $\frac{14}{35}$ are equivalent fractions.

Express the following rational numbers in lowest terms:

1. $\frac{36}{48}$
2. $\frac{100}{250}$
3. $\frac{51}{136}$

Calculate $\frac{23}{42} + \frac{9}{56}$ using Desmos.

Calculate $\frac{13}{28} + \frac{7}{28}$.

Calculate $\frac{45}{136} - \frac{17}{136}$.

Calculate $\frac{11}{18} + \frac{2}{15}$.

Calculate $\frac{14}{25} - \frac{9}{70}$.

Rewrite $\frac{48}{13}$ as a mixed number.

Rewrite $5 \frac{4}{9}$ as an improper fraction.

Round 5.67849 to three decimal digits.

Round 45.11475 to four decimal digits.

Convert $\frac{47}{25}$ into decimal form.

Convert 3.2117 to fraction form.

Calculate $\frac{12}{25} \times \frac{10}{21}$.

Calculate 3.45 ÷ 2.341 using a calculator. Round to three decimal places if necessary.

1. Calculate $\frac{4}{21} \div \frac{6}{35}$.
2. Calculate $\frac{1}{8} \div \frac{5}{28}$.

Correctly apply the rules for the order of operations to accurately compute $\left(\frac{5}{7} - \frac{2}{7}\right) \times 2^{3}$.

Correctly apply the rules for the order of operations to accurately compute $4 + \frac{2}{3} \div \left(\left(\frac{5}{9}\right)^{2} - \left(\frac{2}{3} + 5\right)\right)^{2}$.

Demonstrate the density property of rational numbers by finding a rational number between $\frac{4}{11}$ and $\frac{7}{12}$.

James is mixing soil for a raised garden, in which he plans to grow a variety of vegetables. For the soil to be suitable, he determines that $\frac{2}{5}$ of the soil can be topsoil, but $\frac{2}{5}$ needs to be peat moss and $\frac{1}{5}$ has to be compost. To fill the raised garden bed with 60 cubic feet of soil, how much of each component does James need to use?

At Bella’s Pizza, one-third of the pizzas that are ordered are one of their specialty varieties. If there are 273 pizzas ordered, how many were specialty pizzas?

It is known that 1 liter (L) is 0.264172 gallons (gal). Use this to convert 14 liters into gallons.

It is known that 1 inch is 2.54 centimeters. Use this to convert 100 centimeters into inches.

Rewrite the following as fractions:

1. 31%
2. 93%

Rewrite the following percentages in decimal form:

1. 54%
2. 83%

1. Determine 40% of 300.
2. Determine 64% of 190.

1. What is the total if 28% of the total is 140?
2. What is the total if 6% of the total is 91?

Find the percentage in the following:

1. Total is 300, percentage of the total is 60.
2. Total is 440, percentage of the total is 176.

A study revealed that 70% of students suffer from sleep deprivation, defined to be sleeping less than 8 hours per night. If the survey had 400 participants, how many of those participants had less than 8 hours of sleep per night?

There are 126 million users who are U.S. Amazon Prime subscribers. If there are 328.2 million residents in the United States, what percentage of U.S. residents are Amazon Prime subscribers?

Evander plays on the basketball team at their university and 73% of the athletes at their university receive some sort of scholarship for attending. If they know 219 of the student-athletes receive some sort of scholarship, how many student-athletes are at the university?