Section 1
Ratios
Solve each equation.$2 x+4=38$
Solve each equation.$\frac{x}{2}-4=38$
Solve each equation.$3(x+2)=24$
Solve each equation.$\frac{x-6}{3}=20$
Factor each expression.$2 x+6$
Factor each expression.$x^2-49$
Factor each expression.$2 x^2-x-6$
Factor each expression.$x^3+27$
Fill in the blanks.A ratio is a ___________ of two numbers.
Fill in the blanks.The ___________ of an item is the quotient of its cost to its quantity.
Fill in the blanks.The ratios $\frac{2}{3}$ and $\frac{4}{6}$ are ___________ ratios.
Fill in the blanks.The quotient $\frac{500 \text { miles }}{15 \text { hours }}$ is called a ___________
Fill in the blanks.Give three examples of ratios that you have encountered this past week.
Fill in the blanks.Suppose that a basketball player made 8 free throws out of 12 tries. The ratio of $\frac{8}{12}$ can be simplified as $\frac{2}{3}$. Interpret this result.
Express each phrase as a ratio in lowest terms.5 to 7
Express each phrase as a ratio in lowest terms.3 to 5
Express each phrase as a ratio in lowest terms.17 to 34
Express each phrase as a ratio in lowest terms.19 to 38
Express each phrase as a ratio in lowest terms.22 to 33
Express each phrase as a ratio in lowest terms.14 to 21
Express each phrase as a ratio in lowest terms.7 to 24.5
Express each phrase as a ratio in lowest terms.0.65 to 0.15
Express each phrase as a ratio in lowest terms.4 ounces to 12 ounces
Express each phrase as a ratio in lowest terms.3 inches to 15 inches
Express each phrase as a ratio in lowest terms.12 minutes to 1 hour
Express each phrase as a ratio in lowest terms.8 ounces to 1 pound
Express each phrase as a ratio in lowest terms.3 days to 1 week
Express each phrase as a ratio in lowest terms.4 inches to 2 yards
Express each phrase as a ratio in lowest terms.18 months to 2 years
Express each phrase as a ratio in lowest terms.8 feet to 4 yards
Refer to the monthly family budget shown in the table. Give each ratio in lowest terms.(TABLE CAN'T COPY)Find the total amount of the budget.
Refer to the monthly family budget shown in the table. Give each ratio in lowest terms.(TABLE CAN'T COPY)Find the ratio of the amount budgeted for rent to the total budget.
Refer to the monthly family budget shown in the table. Give each ratio in lowest terms.(TABLE CAN'T COPY)Find the ratio of the amount budgeted for entertainment to the total budget.
Refer to the monthly family budget shown in the table. Give each ratio in lowest terms.(TABLE CAN'T COPY)Find the ratio of the amount budgeted for phone to the amount budgeted for entertainment.
Refer to the tax deductions listed in the table. Give each ratio in lowest terms.(TABLE CAN'T COPY)Find the total amount of deductions.
Refer to the tax deductions listed in the table. Give each ratio in lowest terms.(TABLE CAN'T COPY)Find the ratio of real estate tax deductions to the total deductions.
Refer to the tax deductions listed in the table. Give each ratio in lowest terms.(TABLE CAN'T COPY)Find the ratio of the contributions to the total deductions.
Refer to the tax deductions listed in the table. Give each ratio in lowest terms.(TABLE CAN'T COPY)Find the ratio of the mortgage interest deduction to the union dues deduction.
At a college, there are 125 faculty members and 2,000 students. Find the faculty-to-student ratio.
In a state senate, there are 94 men and 24 women. Find the ratio of men to women.
A driver pumped 17 gallons of gasoline into his tank at a cost of $$\$ 30.09$$. Write a quotient of dollars to gallons, and give the unit cost of gasoline.
A 50-pound bag of grass seed costs $$\$ 222.50$$. Write a quotient of dollars to pounds, and give the unit cost of grass seed.
A 12-ounce can of cranberry juice sells for $84 \phi$. Give the unit cost in cents per ounce.
A 24 -ounce package of green beans sells for $$\$ 1.29$$. Give the unit cost in cents per ounce.
A 6-ounce can of orange juice sells for 89 e, and an 8 -ounce can sells for $$\$ 1.19$$. Which is the better buy?
A car travels 345 miles in 6 hours, and a truck travels 376 miles in 6.2 hours. Which vehicle travels faster?
One seventh-grader read a 54 -page book in 40 minutes, and another read an 80 -page book in 62 minutes. If the books were equally difficult, which student read faster?
A 30-pound bag of fertilizer costs $$\$ 12.25$$, and an 80 -pound bag costs $$\$ 30.25$$. Which is the better buy?
An 11,880-gallon tank can be emptied in 27 minutes. Write a quotient of gallons to minutes, and give the rate of flow in gallons per minute.
Ricardo worked for 27 hours to help insulate a hockey arena. For his work, he received $$\$ 337.50$$. Write a quotient of dollars to hours, and find his hourly rate of pay.
A sweater cost $$\$ 36.75$$ after sales tax had been added. Find the tax rate as a percent if the sweater retailed for $$\$ 35$$.
The real estate taxes on a summer home assessed at $$\$ 75,000$$ were $$\$ 1,500$$. Find the tax rate as a percent.
A car travels 325 miles in 5 hours. Find its rate of speed in mph .
An airplane travels from Chicago to San Francisco, a distance of 1,883 miles, in 3.5 hours. Find the average rate of speed of the plane.
One car went 1,235 miles on 51.3 gallons of gasoline, and another went 1,456 miles on 55.78 gallons. Which car had the better mpg rating?
In one community, a bill for 575 kilowatt hours (kwh) of electricity was $$\$ 38.81$$. In a second community, a bill for 831 kwh was $$\$ 58.10$$. In which community is electricity cheaper?
Some people think that the word ratio comes from the words rational number. Explain why this may be true.
In the fraction $\frac{a}{b}, b$ cannot be 0 . Explain why. In the ratio $\frac{a}{b}, b$ can be 0 . Explain why.
Which ratio is the larger? How can you tell?$$\frac{17}{19} \quad \text { or } \quad \frac{19}{21}$$
Which ratio is the smaller? How can you tell?$$-\frac{13}{29} \quad \text { or } \quad-\frac{17}{31}$$