Q1: A shirt originally priced at $40 is on sale for 25% off. What is the sale price of the shirt? (a) $10 (b) $25 (c) $30 (d) $35
Solution:
Ans: (c) Explanation: First, calculate the discount amount: \(25\% \text{ of } 40 = 0.25 × 40 = 10\). Then subtract the discount from the original price: \(40 - 10 = 30\). The sale price is $30.
Q2: If a car travels 180 miles in 3 hours, what is the unit rate in miles per hour? (a) 54 miles per hour (b) 60 miles per hour (c) 63 miles per hour (d) 90 miles per hour
Solution:
Ans: (b) Explanation: To find the unit rate, divide the total distance by the total time: \(180 ÷ 3 = 60\) miles per hour. This represents the speed of the car.
Q3: What is 45% expressed as a decimal? (a) 0.045 (b) 0.45 (c) 4.5 (d) 45.0
Solution:
Ans: (b) Explanation: To convert a percentage to a decimal, divide by 100: \(45 ÷ 100 = 0.45\). Moving the decimal point two places to the left gives 0.45.
Q4: A store sells 5 apples for $3. At this rate, how much would 15 apples cost? (a) $6 (b) $8 (c) $9 (d) $12
Solution:
Ans: (c) Explanation: First, find the unit rate: \(3 ÷ 5 = 0.60\) per apple. Then multiply by 15: \(0.60 × 15 = 9\). Alternatively, since 15 is 3 times 5, the cost is \(3 × 3 = 9\) dollars.
Q5: A student answered 18 out of 20 questions correctly on a test. What percentage did the student score? (a) 18% (b) 80% (c) 85% (d) 90%
Solution:
Ans: (d) Explanation: To find the percentage, divide the correct answers by total questions and multiply by 100: \(\frac{18}{20} × 100 = 0.9 × 100 = 90\%\). The student scored 90%.
Q6: If 30% of a number is 60, what is the number? (a) 18 (b) 90 (c) 180 (d) 200
Solution:
Ans: (d) Explanation: Let the number be \(x\). Then \(0.30x = 60\). Dividing both sides by 0.30: \(x = 60 ÷ 0.30 = 200\). The number is 200.
Q7: A recipe calls for 2 cups of flour for every 3 cups of sugar. If you use 8 cups of flour, how many cups of sugar do you need? (a) 10 cups (b) 12 cups (c) 14 cups (d) 16 cups
Solution:
Ans: (b) Explanation: Set up a proportion: \(\frac{2}{3} = \frac{8}{x}\). Cross multiply: \(2x = 3 × 8 = 24\). Divide by 2: \(x = 12\). You need 12 cups of sugar.
Q8: A population increases from 500 to 650. What is the percent increase? (a) 15% (b) 23% (c) 30% (d) 35%
Solution:
Ans: (c) Explanation: First, find the amount of increase: \(650 - 500 = 150\). Then calculate the percent increase: \(\frac{150}{500} × 100 = 0.30 × 100 = 30\%\). The population increased by 30%.
Section B: Fill in the Blanks
Q9:A ratio that compares two quantities with different units is called a __________.
Solution:
Ans: rate Explanation: A rate is a special type of ratio that compares quantities measured in different units, such as miles per hour or dollars per pound.
Q10:To convert a fraction to a percentage, multiply the fraction by __________ and add the percent symbol.
Solution:
Ans: 100 Explanation: Multiplying a fraction by 100 converts it to a percentage. For example, \(\frac{1}{4} × 100 = 25\%\).
Q11:The formula to find the percent of a number is: Percent × __________ = Part.
Solution:
Ans: Whole Explanation: The basic percentage formula is: Percent × Whole = Part. This relationship helps solve percentage problems.
Q12:A unit rate is a rate where the second quantity is __________.
Solution:
Ans: 1 (or one) Explanation: A unit rate compares a quantity to one unit of another quantity, such as 60 miles per 1 hour or $2.50 per 1 pound.
Q13:If the sales tax rate is 8%, the decimal form used in calculations is __________.
Solution:
Ans: 0.08 Explanation: To convert 8% to a decimal, divide by 100: \(8 ÷ 100 = 0.08\). This decimal is used to calculate the tax amount.
Q14:When a price decreases from $80 to $60, the percent decrease is __________.
Solution:
Ans: 25% Explanation: The amount of decrease is \(80 - 60 = 20\). The percent decrease is \(\frac{20}{80} × 100 = 25\%\).
Section C: Word Problems
Q15:A book costs $25 and the sales tax rate is 6%. What is the total cost of the book including tax?
Solution:
Ans: First, calculate the sales tax amount: \[6\% \text{ of } 25 = 0.06 × 25 = 1.50\] Then add the tax to the original price: \[25 + 1.50 = 26.50\] Final Answer: $26.50
Q16:Emily earned $120 babysitting last month and $150 this month. What is the percent increase in her earnings?
Solution:
Ans: First, find the amount of increase: \[150 - 120 = 30\] Then calculate the percent increase: \[\frac{30}{120} × 100 = 0.25 × 100 = 25\%\] Final Answer: 25%
Q17:A printer can print 240 pages in 8 minutes. At this rate, how many pages can it print in 15 minutes?
Solution:
Ans: First, find the unit rate (pages per minute): \[240 ÷ 8 = 30 \text{ pages per minute}\] Then multiply by 15 minutes: \[30 × 15 = 450 \text{ pages}\] Final Answer: 450 pages
Q18:A jacket regularly priced at $80 is on sale for 35% off. After the discount, a 7% sales tax is added. What is the final price?
Solution:
Ans: First, calculate the discount amount: \[35\% \text{ of } 80 = 0.35 × 80 = 28\] Subtract the discount from the original price: \[80 - 28 = 52\] Now calculate the sales tax on the sale price: \[7\% \text{ of } 52 = 0.07 × 52 = 3.64\] Add the tax to the sale price: \[52 + 3.64 = 55.64\] Final Answer: $55.64
Q19:In a class of 25 students, 60% are girls. How many boys are in the class?
Solution:
Ans: First, find the number of girls: \[60\% \text{ of } 25 = 0.60 × 25 = 15 \text{ girls}\] Subtract from the total to find the number of boys: \[25 - 15 = 10 \text{ boys}\] Alternatively, if 60% are girls, then 40% are boys: \[40\% \text{ of } 25 = 0.40 × 25 = 10 \text{ boys}\] Final Answer: 10 boys
Q20:A water tank contains 150 gallons of water. If water is being drained at a constant rate of 12 gallons per hour, how many gallons will remain after 7 hours?
Solution:
Ans: First, calculate the total amount drained: \[12 \text{ gallons/hour} × 7 \text{ hours} = 84 \text{ gallons}\] Subtract from the original amount: \[150 - 84 = 66 \text{ gallons}\] Final Answer: 66 gallons
The document Worksheet (with Solutions): Rates And Percentages is a part of the Grade 7 Course Math Grade 7.
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