This study guide covers key concepts in measurements and percents for 6th grade, helping you ace your Unit 2B test. We'll break down the essential topics, provide examples, and offer tips for mastering these important mathematical skills.
I. Understanding Measurement
This section focuses on different types of measurements and how to convert between units.
A. Units of Measurement:
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Length: Remember your basic units: inches, feet, yards, miles (and potentially centimeters, meters, kilometers if your curriculum includes metric). Practice converting between these units. For example, how many inches are in 3 feet? (Hint: 1 foot = 12 inches)
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Weight/Mass: Understand the difference between weight (force of gravity) and mass (amount of matter). Familiarize yourself with units like ounces, pounds, tons (and grams, kilograms, metric tons if applicable). Practice conversions. How many ounces are in 2 pounds? (Hint: 1 pound = 16 ounces)
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Capacity/Volume: Learn the units for measuring liquids: fluid ounces, cups, pints, quarts, gallons (and milliliters, liters if applicable). Practice conversions. How many cups are in 1 quart? (Hint: 1 quart = 4 cups)
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Time: Practice converting between seconds, minutes, hours, days, weeks, months, and years.
B. Converting Units:
The key to unit conversion is understanding the relationships between different units. Use conversion factors to move between units. For example:
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1 foot = 12 inches To convert feet to inches, multiply by 12. To convert inches to feet, divide by 12.
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1 hour = 60 minutes To convert hours to minutes, multiply by 60. To convert minutes to hours, divide by 60.
Practice Problems:
- Convert 5 yards to inches.
- Convert 3.5 pounds to ounces.
- Convert 2 gallons to quarts.
- Convert 180 minutes to hours.
II. Working with Percentages
This section dives into the world of percentages – a crucial part of everyday math.
A. Understanding Percentages:
A percentage represents a fraction out of 100. For example, 50% means 50 out of 100, or ½.
B. Calculating Percentages:
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Finding a percentage of a number: To find x% of a number, multiply the number by x/100. For example, to find 20% of 80, calculate (20/100) * 80 = 16.
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Finding the percentage one number is of another: Divide the first number by the second number, then multiply by 100%. For example, what percentage is 15 of 60? (15/60) * 100% = 25%
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Finding the whole from a percentage: If you know a percentage of a number and the percentage itself, you can find the original number. For example, if 30% of a number is 12, what is the number? 12 / (30/100) = 40
C. Percentage Increase and Decrease:
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Percentage Increase: (New Value - Original Value) / Original Value * 100%
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Percentage Decrease: (Original Value - New Value) / Original Value * 100%
Practice Problems:
- What is 35% of 200?
- What percentage is 12 of 48?
- 25% of a number is 15. What is the number?
- A shirt originally priced at $20 is on sale for $15. What is the percentage decrease in price?
III. Putting it All Together: Real-World Applications
Measurements and percents are used constantly in everyday life. Consider how you might apply these concepts:
- Shopping: Calculating discounts, sales tax, and comparing prices.
- Cooking: Measuring ingredients accurately.
- Construction: Measuring distances and materials.
- Sports: Analyzing statistics and performance.
This study guide provides a strong foundation for your Unit 2B test. Remember to review your class notes, practice problems, and seek help if needed. Good luck!
