Prealgebra & Beginning Algebra Practice: Step-by-Step Guidance

Q1. What is the decimal equivalent of the fraction 175/250?

Background

Topic: Fractions and Decimals

This question tests your ability to convert a fraction to its decimal form by performing division.

Key Terms and Formulas:

• Fraction: A number expressed as one integer divided by another (e.g., $\frac{a}{b}$).

• Decimal: A number that uses a decimal point to show a value less than one.

Key Formula:

$\text{Decimal equivalent} = \frac{\text{Numerator}}{\text{Denominator}}$

Step-by-Step Guidance

1. Identify the numerator and denominator: Numerator = 175, Denominator = 250.

2. Set up the division: $175 \div 250$.

3. Perform the division to find the decimal value. (You can use long division or a calculator.)

Try solving on your own before revealing the answer!

Final Answer: 0.7

$\frac{175}{250} = 0.7$

Dividing 175 by 250 gives 0.7 as the decimal equivalent.

Q2. What is 34.55 rounded to the nearest whole number?

Background

Topic: Rounding Numbers

This question tests your understanding of how to round decimals to the nearest whole number.

Key Terms and Rules:

• Rounding: Adjusting a number to a specified place value.

• To round to the nearest whole number, look at the tenths digit (the first digit after the decimal point).

Step-by-Step Guidance

1. Identify the tenths digit in 34.55 (the digit immediately after the decimal point).

2. If the tenths digit is 5 or greater, round the whole number up by 1. If it is less than 5, keep the whole number as is.

Try solving on your own before revealing the answer!

Final Answer: 35

The tenths digit is 5, so you round up. 34.55 rounded to the nearest whole number is 35.

Q3. Which of the following fractions is the smallest: 2/3, 88/102, 12/25, or 7/16?

Background

Topic: Comparing Fractions

This question tests your ability to compare the sizes of different fractions.

Key Terms and Methods:

• Fraction Comparison: You can compare fractions by converting them to decimals or by finding a common denominator.

Step-by-Step Guidance

1. Convert each fraction to a decimal by dividing the numerator by the denominator.

2. Compare the decimal values to determine which is the smallest.

Try solving on your own before revealing the answer!

Final Answer: 7/16

7 divided by 16 is 0.4375, which is less than the decimal equivalents of the other fractions.

Q4. Which of the following measurements is used in the apothecary system for weight?

Background

Topic: Measurement Systems

This question tests your knowledge of units used in different measurement systems, specifically the apothecary system.

Key Terms:

• Apothecary System: An old system of measurement used in pharmacy, especially for weight and volume.

• Grain: A unit of weight in the apothecary system.

Step-by-Step Guidance

1. Recall which units are part of the apothecary system (grain, dram, ounce, etc.).

2. Identify which of the answer choices is a unit from the apothecary system for weight.

Try solving on your own before revealing the answer!

Final Answer: grain

"Grain" is the unit of weight used in the apothecary system.

Q5. What is the first step to convert a mixed number to an improper fraction?

Background

Topic: Mixed Numbers and Improper Fractions

This question tests your understanding of how to convert a mixed number (a whole number and a fraction) into an improper fraction.

Key Terms and Formula:

• Mixed Number: A number consisting of a whole number and a fraction (e.g., $2\frac{1}{3}$).

• Improper Fraction: A fraction where the numerator is greater than or equal to the denominator.

Key Formula:

$\text{Improper Fraction} = (\text{Whole Number} \times \text{Denominator}) + \text{Numerator}$

Step-by-Step Guidance

1. Multiply the whole number part by the denominator of the fractional part.

2. Add the numerator of the fractional part to the result from step 1.

Try solving on your own before revealing the answer!

Final Answer: Multiply the whole number by the denominator and add the numerator

This is the correct first step to convert a mixed number to an improper fraction.

Q6. How many centimeters are there in one inch?

Background

Topic: Unit Conversion

This question tests your knowledge of the conversion factor between inches and centimeters.

Key Terms and Formula:

• Inch: A unit of length in the imperial system.

• Centimeter: A unit of length in the metric system.

Key Conversion:

$1 \text{ inch} = 2.54 \text{ centimeters}$

Step-by-Step Guidance

1. Recall the standard conversion factor between inches and centimeters.

2. Apply the conversion factor to determine how many centimeters are in one inch.

Try solving on your own before revealing the answer!

Final Answer: 2.54

There are 2.54 centimeters in one inch.

Q7. 18 is what percent of 122?

Background

Topic: Percents

This question tests your ability to find what percent one number is of another.

Key Terms and Formula:

• Percent: A ratio that compares a number to 100.

Key Formula:

$\text{Percent} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100$

Step-by-Step Guidance

1. Identify the "part" (18) and the "whole" (122).

2. Set up the formula: $\left( \frac{18}{122} \right) \times 100$.

3. Divide 18 by 122 to get a decimal.

4. Multiply the result by 100 to convert it to a percent.

Try solving on your own before revealing the answer!

Final Answer: 14.8%

$\left( \frac{18}{122} \right) \times 100 = 14.8\%$

Q8. What is the quotient of 7.5 divided by 2.4?

Background

Topic: Division of Decimals

This question tests your ability to divide decimals.

Key Terms and Formula:

• Quotient: The result of division.

Key Formula:

$\text{Quotient} = \frac{7.5}{2.4}$

Step-by-Step Guidance

1. Set up the division: $7.5 \div 2.4$.

2. Divide 7.5 by 2.4 using long division or a calculator.

Try solving on your own before revealing the answer!

Final Answer: 3.125

$7.5 \div 2.4 = 3.125$

Q9. The fraction 3/4 can also be read as:

Background

Topic: Fraction Terminology

This question tests your understanding of how to read and interpret fractions.

Key Terms:

• Numerator: The top number in a fraction.

• Denominator: The bottom number in a fraction.

Step-by-Step Guidance

1. Recall the standard way to read fractions: "numerator-denominator" (e.g., three-fourths).

2. Recognize that a fraction can also be interpreted as a division (e.g., 3 divided by 4).

3. Check which answer choices match these interpretations.

Try solving on your own before revealing the answer!

Final Answer: both a and c

3/4 can be read as "three-fourths" and as "3 divided by 4".

Q10. What is 257.56 rounded to the nearest tenth?

Background

Topic: Rounding Decimals

This question tests your ability to round a decimal number to the nearest tenth.

Key Terms and Rules:

• Tenth: The first digit to the right of the decimal point.

• To round to the nearest tenth, look at the hundredths digit (the second digit after the decimal point).

Step-by-Step Guidance

1. Identify the tenths and hundredths digits in 257.56.

2. If the hundredths digit is 5 or greater, round the tenths digit up by 1. If it is less than 5, keep the tenths digit as is.

Try solving on your own before revealing the answer!

Final Answer: 257.6

The hundredths digit is 6, so you round the tenths digit up. 257.56 rounded to the nearest tenth is 257.6.

Q11. When comparing two fractions with the same denominator, which has the lesser value?

Background

Topic: Comparing Fractions

This question tests your understanding of how to compare fractions with the same denominator.

Key Terms:

• Denominator: The bottom number in a fraction.

• Numerator: The top number in a fraction.

Step-by-Step Guidance

1. Recall that when denominators are the same, the fraction with the smaller numerator is smaller.

2. Apply this rule to the answer choices.

Try solving on your own before revealing the answer!

Final Answer: the lesser value

The fraction with the smallest numerator has the lesser value when denominators are the same.

Q12. What is the basic unit of weight in the metric system?

Background

Topic: Metric System Units

This question tests your knowledge of the basic units in the metric system.

Key Terms:

• Gram: The basic unit of mass/weight in the metric system.

Step-by-Step Guidance

1. Recall the basic units for length (meter), mass/weight (gram), and volume (liter) in the metric system.

2. Identify which unit is used for weight.

Try solving on your own before revealing the answer!

Final Answer: gram

The gram is the basic unit of weight in the metric system.

Q13. How many micrograms are in one milligram?

Background

Topic: Metric System Conversions

This question tests your ability to convert between metric units of mass.

Key Terms and Conversion:

• Microgram (μg): One millionth of a gram.

• Milligram (mg): One thousandth of a gram.

Key Conversion:

$1 \text{ mg} = 1000 \text{ μg}$

Step-by-Step Guidance

1. Recall the relationship between milligrams and micrograms.

2. Multiply the number of milligrams by the conversion factor to get micrograms.

Try solving on your own before revealing the answer!

Final Answer: 1000

There are 1000 micrograms in one milligram.

Q14. What is the correct way to write the decimal .45?

Background

Topic: Decimal Notation

This question tests your understanding of proper decimal notation.

Key Terms:

• Decimal: A number with a decimal point.

Step-by-Step Guidance

1. Recall that a decimal should have a leading zero if there is no whole number part.

2. Identify which answer choice correctly shows this notation.

Try solving on your own before revealing the answer!

Final Answer: 0.45

The correct way to write the decimal is with a leading zero: 0.45.

Q15. What is the product of the decimals 2.15 and 0.25?

Background

Topic: Multiplying Decimals

This question tests your ability to multiply decimal numbers.

Key Terms and Formula:

• Product: The result of multiplication.

Key Formula:

$2.15 \times 0.25$

Step-by-Step Guidance

1. Set up the multiplication: $2.15 \times 0.25$.

2. Multiply the numbers as if they were whole numbers, then count the total number of decimal places in both factors.

3. Place the decimal point in the product so that it has the correct number of decimal places.

Try solving on your own before revealing the answer!

Final Answer: 0.5375

2.15 times 0.25 equals 0.5375.

Q16. In the metric system, what does the prefix milli- denote?

Background

Topic: Metric Prefixes

This question tests your knowledge of metric system prefixes and their meanings.

Key Terms:

• Milli-: A prefix meaning one thousandth ($\frac{1}{1000}$) of a unit.

Step-by-Step Guidance

1. Recall the meaning of the prefix "milli-" in the metric system.

2. Identify which answer choice matches this meaning.

Try solving on your own before revealing the answer!

Final Answer: one thousandth of a unit

"Milli-" means one thousandth of a unit.

Q17. What is the top number of a fraction called?

Background

Topic: Fraction Terminology

This question tests your knowledge of the parts of a fraction.

Key Terms:

• Numerator: The top number in a fraction, representing the number of parts being considered.

• Denominator: The bottom number in a fraction, representing the total number of equal parts.

Step-by-Step Guidance

1. Recall the definitions of numerator and denominator.

2. Identify which term refers to the top number.

Try solving on your own before revealing the answer!

Final Answer: numerator

The top number of a fraction is called the numerator.

Q18. What is the lowest terms form of the fraction 4/16?

Background

Topic: Reducing Fractions

This question tests your ability to simplify fractions to their lowest terms.

Key Terms and Formula:

• Lowest Terms: A fraction is in lowest terms when the numerator and denominator have no common factors other than 1.

Key Formula:

$\frac{a}{b} = \frac{a \div \gcd(a, b)}{b \div \gcd(a, b)}$

Step-by-Step Guidance

1. Find the greatest common divisor (GCD) of 4 and 16.

2. Divide both the numerator and denominator by the GCD to simplify the fraction.

Try solving on your own before revealing the answer!

Final Answer: 1/4

4 and 16 have a GCD of 4, so $\frac{4}{16} = \frac{1}{4}$.

Q19. The fraction 4/5 is considered a(n):

Background

Topic: Types of Fractions

This question tests your understanding of the different types of fractions.

Key Terms:

• Proper Fraction: Numerator is less than the denominator.

• Improper Fraction: Numerator is equal to or greater than the denominator.

Step-by-Step Guidance

1. Compare the numerator (4) and denominator (5).

2. Determine if the numerator is less than, equal to, or greater than the denominator to classify the fraction.

Try solving on your own before revealing the answer!

Final Answer: proper fraction

4/5 is a proper fraction because the numerator is less than the denominator.

Q20. What is the result of subtracting 0.067 from 1.5892?

Background

Topic: Subtracting Decimals

This question tests your ability to subtract decimal numbers.

Key Terms and Formula:

• Subtraction: The process of finding the difference between two numbers.

Key Formula:

$1.5892 - 0.067$

Step-by-Step Guidance

1. Align the decimal points of the two numbers.

2. Subtract 0.067 from 1.5892, making sure to add zeros as needed for place value.

Try solving on your own before revealing the answer!

Final Answer: 1.5222

1.5892 minus 0.067 equals 1.5222.

Q21. In the metric system, what does the prefix micro- denote?

Background

Topic: Metric Prefixes

This question tests your knowledge of metric system prefixes and their meanings.

Key Terms:

• Micro-: A prefix meaning one millionth ($\frac{1}{1,000,000}$) of a unit.

Step-by-Step Guidance

1. Recall the meaning of the prefix "micro-" in the metric system.

2. Identify which answer choice matches this meaning.

Try solving on your own before revealing the answer!

Final Answer: one millionth of a unit

"Micro-" means one millionth of a unit.

Q22. In the metric system, what does the prefix kilo- denote?

Background

Topic: Metric Prefixes

This question tests your knowledge of metric system prefixes and their meanings.

Key Terms:

• Kilo-: A prefix meaning one thousand (1000) units.

Step-by-Step Guidance

1. Recall the meaning of the prefix "kilo-" in the metric system.

2. Identify which answer choice matches this meaning.

Try solving on your own before revealing the answer!

Final Answer: one thousand units

"Kilo-" means one thousand units.

Q23. What is the sum of the decimals 213.567 and 13.125?

Background

Topic: Adding Decimals

This question tests your ability to add decimal numbers.

Key Terms and Formula:

• Sum: The result of addition.

Key Formula:

$213.567 + 13.125$

Step-by-Step Guidance

1. Align the decimal points of the two numbers.

2. Add the numbers column by column, starting from the rightmost digit.

Try solving on your own before revealing the answer!

Final Answer: 226.692

213.567 plus 13.125 equals 226.692.

Q24. What is the decimal equivalent of 6/1000?

Background

Topic: Fractions and Decimals

This question tests your ability to convert a fraction to its decimal form.

Key Terms and Formula:

• Decimal Equivalent: The result of dividing the numerator by the denominator.

Key Formula:

$\frac{6}{1000}$

Step-by-Step Guidance

1. Divide 6 by 1000 to get the decimal equivalent.

Try solving on your own before revealing the answer!

Final Answer: 0.006

6 divided by 1000 equals 0.006.

Q25. What is the lowest terms form of the fraction 3/8?

Background

Topic: Reducing Fractions

This question tests your ability to simplify fractions to their lowest terms.

Key Terms and Formula:

• Lowest Terms: A fraction is in lowest terms when the numerator and denominator have no common factors other than 1.

Key Formula:

$\frac{a}{b} = \frac{a \div \gcd(a, b)}{b \div \gcd(a, b)}$

Step-by-Step Guidance

1. Find the greatest common divisor (GCD) of 3 and 8.

2. Divide both the numerator and denominator by the GCD to simplify the fraction.

Try solving on your own before revealing the answer!

Final Answer: 3/8

3 and 8 have no common factors other than 1, so 3/8 is already in lowest terms.