Q1. Evaluate the following expression for x: 4x + 3 / 5x

Background

Topic: Evaluating Algebraic Expressions

This question tests your ability to substitute a value for a variable and simplify the resulting expression.

Key Terms and Formulas:

• Algebraic Expression: An expression containing variables, numbers, and operations.

• To evaluate, substitute the given value for the variable and simplify.

Step-by-Step Guidance

1. Identify the value of you are supposed to use (if not given, check the instructions or context).

2. Substitute the value of into the expression .

3. Simplify the numerator and denominator separately.

4. Write the simplified fraction or decimal form, but do not compute the final value yet.

Try solving on your own before revealing the answer!

Q2. Write the English phrase as an algebraic expression: Seven less than a number (let x represent the number)

Background

Topic: Translating Words to Algebraic Expressions

This question tests your ability to convert a verbal phrase into an algebraic expression using a variable.

Key Terms and Formulas:

• "Less than" means subtraction, but the order is important: "seven less than x" means .

Step-by-Step Guidance

1. Identify the variable: Let represent the number.

2. Translate "seven less than a number" into an algebraic expression. Remember, "less than" reverses the order.

3. Write the expression in the correct order, but do not simplify further.

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Q3. Write the following phrase as a variable expression: nine times a number, decreased by nine (use x to represent "a number")

Background

Topic: Translating Words to Algebraic Expressions

This question tests your ability to translate a verbal phrase into an algebraic expression using multiplication and subtraction.

Key Terms and Formulas:

• "Nine times a number" means .

• "Decreased by nine" means subtract 9.

Step-by-Step Guidance

1. Let represent the number.

2. Translate "nine times a number" to .

3. "Decreased by nine" means subtract 9 from .

4. Write the full expression, but do not simplify further.

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Q4. Write the English phrase as an algebraic expression: four more than the quotient of a number and 6 (let x represent the number)

Background

Topic: Translating Words to Algebraic Expressions

This question tests your ability to translate a phrase involving division and addition into an algebraic expression.

Key Terms and Formulas:

• "Quotient of a number and 6" means .

• "Four more than" means add 4 to the previous result.

Step-by-Step Guidance

1. Let represent the number.

2. Translate "quotient of a number and 6" to .

3. "Four more than" means add 4 to .

4. Write the expression as .

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Q5. Determine whether the given number is a solution of the equation: ,

Background

Topic: Solving Linear Equations

This question tests your ability to substitute a value into an equation and check if it makes the equation true.

Key Terms and Formulas:

• Solution: A value that makes the equation true when substituted for the variable.

Step-by-Step Guidance

1. Substitute into both sides of the equation .

2. Calculate and .

3. Multiply each result by the coefficients (4 and 5, respectively).

4. Compare the two sides to see if they are equal, but do not state the final comparison yet.

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Q6. Write the sentence as an equation: The sum of three times a number and 4 is 16 (let x represent the number)

Background

Topic: Translating Sentences to Equations

This question tests your ability to write an equation from a verbal statement.

Key Terms and Formulas:

• "Three times a number" is .

• "Sum of three times a number and 4" is .

• "Is" means equals ().

Step-by-Step Guidance

1. Let represent the number.

2. Translate "three times a number" to .

3. Add 4 to get .

4. Set the expression equal to 16.

Try solving on your own before revealing the answer!

Q7. Write the sentence as an equation: The product of 5 and a number increased by 7 is 38 (let x represent the number)

Background

Topic: Translating Sentences to Equations

This question tests your ability to write an equation from a verbal statement involving multiplication and addition.

Key Terms and Formulas:

• "Product of 5 and a number increased by 7" means .

• "Is" means equals ().

Step-by-Step Guidance

1. Let represent the number.

2. "A number increased by 7" is .

3. "Product of 5 and (x + 7)" is .

4. Set the expression equal to 38.

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Q8. Convert the mixed number to an improper fraction

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Topic: Mixed Numbers and Improper Fractions

This question tests your ability to convert a mixed number to an improper fraction.

Key Terms and Formulas:

• Mixed Number: A number with a whole part and a fractional part.

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

• Formula:

Step-by-Step Guidance

1. Identify the whole number part () and the fractional part ().

2. Multiply the whole number by the denominator: .

3. Add the numerator: .

4. Write the result over the original denominator, but do not simplify yet.

Try solving on your own before revealing the answer!

Q9. Convert the improper fraction to a mixed number

Background

Topic: Improper Fractions and Mixed Numbers

This question tests your ability to convert an improper fraction to a mixed number.

Key Terms and Formulas:

• Improper Fraction: Numerator is greater than denominator.

• Mixed Number: Whole number plus a proper fraction.

Step-by-Step Guidance

1. Divide the numerator by the denominator to find the whole number part.

2. The remainder becomes the numerator of the fractional part.

3. The denominator stays the same.

4. Write the mixed number, but do not simplify further.

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Q10. Perform the multiplication:

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Topic: Multiplying Fractions

This question tests your ability to multiply several fractions and reduce the result to lowest terms.

Key Terms and Formulas:

• To multiply fractions: Multiply numerators together, multiply denominators together.

• Simplify by reducing common factors.

Step-by-Step Guidance

1. Multiply the numerators: .

2. Multiply the denominators: .

3. Write the resulting fraction.

4. Simplify the fraction by dividing numerator and denominator by any common factors, but do not state the final reduced form yet.

Try solving on your own before revealing the answer!

Q11. Perform the indicated operation:

Background

Topic: Dividing Fractions

This question tests your ability to divide fractions and reduce the answer to lowest terms.

Key Terms and Formulas:

• To divide by a fraction, multiply by its reciprocal:

Step-by-Step Guidance

1. Write the reciprocal of the divisor: becomes .

2. Multiply .

3. Multiply numerators and denominators.

4. Simplify the resulting fraction, but do not state the final reduced form yet.

Try solving on your own before revealing the answer!

Q12. Perform the indicated operation:

Background

Topic: Dividing Fractions by Whole Numbers

This question tests your ability to divide a fraction by a whole number.

Key Terms and Formulas:

• To divide by a whole number, multiply by its reciprocal:

Step-by-Step Guidance

1. Rewrite 3 as .

2. Take the reciprocal: .

3. Multiply .

4. Simplify the resulting fraction, but do not state the final reduced form yet.

Try solving on your own before revealing the answer!

Q13. Perform the indicated operation:

Background

Topic: Adding and Subtracting Fractions

This question tests your ability to add or subtract fractions with like denominators.

Key Terms and Formulas:

• When denominators are the same, add or subtract numerators directly.

Step-by-Step Guidance

1. Write both fractions with the common denominator (already $5$).

2. Add or subtract the numerators: .

3. Write the result over the denominator.

4. Simplify the fraction if possible, but do not state the final value yet.

Try solving on your own before revealing the answer!

Q14. Perform the indicated operation:

Background

Topic: Adding Fractions with Unlike Denominators

This question tests your ability to add fractions by finding a common denominator.

Key Terms and Formulas:

• Find the least common denominator (LCD).

• Convert each fraction to an equivalent fraction with the LCD.

• Add the numerators.

Step-by-Step Guidance

1. Find the LCD of 7 and 4 (which is 28).

2. Convert to and to .

3. Add the numerators: .

4. Write the sum over the common denominator, but do not simplify further yet.

Try solving on your own before revealing the answer!

Q15. Perform the indicated operation:

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Topic: Operations with Mixed Numbers

This question tests your ability to add and subtract mixed numbers.

Key Terms and Formulas:

• Convert mixed numbers to improper fractions for easier calculation.

• Add or subtract as with fractions.

Step-by-Step Guidance

1. Convert and to improper fractions.

2. Rewrite 9 as a fraction with a common denominator.

3. Subtract and add the fractions in order.

4. Simplify the result, but do not state the final value yet.

Try solving on your own before revealing the answer!

Q16. Write a positive or negative integer that describes the situation: Meteorology: 5° below zero

Background

Topic: Integers and Real-World Contexts

This question tests your understanding of how to represent real-world situations with integers.

Key Terms and Formulas:

• Below zero: Use a negative integer.

Step-by-Step Guidance

1. Recognize that "below zero" means a negative value.

2. Write the integer as .

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Q17. Write as a decimal:

Background

Topic: Converting Fractions to Decimals

This question tests your ability to convert a negative fraction to a decimal.

Key Terms and Formulas:

• Divide the numerator by the denominator.

Step-by-Step Guidance

1. Divide 7 by 15 to get the decimal value.

2. Apply the negative sign to the result.

3. Write the decimal to two decimal places, but do not state the final value yet.

Try solving on your own before revealing the answer!

Q18. List all numbers from the given set that are: a. natural numbers, b. whole numbers, c. integers, d. rational numbers, e. irrational numbers, f. real numbers. Set:

Background

Topic: Number Sets and Classification

This question tests your ability to classify numbers as natural, whole, integer, rational, irrational, or real.

Key Terms and Formulas:

• Natural numbers:

• Whole numbers:

• Integers:

• Rational numbers: Can be written as a fraction.

• Irrational numbers: Cannot be written as a fraction (non-repeating, non-terminating decimals).

• Real numbers: All rational and irrational numbers.

Step-by-Step Guidance

1. Go through each number in the set and determine which categories it fits.

2. List the numbers for each category (a–f), but do not state the final lists yet.

Try solving on your own before revealing the answer!

Q19. Insert < or > between the given pair of integers to make a true statement: ___

Background

Topic: Comparing Integers

This question tests your understanding of the order of negative numbers.

Key Terms and Formulas:

• On the number line, numbers to the left are less than those to the right.

Step-by-Step Guidance

1. Recall that is less than because it is further left on the number line.

2. Insert the correct symbol ( or ) between the numbers, but do not state which yet.

Try solving on your own before revealing the answer!

Q20. Simplify:

Background

Topic: Properties of Negative Numbers

This question tests your understanding of the rules for multiplying or applying negatives.

Key Terms and Formulas:

• Negative of a negative:

Step-by-Step Guidance

1. Recognize that taking the negative of a negative number results in a positive number.

2. Apply the rule to , but do not state the final value yet.

Try solving on your own before revealing the answer!

Q21. Simplify the algebraic expression:

Background

Topic: Combining Like Terms and Distributive Property

This question tests your ability to use the distributive property and combine like terms in algebraic expressions.

Key Terms and Formulas:

• Distributive Property:

• Combine like terms: Add coefficients of the same variable.

Step-by-Step Guidance

1. Apply the distributive property to both terms: and .

2. Multiply out each term.

3. Add the like terms together.

4. Write the simplified expression, but do not state the final combined form yet.

Try solving on your own before revealing the answer!