MTH 098 Chapter 1 Study Guide – Step-by-Step Algebra Guidance

Q1. Simplify the expression: -16 + 5 - 8

Background

Topic: Order of Operations and Integer Arithmetic

This question tests your ability to simplify an expression by combining integers using addition and subtraction.

Key Terms and Concepts:

• Addition and subtraction of integers

• Order of operations (left to right for addition/subtraction)

Step-by-Step Guidance

1. Start by identifying the numbers and operations: $-16 + 5 - 8$.

2. First, add $-16$ and $5$ together. Remember, adding a positive number to a negative number is the same as subtracting the smaller from the larger and keeping the sign of the larger absolute value.

3. Take the result from step 2 and subtract $8$ from it.

Try solving on your own before revealing the answer!

Final Answer: -19

$-16 + 5 = -11$

$-11 - 8 = -19$

The simplified value is $-19$.

Q2. Evaluate the expression $x^2 + y^2$ for $x = 5$, $y = -3$

Background

Topic: Substitution and Exponents

This question tests your ability to substitute given values into an algebraic expression and evaluate using exponents.

Key Terms and Formulas:

• Substitution: Replace variables with given values.

• Exponent: $x^2$ means $x$ multiplied by itself.

Step-by-Step Guidance

1. Substitute $x = 5$ and $y = -3$ into the expression: $x^2 + y^2$ becomes $5^2 + (-3)^2$.

2. Calculate $5^2$ (which means $5 \times 5$).

3. Calculate $(-3)^2$ (which means $-3 \times -3$).

4. Add the two results from steps 2 and 3 together.

Try solving on your own before revealing the answer!

Final Answer: 34

$5^2 = 25$

$(-3)^2 = 9$

$25 + 9 = 34$

Q3. Simplify the expression: 8 - 379

Background

Topic: Integer Subtraction

This question tests your ability to subtract a larger number from a smaller number, resulting in a negative integer.

Key Terms and Concepts:

• Subtraction of integers

Step-by-Step Guidance

1. Write the expression as $8 - 379$.

2. Since $379$is greater than $8$, the result will be negative.

3. Subtract $8$from $379$ to find the difference, then attach a negative sign.

Try solving on your own before revealing the answer!

Final Answer: -371

$8 - 379 = -371$

Subtracting a larger number from a smaller number gives a negative result.

Q4. Round 1.7877 to the nearest tenth

Background

Topic: Rounding Decimals

This question tests your ability to round a decimal number to a specified place value (the tenths place).

Key Terms and Concepts:

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

• Rounding rules: If the next digit is 5 or greater, round up; if less than 5, round down.

Step-by-Step Guidance

1. Identify the tenths place in $1.7877$ (the first digit after the decimal point).

2. Look at the digit in the hundredths place (the second digit after the decimal point) to decide whether to round up or down.

3. Apply the rounding rule based on the value of the hundredths digit.

Try solving on your own before revealing the answer!

Final Answer: 1.8

The tenths digit is 7, and the hundredths digit is 8 (which is 5 or greater), so you round up to 1.8.

Q5. Write the fraction 6 as a terminating or repeating decimal

Background

Topic: Fractions and Decimals

This question tests your ability to convert a whole number (which can be written as a fraction) into a decimal and classify it as terminating or repeating.

Key Terms and Concepts:

• Terminating decimal: A decimal that ends.

• Repeating decimal: A decimal that repeats a pattern forever.

• Whole numbers can be written as decimals (e.g., $6 = 6.0$).

Step-by-Step Guidance

1. Recognize that $6$as a fraction is $6/1$.

2. Divide $6$by $1$ to write it as a decimal.

3. Determine if the decimal terminates or repeats.

Try solving on your own before revealing the answer!

Final Answer: 6 as a terminating decimal (6.0)

$6 \div 1 = 6.0$

Since the decimal ends, it is a terminating decimal.

Q6. Find the sum: -49 + (-20)

Background

Topic: Addition of Negative Integers

This question tests your ability to add two negative numbers together.

Key Terms and Concepts:

• Adding negative numbers: The sum is more negative.

Step-by-Step Guidance

1. Write the expression: $-49 + (-20)$.

2. Combine the two negative numbers by adding their absolute values and keeping the negative sign.

Try solving on your own before revealing the answer!

Final Answer: -69

$-49 + (-20) = -69$

Adding two negatives results in a more negative number.

Q7. Find the sum: 9 + (-10) + 15 + (-7)

Background

Topic: Addition of Integers

This question tests your ability to add positive and negative integers together.

Key Terms and Concepts:

• Addition of positive and negative numbers

• Grouping like terms can help simplify the process

Step-by-Step Guidance

1. Group the positive numbers: $9 + 15$.

2. Group the negative numbers: $-10 + (-7)$.

3. Add the results from steps 1 and 2 together.

Try solving on your own before revealing the answer!

Final Answer: 7

$9 + 15 = 24$

$-10 + (-7) = -17$

$24 + (-17) = 7$

Q8. Jared borrowed $200 from his friend Linda. He paid her back $29, but then had to borrow another $90. How much does he still owe her?

Background

Topic: Integer Operations in Word Problems

This question tests your ability to model a real-life situation with integer operations (borrowing and repaying money).

Key Terms and Concepts:

• Borrowing money increases the amount owed (add to debt).

• Paying back money decreases the amount owed (subtract from debt).

Step-by-Step Guidance

1. Start with the initial amount Jared owes: $200$.

2. Subtract the amount he paid back: $200 - 29$.

3. Add the new amount he borrowed: Take the result from step 2 and add $90$.

Try solving on your own before revealing the answer!

Final Answer: $261

$200 - 29 = 171$

$171 + 90 = 261$

Jared still owes Linda $261.

Q9. Find the difference: -16 - 20

Background

Topic: Subtraction of Integers

This question tests your ability to subtract a positive number from a negative number.

Key Terms and Concepts:

• Subtracting a positive from a negative makes the result more negative.

Step-by-Step Guidance

1. Write the expression: $-16 - 20$.

2. Think of subtraction as adding the opposite: $-16 + (-20)$.

3. Add the two negative numbers together.

Try solving on your own before revealing the answer!

Final Answer: -36

$-16 - 20 = -16 + (-20) = -36$

Q10. Find the difference: 7 - (-23)

Background

Topic: Subtraction of Negative Numbers

This question tests your ability to subtract a negative number, which is the same as adding its positive.

Key Terms and Concepts:

• Subtracting a negative: $a - (-b) = a + b$

Step-by-Step Guidance

1. Write the expression: $7 - (-23)$.

2. Recall that subtracting a negative is the same as adding the positive: $7 + 23$.

3. Add the two numbers together.

Try solving on your own before revealing the answer!

Final Answer: 30

$7 - (-23) = 7 + 23 = 30$