Step-by-Step Guidance for Developmental Math 2 Skills Assessment

Q1. Simplify: -4 + 3 - 12

Background

Topic: Integer Operations (Addition and Subtraction)

This question tests your ability to add and subtract integers, which is a foundational skill in algebra.

Key Terms and Concepts:

• Addition and subtraction of positive and negative numbers

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

Step-by-Step Guidance

1. Start by adding the first two numbers: $-4 + 3$.

2. Take the result from step 1 and subtract 12: $(\text{result}) - 12$.

Try solving on your own before revealing the answer!

Q2. Simplify: $\frac{2}{5} - \frac{3}{6}$

Background

Topic: Operations with Fractions

This question tests your ability to subtract fractions with different denominators.

Key Terms and Formulas:

• Common denominator: The least common multiple (LCM) of the denominators

• Fraction subtraction: $\frac{a}{b} - \frac{c}{d} = \frac{ad - bc}{bd}$ (after finding a common denominator)

Step-by-Step Guidance

1. Find the least common denominator (LCD) for 5 and 6.

2. Rewrite both fractions with the LCD as the denominator.

3. Subtract the numerators and keep the common denominator.

Try solving on your own before revealing the answer!

Q3. Simplify: -11.5 - (-7.2)

Background

Topic: Operations with Decimals and Negative Numbers

This question tests your understanding of subtracting negative numbers and working with decimals.

Key Terms and Concepts:

• Subtracting a negative is the same as adding the positive: $a - (-b) = a + b$

Step-by-Step Guidance

1. Recognize that subtracting a negative is the same as adding: $-11.5 - (-7.2) = -11.5 + 7.2$.

2. Add $-11.5$ and $7.2$ together.

Try solving on your own before revealing the answer!

Q4. Simplify: $\frac{1}{12} - \frac{1}{20} + \frac{1}{4}$

Background

Topic: Adding and Subtracting Fractions

This question tests your ability to find a common denominator and combine fractions.

Key Terms and Formulas:

• Common denominator: The least common multiple (LCM) of 12, 20, and 4

• Adding/subtracting fractions: $\frac{a}{b} \pm \frac{c}{d} = \frac{ad \pm bc}{bd}$ (after finding a common denominator)

Step-by-Step Guidance

1. Find the least common denominator (LCD) for 12, 20, and 4.

2. Rewrite each fraction with the LCD as the denominator.

3. Combine the numerators according to the operation signs.

Try solving on your own before revealing the answer!

Q5. Simplify: 8 + (−5) − (−6) − 10

Background

Topic: Integer Operations

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

Key Terms and Concepts:

• Subtracting a negative is the same as adding: $a - (-b) = a + b$

Step-by-Step Guidance

1. Rewrite the expression, changing $-(-6)$ to $+6$.

2. Combine the numbers from left to right: $8 + (-5) + 6 - 10$.

3. Add and subtract in order.

Try solving on your own before revealing the answer!