Algebra Class Test: Chapters 1 and 2

Questions and Answers

What is the result of simplifying the expression $-6 - (-10)$?

$-4$

$4$ (correct)

$-16$

$-20$

What is the simplified result of $(-5) + (-6) - (-7) - (+4) + (+3)$?

$-3$ (correct)

$-5$

$-9$

$-7$

What is the proper mixed number form of the improper fraction $\frac{35}{6}$?

7 $\frac{1}{6}$

5 $\frac{5}{6}$ (correct)

6 $\frac{1}{6}$

4 $\frac{1}{6}$

Evaluate the following expression: $18 \div 2 \cdot 5 \div -6 + 4 \cdot 7$. What is the result?

<p>$-8$</p> Signup and view all the answers

What is the rounded result of $27.2847$ to the nearest hundredth?

<p>27.28</p> Signup and view all the answers

Study Notes

Simplification of Expressions

Addition of integers: Simplify expressions like −7 + (+9) by adding or subtracting the numbers.
Addition of negative integers: For −28 + (−11), add the absolute values and keep the negative sign.
Subtracting negatives: When simplifying −6 − (−10), convert it to addition: −6 + 10.
Combining multiple integers: For (−5) + (−6) − (−7) − (+4) + (+3), carefully add and subtract each term to arrive at the final value.

Evaluation of Expressions

Follow the order of operations (PEMDAS/BODMAS) when evaluating:
- In 18 ÷ 2 ∙ 5 ÷ −6 + 4 ∙ 7, perform division and multiplication from left to right before addition.
- For the complex expression (2 ∙ 42 + 3(4+5)²), work inside parentheses first and apply exponentiation.

Operations with Powers and Fractions

Evaluate simple power and product: In 102 − 3 ∙ 52, compute each term separately.
For 36, remember it represents a squared number (6²).
Simplifying fractions involves reducing them: In 56/25, identify common factors.

Conversion Between Fraction Forms

Improper fractions to mixed numbers: To change 6/5, divide the numerator by the denominator to find the whole number and remainder.
Mixed numbers to improper fractions: Convert 2 3/8 by multiplying the whole number by the denominator and adding the numerator.

Additional Simplifications

When simplifying expressions with fractions: For 8 + 4/5, convert to a common denominator before addition.
Simplifying complex fractions like 10 2/16 − 3/16 involves converting mixed numbers to improper fractions first.

Current in Circuits

Finding the total current: Add up all individual currents in a given circuit context to calculate the total.

Rounding Numbers

Rounding to significant digits requires identifying the desired precision in values.
Round 27.2847 to the nearest hundredth, focusing on the second decimal place for rounding decisions.
For rounding to the nearest unit, look at the first decimal place.
When rounding large numbers like 63,914 to two significant digits, keep the first two non-zero digits.
Round small decimal numbers like 0.003275 by focusing on relevant significant figures after adjusting the decimal point.

Description

This quiz assesses your understanding of the key concepts from Chapters 1 and 2 of Algebra. You will need to simplify expressions, evaluate mathematical operations, and convert improper fractions. Show all your work for full credit!