Podcast
Questions and Answers
Simplify: −7 + (+9)
Simplify: −7 + (+9)
2
Simplify: −28 + (−11)
Simplify: −28 + (−11)
-39
Simplify: −6 − (−10)
Simplify: −6 − (−10)
4
Simplify: (−5) + (−6) − (−7) − (+4) + (+3)
Simplify: (−5) + (−6) − (−7) − (+4) + (+3)
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Evaluate: 18 ÷ 2 ∙ 5 ÷ −6 + 4 ∙ 7
Evaluate: 18 ÷ 2 ∙ 5 ÷ −6 + 4 ∙ 7
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Evaluate: 2 ∙ 42 + 3(4+5)2
Evaluate: 2 ∙ 42 + 3(4+5)2
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Evaluate: 102 − 3 ∙ 52
Evaluate: 102 − 3 ∙ 52
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Simplify: 56/25
Simplify: 56/25
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Change the improper fraction 6/5 to a mixed number
Change the improper fraction 6/5 to a mixed number
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Change the mixed number 2 3/8 to an improper fraction
Change the mixed number 2 3/8 to an improper fraction
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Simplify: 8 + 4/5
Simplify: 8 + 4/5
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Simplify: 10 2/16 − 3/16
Simplify: 10 2/16 − 3/16
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Simplify: 8 ∙ 27/5
Simplify: 8 ∙ 27/5
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Simplify: 8 ÷ 3/16
Simplify: 8 ÷ 3/16
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Find the total current in the circuit.
Find the total current in the circuit.
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Round 27.2847 to the nearest hundredth.
Round 27.2847 to the nearest hundredth.
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Round 27.2847 to the nearest unit.
Round 27.2847 to the nearest unit.
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Round the number 63,914 to two significant digits.
Round the number 63,914 to two significant digits.
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Round the number 0.003275 to two significant digits.
Round the number 0.003275 to two significant digits.
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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.
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Description
Test your understanding of concepts from Algebra Chapters 1 and 2. This quiz includes simplifying expressions, evaluating mathematical operations, and converting improper fractions to mixed numbers. Show all your work for full credit!
