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Questions and Answers
What is the result of simplifying the expression $-6 - (-10)$?
What is the result of simplifying the expression $-6 - (-10)$?
- $-4$
- $4$ (correct)
- $-16$
- $-20$
What is the simplified result of $(-5) + (-6) - (-7) - (+4) + (+3)$?
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 $\frac{35}{6}$?
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?
Evaluate the following expression: $18 \div 2 \cdot 5 \div -6 + 4 \cdot 7$. What is the result?
What is the rounded result of $27.2847$ to the nearest hundredth?
What is the rounded result of $27.2847$ to the nearest hundredth?
Flashcards
Adding Integers
Adding Integers
Add/subtract numbers directly, paying attention to signs.
Adding/Subtracting Fractions
Adding/Subtracting Fractions
Convert to improper, find a common denominator, then add/subtract.
Order of Operations
Order of Operations
Remember PEMDAS/BODMAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.
Improper to Mixed Number
Improper to Mixed Number
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Mixed to Improper Fraction
Mixed to Improper Fraction
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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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