Questions and Answers
Match the following with their correct descriptions:
Fractions = Ordered by the values of their numerators and denominators Decimals = Ordered by their numerical values Negative Numbers = Added from least to greatest absolute value Rational Numbers = Real numbers expressed as ratios of integers
Match the following with their correct types of rational numbers:
rac{17}{4} = Fraction 0.375 = Decimal 4 rac{1}{2} = Fraction -8 = Negative Number
Match the following with their correct properties:
Positive Rational Numbers = Added before negative rational numbers Negative Rational Numbers = Considered separately when adding to other rationals Fractions = Can be simplified to mixed numbers Decimals = Expressed by dividing one integer by another
Match the following with their correct ordering criteria:
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Match the following with their correct examples:
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Match the following with their correct divisions:
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What is the relationship between the variables x and y in a linear equation?
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What is the highest power of the variables in a quadratic equation?
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What type of equation models growth or decay over time?
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What is the general form of a quadratic equation in the vertex form of a parabola?
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Which of the following is NOT a characteristic of a linear equation?
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What is the general form of a simple exponential function?
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What method is typically used when two equations have a common variable that can be eliminated?
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In the equation y = 3x + 4 and 5x - y = 8, what is the value of x after applying the elimination method?
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When is the substitution method most commonly used in solving equations?
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In the context of equations, what role do graphical methods play when algebraic methods become complex?
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Which field uses equations to design structures, predict performance, and optimize systems?
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How are equations applied in computer science?
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Study Notes
Ordering Rational Numbers
Rational numbers are the set of all real numbers that can be expressed as ratios of two integers. They include integers, fractions, and decimals that can be expressed as ratios of integers. There are two main types of rational numbers: fractions (ratios of whole number) and decimals (ratios of whole numbers).
Fractional Parts
Fractional parts are found by dividing one integer by another. For example, if you divide 17 by 4, you get the fraction \(\frac{17}{4}\). However, this fraction can be simplified to \(4 \frac{1}{2}\), which is equivalent to `(4 + \frac{1}{2}). Fractions are ordered using their values. If one fraction is greater than another, then the numerator of the larger fraction is greater than the numerator of the smaller fraction, and the denominator of the larger fraction is less than the denominator of the smaller fraction.
Decimal Parts
Decimal parts are found by dividing one integer by another and expressing the result as a decimal. For example, if you divide 15 by 4, you get the decimal 0.375. Decimals are also ordered using their values. If one decimal is greater than another, then its value is greater than the other decimal's value.
Negative Numbers
Negative numbers are added to rational numbers in order from least absolute to greatest absolute. This means that when adding negative rational numbers, you should consider the sign of each number separately. Positive rational numbers are always added before negative ones. For example, when adding \(-3 + (-4)\), you first add the two negative signs together to get negative: `((-3) + (-4) = -7).
Adding and Subtracting Rational Numbers
To add or subtract rational numbers, you can use the methods described above for adding decimals and fractions. If the signs of the numbers are the same, you add the numerators and keep the same denominator. If the signs are different, you subtract the numerators and keep the same denominator. You may need to simplify your answer after adding or subtracting.
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