Questions and Answers
How many terms are in the expression $3x + \frac{5a}{2y}$?
2
In the expression $2y - 7z^3$, which of the following is an exponent?
In the expression $6x^2 + 5$, which of the following correctly identifies the 6?
Which notation best represents the relationship between the two numbers plotted on the number line below?
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In the expression $[1 + 7 \cdot (2 - 9)] \div 3 + 12$, which of the following operations is done first?
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What is the opposite of 6?
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What type of number is $\sqrt{23}$?
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Which of the following is true for multiplying two signed numbers with opposite signs?
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What is an unknown value called?
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What are natural numbers and zero called?
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What is a number's distance from zero called?
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What are quantities combined by only addition or subtraction called?
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Express the sum of x and 3 divided by 2.
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Half of g multiplied by t squared is equal to d.
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The length l of a rectangle is equal to its area A divided by its width w.
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Represent the length of the other piece if a piece of yarn 29 inches long is cut into two parts, with one part being m inches long.
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The perimeter of a rectangle is twice the sum of its length l and width w.
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The circumference C of a circle is equal to the product of π and the diameter d.
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Express the gross profit GP of an item if the selling price p minus the cost of 2 dollars is considered.
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Evaluate the expression $4 + 3^2 ÷ (-1)(4)(-2) - 1$.
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What is the value of $-3^2/2^3 + 1$?
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What is the result of $\frac{5}{12} + \frac{1}{12} -\frac{1}{4}$?
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Simplify $3x + 2y + 5x - y$.
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Simplify $8mn + 10 - 2(3mn - 1) + 2mn - 5 + 8$.
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Simplify $a + [a + b - a - (2a - b)]$.
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If $x = -3$ and $y = 5$, find the value of the expression $2x^2 + 4y - 5$.
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If $a = -2$, find the value of the expression $|2a + 5|$.
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Phil drove for 5 hours at 65 miles per hour. How far did he drive if $d = rt$?
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Find the value of A in the formula $A = \frac{1}{2}h (a + b)$ when $h = 6$ in., $a = 12$ in., and $b = 8$ in.
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What property is represented by $(a + b)c = ac + bc$?
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What property is represented by $r(s + t) = (s + t)r$?
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What property is represented by $\frac{3}{5}(\frac{2}{5}) = \frac{3}{5}$?
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What property is represented by $x + (y + z) = (x + y) + z$?
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What property is represented by $3x + 0 = 3x$?
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Study Notes
Algebra Expressions and Terms
- The expression 3x + 5a/2y contains two terms.
- In 2y − 7z³, the number 3 is identified as the exponent of z.
- The coefficient in 6x² + 5 is 6.
Mathematical Relationships and Inequalities
- The notation -1 < 5 illustrates the relationship between the two plotted numbers on a number line.
Order of Operations
- In the expression [1 + 7 · (2 − 9)] ÷ 3 + 12, the first operation performed is 2 − 9.
Number Properties
- The opposite of the number 6 is -6.
- The value of √23 is classified as an irrational number.
- When multiplying two numbers with opposite signs, the resultant product is negative.
Fundamental Algebra Concepts
- Variable represents an unknown value in algebra.
- Whole numbers include natural numbers and zero.
- Absolute value measures a number's distance from zero in a number line.
Composition of Expressions
- Terms are quantities combined solely through addition or subtraction.
- The expression for “the sum of x and 3 divided by 2” can be written as (x + 3) ÷ 2.
Formulas and Equations
- The relationship for half of g multiplied by t squared equal to d is represented by 1/2gt² = d.
- The formula for the length l of a rectangle is l = A/w where A is the area and w is the width.
- The perimeter of a rectangle is calculated as P = 2(l + w).
Mathematical Constants and Dimensions
- The circumference C of a circle is expressed as C = πd.
Financial Calculations
- The gross profit GP from an item is calculated as GP = p - 2, where p is the selling price.
Simplifying Mathematical Expressions
- The expression 4 + 3² ÷ (-1)(4)(-2) − 1 simplifies to 75.
- The result of -3²/2³ + 1 is -1.
- The expression 5/12 + 1/12 − 1/4 simplifies to 1/4.
Combining Like Terms
- The expression 3x + 2y + 5x − y can be simplified to 8x + y.
- For 8mn + 10 − 2(3mn − 1) + 2mn − 5 + 8, the result is simplified to 4mn + 15.
Value Evaluation Examples
- When substituting x = -3 and y = 5 in the expression 2x² + 4y − 5, the resulting value is 33.
- If a = -2, the absolute value expression | 2a + 5 | evaluates to 1.
Real-life Applications
- Phil drives for 5 hours at a rate of 65 miles per hour, covering a total distance of 325 miles.
- In the formula A = 1/2h(a + b) with values h = 6 in, a = 12 in, b = 8 in, the area A is calculated as 60 sq. in..
Algebraic Properties
- The distributive property states that (a + b)c = ac + bc.
- The commutative property highlights that r(s + t) = (s + t)r.
- The identity property is demonstrated with the expression 3/5(2/5) = 3/5.
- The associative property allows for grouping changes as shown in x + (y + z) = (x + y) + z.
- The expression 3x + 0 = 3x exemplifies the identity property in algebra.
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