Questions and Answers
What is an equation?
What is a constant?
A term that contains only a number
Define a variable.
A letter that represents an unknown value
What is a coefficient?
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What does inverse refer to?
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What is a solution set?
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What are like terms?
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What is substitution?
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How old is Ben if he is 5 years younger than twice his brother's age?
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If Maria takes 5 more cookies than her friend Jackie and puts 1 cookie back, how many cookies does she have?
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If Ana ran 3 miles on Monday, 5 miles yesterday, and 7 miles today, how many miles will she have run in all after an unknown number tomorrow?
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How far will Pedro drive each day if he drives the same distance for 3 days at the beach?
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How much will Ivan earn if he delivers pizza for 5 hours?
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How many objects did Spot fetch in all if he fetched 7 sticks and some rocks?
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How many cookies did Mari's grandmother bake if she baked 5 for Mari and 3 for each of her friends?
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If Ali answered 5 problems incorrectly and didn't finish the last problem, how many problems did she answer correctly?
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If Farmer Jones has 5 hens and each hen laid 3 eggs, but some eggs cracked, how many eggs did not crack?
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If Alex feeds his turtle the same amount of food twice a day, how much food will he feed the turtle in a week?
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If 88 + 5 = n, how many candies does Lily have now?
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If 3 X $12.00 = n, how much do 3 tickets cost?
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If 164 / 4 = n, how many soda machines are there in the school?
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If 5 X 10 = n, how many marbles did Jane buy last month?
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If 58 - 8 = n, how many more salads does the restaurant expect to serve?
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If 676 + 47 = n, how many pumpkins did Michael grow in both years?
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If 4 X 35 = n, how many passengers can 4 buses carry?
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If 217 / 7 = n, how many cars can be parked in each row?
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If 49 - 43 = n, how many people are on the sand?
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If 5n = 35, how many people can enter the amusement park with $35?
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If y = 25n + 350, how much does it cost for 50 people?
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Define like terms.
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What is a coefficient?
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What is a constant?
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What does simplify mean?
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What is a variable?
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What does combine mean?
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Study Notes
Key Algebraic Concepts
- Equation: A mathematical expression with an equals sign, showing equivalence (e.g., x + 3 = 5).
- Constant: A term that is purely numerical, without any variables.
- Variable: A symbol (usually a letter) representing an unknown value in equations and expressions.
- Coefficient: The numerical part of a term that contains a variable, indicating how many times the variable is being counted.
- Inverse: A mathematical operation that reverses the effect of another operation (e.g., addition and subtraction are inverses).
- Solution set: A collection of all values that satisfy a given equation or inequality.
Algebraic Operations
- Like Terms: Terms with the same variable(s); can be combined in expressions (e.g., x + x = 2x).
- Substitution: Replacing a variable with a specific number to check the correctness of a solution.
Word Problems and Their Representations
- Ben's Age Problem: Involves comparing Ben's age with his brother's age using expressions.
- Maria's Cookie Problem: Focuses on the relationship between the number of cookies taken by Maria and Jackie.
- Ana's Running Miles: Summation of distances run over multiple days plus an unknown future distance.
- Pedro's Driving Distance: Calculation of daily driving distance over a set number of days.
- Ivan's Earnings: Earnings calculation for a specific number of working hours.
- Spot's Fetching Objects: Summation of different types of objects fetched.
- Mari's Cookies: Total cookies made based on individual distribution to Mari and her friends.
- Ali's Test Questions: Calculation of correctly answered questions based on incorrect ones.
- Farmer Jones' Eggs: Total of unbroken eggs resulting from a known quantity laid by hens.
- Alex's Turtle Feeding: Calculation of food given to the turtle over a week based on daily feeding.
Equation Representations of Word Problems
- Lily's Candies: 88 + 5 = n, calculates the total candies after receiving more.
- Ticket Costs: 3 x $12.00 = n, finds total cost of multiple tickets.
- Soda Machines: 164 / 4 = n, determines the number of machines based on soda cases.
- Jane's Marbles: 5 x 10 = n, totals marbles bought over multiple purchases.
- Salads at Restaurant: 58 - 8 = n, finds remaining salads to be served.
- Pumpkin Growth: 676 + 47 = n, calculates total pumpkins grown across two years.
- Bus Capacity: 4 x 35 = n, determines total passenger capacity for multiple buses.
- Parking Lot Spaces: 217 / 7 = n, calculates parking capacity per row.
- Beach Attendance: 49 - 43 = n, determines how many people are sunbathing.
- Amusement Park Entry: 5n = 35, finds how many people can enter with a limited budget.
Additional Definitions
- Simplify: To make an expression easier to understand or compute.
- Combine: The process of grouping similar numbers or variables together for simplification.
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Description
Test your understanding of algebraic expressions, equations, and their components. This quiz includes matching definitions and understanding the roles of constants, variables, and coefficients in mathematical sentences. Perfect for anyone studying algebraic expressions in depth.
