Pre algebra basics
63 flashcards covering Pre algebra basics for the ACT Math section.
Pre-algebra basics form the foundation of math by introducing key concepts that build toward more complex topics. This includes working with integers, fractions, decimals, ratios, percentages, and simple equations, as well as basic operations like addition, subtraction, multiplication, and division. These skills help you solve everyday problems and are crucial for advancing in math, making them essential for academic success.
On the ACT Math section, pre-algebra questions often appear in multiple-choice formats, testing your ability to manipulate numbers in word problems, equations, or data interpretations. Common traps include misreading questions, such as confusing percentages with fractions, or making calculation errors with negative numbers, so accuracy is key. Focus on practicing operations with different number types and recognizing patterns in problems to improve speed and confidence.
A concrete tip: Always simplify expressions step by step to catch potential mistakes.
Terms (63)
- 01
Integer
An integer is a whole number that can be positive, negative, or zero, such as -3, 0, or 5, and it does not include fractions or decimals.
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Whole number
A whole number is a non-negative integer, including zero and positive numbers like 0, 1, 2, but not negative numbers or fractions.
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Natural number
A natural number is a positive integer starting from 1, such as 1, 2, 3, and sometimes including 0 depending on the context, but not negative numbers.
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Fraction
A fraction represents a part of a whole and is written as one number over another, like 1/2, where the top is the numerator and the bottom is the denominator.
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Proper fraction
A proper fraction is a fraction where the numerator is less than the denominator, such as 3/4, which is less than 1.
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Improper fraction
An improper fraction is a fraction where the numerator is greater than or equal to the denominator, such as 5/3, which is greater than 1.
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Mixed number
A mixed number combines a whole number and a proper fraction, like 2 1/2, which equals 5/2.
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Decimal
A decimal is a number expressed in base-10 with a decimal point, such as 0.75, where digits after the point represent parts of a whole.
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Percent
A percent is a fraction out of 100, represented with a % symbol, such as 50%, which means 50 per 100 or 0.50.
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Ratio
A ratio compares two quantities by division, often written as a:b or a to b, like 2:3, meaning 2 parts to 3 parts.
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Proportion
A proportion is an equation stating that two ratios are equal, such as 1/2 = 3/6, which can be used to solve for unknown values.
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Exponent
An exponent is a small number written above and to the right of a base that indicates how many times to multiply the base by itself, like in 2^3 which means 2 multiplied by 2 by 2.
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Base
In an exponential expression, the base is the number being multiplied by itself, as in 3^4 where 3 is the base and 4 is the exponent.
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Order of operations
Order of operations is the rule that dictates the sequence for solving expressions: parentheses first, then exponents, multiplication and division from left to right, and addition and subtraction from left to right.
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Commutative property
The commutative property states that the order of addition or multiplication of numbers does not change the result, such as 2 + 3 = 3 + 2.
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Associative property
The associative property means that the grouping of numbers in addition or multiplication does not affect the result, like (2 + 3) + 4 = 2 + (3 + 4).
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Distributive property
The distributive property allows multiplying a number by a sum inside parentheses, such as 2(3 + 4) = 23 + 24.
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Absolute value
Absolute value is the distance of a number from zero on the number line, always positive, so the absolute value of -5 is 5.
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Opposite of a number
The opposite of a number is another number that is the same distance from zero but on the other side, like the opposite of 4 is -4.
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Reciprocal
The reciprocal of a number is 1 divided by that number, such as the reciprocal of 2 being 1/2, used in division of fractions.
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Greatest common divisor
The greatest common divisor of two numbers is the largest number that divides both without a remainder, like 6 for 12 and 18.
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Least common multiple
The least common multiple of two numbers is the smallest number that is a multiple of both, such as 12 for 4 and 6.
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Prime number
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself, like 7.
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Composite number
A composite number is a positive integer greater than 1 that is not prime, meaning it has divisors other than 1 and itself, like 6.
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Factor
A factor of a number is an integer that divides that number exactly without a remainder, such as 2 and 3 being factors of 6.
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Multiple
A multiple of a number is the product of that number and an integer, like 10, 15, and 20 being multiples of 5.
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Adding fractions
To add fractions, they must have the same denominator; add the numerators and keep the denominator, or find a common denominator first.
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Subtracting fractions
Subtracting fractions requires a common denominator; subtract the numerators and keep the denominator the same.
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Multiplying fractions
Multiplying fractions involves multiplying the numerators together and the denominators together, then simplifying if possible.
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Dividing fractions
Dividing fractions means multiplying the first fraction by the reciprocal of the second, such as (1/2) ÷ (3/4) = (1/2) (4/3).
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Converting fractions to decimals
Converting a fraction to a decimal involves dividing the numerator by the denominator, like 1/4 becoming 0.25.
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Percent increase
Percent increase is calculated by finding the difference between the new and original values, dividing by the original, and multiplying by 100.
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Percent decrease
Percent decrease is found by subtracting the new value from the original, dividing by the original, and multiplying by 100.
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Simple interest
Simple interest is calculated using the formula I = P R T, where I is interest, P is principal, R is rate, and T is time in years.
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Ratio of two quantities
The ratio of two quantities expresses their comparison, such as the ratio of 10 apples to 15 oranges being 10:15 or 2:3 after simplifying.
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Solving proportions
Solving proportions involves cross-multiplying to find an unknown value, like in 2/3 = x/6, where x = 4.
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Basic linear equation
A basic linear equation is an equation like 2x + 3 = 7, which can be solved by isolating the variable using addition, subtraction, multiplication, or division.
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Inequality
An inequality is a mathematical statement using symbols like >, <, ≥, or ≤ to compare two expressions, such as x > 5.
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Number line
A number line is a straight line with numbers marked at equal intervals, used to visualize and compare numbers, including positive and negative values.
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Positive number
A positive number is a number greater than zero, like 5, and is located to the right of zero on the number line.
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Negative number
A negative number is a number less than zero, like -3, and is located to the left of zero on the number line.
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Adding integers
Adding integers involves combining them based on their signs; add two positives or two negatives, or subtract the absolute values and use the sign of the larger.
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Subtracting integers
Subtracting integers means adding the opposite, such as 5 - 3 = 5 + (-3), and then following the rules for adding integers.
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Multiplying integers
Multiplying integers results in a positive product if both are positive or both negative, and negative if one is positive and one negative.
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Dividing integers
Dividing integers gives a positive quotient if both are positive or both negative, and negative if one is positive and one negative.
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Square root
The square root of a number is a value that, when multiplied by itself, gives the original number, like the square root of 9 being 3.
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Cube root
The cube root of a number is a value that, when multiplied by itself three times, gives the original number, such as the cube root of 8 being 2.
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Scientific notation
Scientific notation expresses numbers as a product of a number between 1 and 10 and a power of 10, like 5.6 × 10^3 for 5600.
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Evaluating expressions
Evaluating an expression means substituting values for variables and following the order of operations to find the result, such as 2x + 3 when x=4 equals 11.
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Translating words to math
Translating words to math involves converting phrases like 'five more than x' to expressions such as x + 5 for use in equations.
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Mean
The mean of a set of numbers is the sum of the values divided by the count of values, like the mean of 1, 2, and 3 being 2.
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Median
The median of a set of numbers is the middle value when ordered, or the average of the two middle values if even, like 3 for the set 1, 3, 5.
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Mode
The mode of a set of numbers is the value that appears most frequently, such as 2 in the set 1, 2, 2, 3.
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Range
The range of a set of numbers is the difference between the largest and smallest values, like 4 for the set 1, 2, 5.
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Basic probability
Basic probability is the likelihood of an event, calculated as the number of favorable outcomes divided by the total possible outcomes, like 1/6 for rolling a 6 on a die.
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Common trap in fractions
A common trap in fractions is adding numerators and denominators separately without a common denominator, which leads to incorrect results.
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Order of operations mistake
A frequent mistake in order of operations is performing multiplication before parentheses, which violates the correct sequence.
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Misinterpreting percentages
Misinterpreting percentages often involves confusing 'percent of' with 'percent more than,' such as thinking 10% of 100 is the same as 100% more than 10.
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Example: Adding mixed numbers
For example, adding 2 1/2 and 1 3/4 involves converting to improper fractions, adding 5/2 + 7/4, finding a common denominator of 4, and getting 3 1/4.
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Example: Solving a proportion
For instance, solving 4/5 = x/10 involves cross-multiplying to get 410 = 5x, so x=8.
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Strategy for word problems
A strategy for word problems is to identify key phrases that indicate operations, define variables for unknowns, and set up equations to solve.
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Example: Percent decrease
For example, if a price decreases from $50 to $40, the percent decrease is (50-40)/50 100 = 20%.
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Common trap in exponents
A common trap in exponents is confusing negative exponents with reciprocals, like thinking 2^-1 means -2 instead of 1/2.