Prealgebra Flashcards
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| 1786861166 | Addition Principle of Equality | If the same number is added to both sides of an equation, the results on both sides are equal in value. We can restate this principle in symbols this way. For any numbers a,b, and c. if a+b, then a+c=b+c | 0 | |
| 1786861167 | opposites | 2 and -2 | 1 | |
| 1786861168 | additive inverse property | a+(-a)=0 and -a+a=0 | 2 | |
| 1786861169 | line | extends indefinitely | 3 | |
| 1786861170 | line segment | has a beginning and an end | 4 | |
| 1786861171 | ray | starts at a point and extends indefinitely in one direction | 5 | |
| 1786861172 | angle | is formed whenever two rays meet at the same endpoint | 6 | |
| 1786861173 | vertex | the point at which they meet is called | 7 | |
| 1786861174 | supplementary angles | two angles that have a sum of 180 | 8 | |
| 1786861175 | adjacent angles | two angles that share a common side | 9 | |
| 1786861176 | Division Principle of Equality | If both sides of an equation are divided by the same nonzero number, the results on both sides are equal in value. We can restate it in symbols this way. For any numbers a,b,c, with c not equal to 0. if a+b, then a/c=b/c | 10 | |
| 1786861177 | Perimeter of a rectangle | The perimeter of a rectangle is twice the length plus twice the width P=2L+2W | 11 | |
| 1786861178 | Perimeter of a square | The perimeter of a square is four times the length of a side. P=4s | 12 | |
| 1786861179 | Parallelogram | is a four-sided figure in which both pairs of opposite sides are parallel. | 13 | |
| 1786861180 | Parallel lines | are straight lines that are always the same distance apart. | 14 | |
| 1786861181 | Area of a rectangle | is the length times the width A=LW | 15 | |
| 1786861182 | Area of a square | is the length of one side squared. A=s2 | 16 | |
| 1786861183 | Area of a parallelogram | is the base times the height A=bh | 17 | |
| 1786861184 | quadrilaterals | four sided figures | 18 | |
| 1786861185 | Volume | the volume of a rectangle solid is the product of the length times the width times the height V=LWH | 19 | |
| 1786861186 | Product Rule for Exponents | To multiply constants or variables in exponent form that have the same base, add the exponents but keep the base unchanged. | 20 | |
| 1786861187 | Procedure for multiplying algebraic expressions with exponents | 1. multiply the numerical coefficients. 2. Use the product rule for exponents. | 21 | |
| 1786861188 | monomial | has one term | 22 | |
| 1786861189 | binomial | has two terms | 23 | |
| 1786861190 | trinomial | has three terms | 24 | |
| 1786861191 | Divisibility Tests | 1. A number is divisible by 2 if its is even. This means that the last digit is 0,2,4,6. or 8. 2. A number is divisible by 3 is the sum of its digits is divisible by 3. 3. A number is divisible by 5 if its last digit is 0 or 5. | 25 | |
| 1786861192 | Prime number | is a whole number greater than 1 that is divisible only by itself and 1. | 26 | |
| 1786861193 | Composite number | is a whole number greater than 1 that can by divided by whole numbers other than itself and 1. | 27 | |
| 1786861194 | first few prime numbers are | 2,3,5,7,11,13,17,19,23,29... | 28 | |
| 1786861195 | factors | are numbers that are multiplied together. | 29 | |
| 1786861196 | prime factors | are factors that are prime. | 30 | |
| 1786861197 | Procedure to find prime factors using a division ladder | 1. Determine if the original number is divisible by a prime number. If so, divide and find the quotient. 2. Divide the quotient by prime numbers until the final quotient is a prime number. 3. Write the divisors and the final quotient as a product of prime factors. | 31 | |
| 1786861198 | Procedure to build a factor tree to find prime factors | 1. Write the number to be factored as a product of any two numbers other than 1 and itself. 2. In this product, circle any prime factor(s). 3. Write all factors that are not prime as products. 4. Circle any prime factor(s). 5. Repeat step 3 and 4 until all factors are primed. 6. Write the numbers that are circled as a product of prime numbers. | 32 | |
| 1786861199 | numerator | the top of a fraction shows the number of equal parts in the whole. | 33 | |
| 1786861200 | denominator | the bottom of a fraction shows the number of parts being talked about or being used. | 34 | |
| 1786861201 | Division Problems involving the numbers one and zero | 1. Any nonzero number divided by itself is 1. 2. Zero can never be the divisor in a division problem. 3. Zero may be divided by any number except zero; the result is always zero. In other words, any fraction with 0 in the numerator and a nonzero denominator equals 0. | 35 | |
| 1786861202 | Proper fraction | used to describe a quantity less than 1. | 36 | |
| 1786861203 | Improper fraction | used to describe a quantity greater than or equal to l. | 37 | |
| 1786861204 | Procedure to Change an Improper fraction to a mixed number | 1. Divide the numerator by the denominator. 2. The quotient is the whole number part of the mixed number. 3. The remainder from the division will be the numerator of the fraction. The denominator of the fraction remains unchanged. A mixed number is in the following form: quotient remainder/denominator | 38 | |
| 1786861205 | Procedure to Change a Mixed Number to an Improper Fraction | 1. Multiply the whole number by the denominator of the fraction. 2. Add this product to the numerator. The result is the numerator of the improper fraction. The denominator does not change. | 39 | |
| 1786861206 | Procedure to find Equivalent Fractions | To find an equivalent fraction, we multiply both the numerator and denominator by the same nonzero number. | 40 | |
| 1786861207 | reduced to lowest terms | (or written in simplest form) if the numerator and denominator have no common factors other than 1. | 41 | |
| 1786861208 | Procedure to Reduce a Fraction to lowest terms | 1. Write the numerator and denominator of the fraction each as a product of prime factors. 2. Any factor that appears in both the numerator and denominator is a common factor. Rewrite the common factors as the equivalent fraction and multiply. | 42 | |
| 1786861209 | The Quotient Rule | If the bases in the numerator and denominator of a fractional expression are the same and a and b are positive integers, then Use this form if the larger exponent is in the numerator and x=0. Use this form if the larger exponent is in the denominator and x=0. | 43 | |
| 1786861210 | Nonzero | For any nonzero number The expression 0 is not defined | 44 | |
| 1786861211 | Raising A Power to a Power or a Product to a Power | To raise a power to a power, keep the same base and multiply the exponents. To raise a product to a power, raise each factor to that power. | 45 | |
| 1786861212 | Additional Power Rule | If a fraction in parentheses is raised to a power, the parentheses indicate that the numerator and denominator are each raised to that power. | 46 | |
| 1786861213 | Ratio | is a comparison of two quantities that have the same units. | 47 | |
| 1786861214 | Rate | is a comparison of two quantities with different units. | 48 | |
| 1786861215 | Unit rates | ... | 49 | |
| 1786861216 | Multiplying fractions | 1. Simplify by factoring out common factors whenever possible. 2. Multiply numerators. 3. Multiply denominators. | 50 | |
| 1786861217 | Dividing fractions | To divide two fractions, we find the reciprocal of (invert) the second fraction and multiply. | 51 | |
| 1786861218 | Finding the least common denominator (LCD) | To find the LCD: 1. Write each denominator as the product of prime factors. 2. List the requirements for the factorization of the LCD. 3. Build an LCD that has all the factors of each denominator, using a minimum number of factors. | 52 | |
| 1786861219 | Adding or subtracting fractions with a common denominator | 1. Add or subtract the numerators. 2. Keep the common denominator. 3. Simplify the answer if necessary. | 53 | |
| 1786861220 | Adding or subtracting fractions with different denominators | 1. Find the LCD of the fractions. 2. Write equivalent fractions that have the LCD as the denominator. 3. Follow the steps for adding and subtracting fractions with a common denominator. | 54 | |
| 1786861221 | Adding mixed numbers | 1. Change fractional parts to equivalent fractions with the LCD as a denominator, if needed. 2. Add whole numbers and fractions separately. 3. If improper fractions occur, change to mixed numbers and simplify. | 55 | |
| 1786861222 | Subtracting mixed numbers | 1. Change fractional parts to equivalent fractions with the LCD as a denominator, if needed. 2. If necessary, borrow from the whole number to subtract fractions. 3. Subtract whole numbers and fractions separately. 4. Simplify the answer if necessary. | 56 | |
| 1786861223 | Multiplying and dividing mixed and/or whole numbers. | 1. Change any whole number to a fraction with a denominator of 1. 2. Change any mixed numbers to improper fractions. 3. Use the rule for multiplication or division of fractions. | 57 | |
| 1786861224 | Order of operations with fractions | To simplify fractions, perform operations in the following order: 1. Perform operations inside parentheses. 2. Simplify exponents. 3. Multiply and divide, working left to right. 4. Add and subtract, working left to right. | 58 | |
| 1786861225 | Solving equations using the multiplication principle | 1. If the variable is divided by a number, undo the division by multiplying both sides of the equation by this number. 2. If the variable is multiplied by a fraction, multiply both sides of the equation by the reciprocal of that fraction. 3. Check by substituting your answer back into the original equation. | 59 | |
| 1786861226 | Adding polynomials | To add two polynomials, we add like terms. | 60 | |
| 1786861227 | Finding the opposite of a polynomial | When a negative sign precedes parentheses, we remove parentheses and change the sign of each term inside the parentheses. | 61 | |
| 1786861228 | Subtracting polynomials | To subtract two polynomials, change the signs of all terms in the second polynomial and then add. | 62 | |
| 1786861229 | Multiply a binomial times a trinomial | When we multiply a binomial times a trinomial, we multiply each term of the binomial times the trinomial. | 63 | |
| 1786861230 | Multiplying binomials using FOIL | F--Multiply the first terms O--multiply the Outer terms I--multiply the Inner terms L--multiply the Last terms Combine like terms | 64 | |
| 1786861231 | Write variable expressions when two or more quantities are being compared | When two or more quantities are being compared, we let a variable represent the quantity to which things are being compared. | 65 | |
| 1786861232 | Length | 12 inches=1 foot 2 feet = l yard 5280 feet = 1 mile | 66 | |
| 1786861233 | Volume | 2 cups = 1 pint 2 pints = 1 quart 4 quarts = 1 gallon | 67 | |
| 1786861234 | Weight | 16 oz = 1 pound 2000 pounds = 1 ton | 68 | |
| 1786861235 | Time | 60 seconds = 1 minute 60 minutes = 1 hour 24 hours - 1 day 7 days = 1 week | 69 | |
| 1786861236 | Procedure to convert from one unit to another | 1. Write the relationship between the units. 2. Identify the unit you want to end up with. 3. Write a unit fraction that has the unit you want to end up with in the numerator. 4. Multiply by the unit fraction. | 70 | |
| 1786861237 | Metric Measurements Weight | 1 kilogram = 1000 grams 1 gram = the basic unit 1 milligram = 0.001 gram | 71 | |
| 1786861238 | Metric Measurements Length | 1 kilometer = 1000 meters 1 meter= the basic unit 1 centimeter = 0.01 meter l millimeter = 0.001 meter | 72 | |
| 1786861239 | Metric Measurements Volume | 1 kiloliter = 1000 liters 1 liter = the basic unit 1 milliliter = 0.001 liter | 73 | |
| 1786861240 | kilo hecto deka basic unit deci centi milli | changing from larger metric units to smaller ones: moving to the right on chart move the decimal point to the right the same number of places. | 74 | |
| 1786861241 | kilo hecto deka basic unit deci centi milli | changing from smaller metric units to larger ones: moving to the left on chart move the decimal point to the left the same number of places. | 75 | |
| 1786861242 | perpendicular | one fourth revolution is 90 degrees | 76 | |
| 1786861243 | right angle | one half revolution is 180 degrees | 77 | |
| 1786861244 | full angle | one complete revolution is 360 degrees | 78 | |
| 1786861245 | supplementary angles | sum of 180 degrees | 79 | |
| 1786861246 | complementary angles | two angles that have a sum of 90 degrees | 80 | |
| 1786861247 | vertical angles | two angles that are opposite each other | 81 | |
| 1786861248 | adjacent angles | two angles that share a common side | 82 | |
| 1786861249 | Parallel lines cut by a Transversal | if two parallel lines are cut by a transversal, then the measures of corresponding angles are equal and the measures of alternate interior angles are equal. | 83 | |
| 1786861250 | Parallel lines | never meet, and the distance between them is always the same | 84 | |
| 1786861251 | transversal | a line that intersects two or more lines at different points | 85 | |
| 1786861252 | alternate interior angles | two angles that are opposite sides of the transversal and between the other two lines | 86 | |
| 1786861253 | corresponding angles | two angles that are on the same side of the transversal and are both above (or below) the other two lines. | 87 |