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49 Cards in this Set
- Front
- Back
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How do you change an improper fraction to a mixed number? |
Divide the numerator by the denominator and write the remainder in the numerator of the new fraction. The denominator remains the same. |
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How do you change a mixed number into an improper fraction? |
Multiply the whole number by the denominator and add it to the numerator. The denominator remains the same. |
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How do you make an equivalent fraction? |
Multiply both the numerator and denominator by the same number. |
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Given a proportion a/b = c\d, then what is also true? |
3 things: 1st, the cross products form an equation: a*d equals C multiplied by b. 2nd, the flip of the equation is also true. B / a equals D / C. 3rd, you can reduce either fraction vertically or horizontally.k |
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How do you find the a common denominator for two fractions? |
You find the least common multiple which is the smallest number that each of the denominators can divide into without a remainder. If all else fails multiply the denominators together to find a common denominator in order to add or subtract the two fractions. |
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How do you add or subtract fractions from each other? |
First find a common denominator for the two fractions. Then multiply the numerator by the same number to get an equivalent fraction. Then add or subtract the two fractions from each other. |
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How do you multiply two fractions? |
First reduce your fractions by pairing up the numerator of a fraction with the denominator of another fraction and then dividing each by the same number. Then multiply all the numerators by each other and all the denominators by each other to get your new fraction. Finally be sure to reduce your fraction. |
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How do you divide fractions? |
There's no good way to divide fractions. Instead change it to a multiplication problem by multiplying one fraction by the reciprocal of the other fraction. |
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What is a complex fraction? |
A complex fraction is a fraction within a fraction. |
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How do you simplify a complex fraction? |
First create improper fractions are integers in the numerator and the denominator. Then divide the numerator by the denominator by multiplying the numerator by the reciprocal of the denominator. |
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How do you change a fraction into a decimal? |
First divide the denominator into the numerator and add zeros after the decimal point until the division problem either ends or shows a repeating pattern. To indicate a repeating pattern draw a line across the top of the digits that repeat. |
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How do you change a decimal into a fraction? |
For a terminating decimal place, its digits over a power of 10 with as many zeros as there are decimal values. Then reduce the fraction. To change a repeating decimal into a fraction, place the repeating digits in the numerator of a fraction that has nines in the denominator. It should have as many 9s as digits that repeat. Then reduce the fraction. |
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How do you add or subtract decimals? |
Simply line up the decimal points and fill in zeros if necessary then perform the germane operation. |
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How do you multiply a decimal? |
Multiply the digits ignoring the decimal point until the very end. Then count the number of the digits to the right of the decimal point in each multiplier and the total number of digits is how many decimal places you should have in your answer. |
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How do you divide decimals? |
First make your divisor a whole number by moving the decimal point to the right. Then move the decimal point the same number of places for the number that you are dividing into. Put the decimal point in your answer directly above the decimal point in the dividend. Then divide as you normally would. |
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How do you multiply exponents of numbers with the same base? |
To multiply exponents of numbers with the same base simply add their exponents together. |
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How do you divide exponents with the same base? |
To divide exponents with the same base simply subtract the exponents from each other. |
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How do you raise a power to a power? |
To raise a power to a power simply multiply the two exponents by each other if their base is the same. |
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How do you change a negative exponent into a positive exponent? |
Move the base with a negative exponent into the denominator and and place a 1 as its numerator. Therefore b^-n equals 1 /b^n. |
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If the negative exponent is in the denominator how do you change it to a positive exponent? |
To change it to a positive exponent simply get rid of the fraction. Make B a whole number raised to a positive exponent. 1/b^-n = b^n. |
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If you are raising the powers of a fraction to a negative power, how do you change that negative power to a positive one? |
To change the negative power to a positive power simply take the reciprocal of the original fraction and raise it to the equivalent positive power. |
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How do you simplify radical expressions that are not perfect squares? |
To simplify a radical expression, you may separate the expression into its factors. Try to find at least one factor that is a perfect square and then Square it accordingly. For example, the square root of 40 is equal to the square root of 4 x 10. As a perfect square, 4 can be squared to 2. This radical expression can thus be simplified to 2 multiplied by the square root of 10. |
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How do you rationalize a fraction with a radical in its denominator? |
To rationalize a fraction with a radical in the denominator, multiply both the numerator and the denominator by that fraction. This moves the the radical to the numerator and creates a perfect square in the denominator which can then be reduced 2 regular number. Next reduce the fraction. |
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How do you write a radical as an exponential term? |
To write a radical as an exponential term, first note what power the number in question is raised to. Place this power as the numerator in the fractional exponent. Next note whether the base number is squared, cubed, xcetera. Place this root as the denominator in the fractional exponent. For example, the cubed root of 7 raised to the 5th power would be written as a fractional exponent as 7^5/3. |
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How do I use a fractional exponent? |
First find the root of the base number. Then raise it to the power in question. Remember of the number one raised any power is always equal to 1. |
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What is the square root of 2? What is the square root of 3? What is the square root of 5? |
The square root of 2 is 1.4. The square root of 3 is 1.7. The square root of 5 is 2.2. Remembering these numbers can help you quickly arrive edit estimate root. |
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What is the order of operations? |
Always remember please excuse my dear aunt Sally. This stands for parentheses, exponents, multiplication, division, addition, and subtraction. |
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What is the distributive rule? |
The distributive rule requires you 2 multiply value X a sum or difference within a set of parentheses. |
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What is a binomial? |
A binomial is an algebraic expression with two terms. For example, x + 10 is a binomial. |
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What does FOIL stand for? |
FOIL stands for first, outside, inside, and last. This indicates how you should multiply two binomials. |
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What are the two patterns that occur when two binomials are cubed? |
The first pattern is that the coefficients in the answer go 1 3 3 1. Therefore the first coefficient will be one, the second coefficient will be 3 so on and so forth.The second pattern is is that the powers on the variables decrease and increase by 1. Therefore the powers of the first term in the binomial go down by 1 well the powers of the second term go up by one each time. The second pattern is is that the powers on the variables decrease and increase by 1. Therefore the powers of the first term in the binomial go down by 1 well the powers of the second term go up by one each time. The second pattern is is that the powers on the variables decrease and increase by 1. Therefore the powers of the first term in the binomial go down by 1 well the powers of the second term go up by one each time. |
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How do you Cube a binomial? |
The cube of a binomial follows this pattern: ( a+b)^3 = a^3+3a^2b +3ab^2 +b^3. |
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What does dividing by a binomial mean? |
It means that two terms as a unit have to divide into another expression and there should be no remainder. |
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How do you divide synthetically? |
First place the opposite of the number in the divisor in front of the problem then write the coefficients in order using zeros to hold the places of any powers that are missing. Bring down the first coefficient below the horizontal line and then multiply it times the number in front. Write the result under the second coefficient and add the two numbers put the result below the bottom line. Repeat this process all the way down the line. If there is a remainder place it as the numerator with the divisor as the denominator. |
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What is factoring? |
Factoring is the process of simplifying an expression from one consisting of addition and subtraction to one that uses multiplication and division. |
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What is prime factorization? |
Prime factorization is listing all of the primary numbers whose product is the number that you are factoring. |
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What is the first step that you should take when factoring an expression? |
The first step you should take is to look for the greatest common factor and then divide each term by that factor. |
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What are the four methods that you can use to factor a binomial? |
The first method is to factor out the greatest common factor. The second method is to write the expression as the product of two binomials. The third method is to write the expression as a product of a binomial and trinomial. The 4th method is to use two or more of the above. |
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How would you factor a binomial when is the difference of two perfect squares? |
a^2-b^2=(a+b)(a-b) |
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How would you factor a trinomial made up of a perfect square? |
If subtracting, you would use the following formula: a^3-b^3=(a^2+a-b+b^2). If adding, you would use the following formula: a^3+b^3=(a+b)(a^2-ab+b^2) |
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What is a polynomial? |
A polynomial is an expression with four or more terms. |
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When would you use the unFOIL method? |
This method would be used to figure out what two binomials or multiplied together to create a trinomial. |
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How do you use the unFOIL method? |
First write the trinomial in descending powers of a variable. Then find all possible combinations of factors whose product give you the first term in the trinomial. Then find all the possible sets of factors whose products give you the last term in the trinomial. Try different combinations of these choices of factors in the binomials so that the middle term is the result of combining the outer and inner products. |
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What is a quadratic like trinomial? |
A quadratic like trinomial has a first-term who's power on the variable is twice that in the second and the last term is a constant. |
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What two characteristics do expressions that can be factored by grouping have? |
First a common factor occurs in each pairing of terms. Second the factorization of each individual grouping results in a new greatest common factor common to each group. |
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What is a linear equation? |
A linear equation is an algebraic equation that has no powers on the variables that are greater than the first power. |
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What is a quadratic equation? |
It is an equation that is usually written ax squared + bx + c equals 0. |
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What is a real number? |
Real numbers are whole numbers , fractions , negatives and positives , radicals , and irrational decimals. |
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What is the square root rule? |
This rule says if x squared equals k then X equals the + or - square root of k provided that K isn't a negative number. |
