# Grade 10 Math Unit 1

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- Grade 10 Math Unit 1

**Created:**2013-12-25

**Last Modified:**2014-06-14

reducing fractions

reduce by dividing. divide both top and bottom by a common factor. ex. 4\12 = 1/3 when divided by 4.

cross reducing: when multiplying two factors together if the diagonal #s have common denominators then u can divide it out. ex. 5/2 × 7/5= 1/2 × 7/__1__

reducing fractions

reduce by dividing. divide both top and bottom by a common factor. ex. 4\12 = 1/3 when divided by 4.

cross reducing: when multiplying two factors together if the diagonal #s have common denominators then u can divide it out. ex. 5/2 × 7/5= 1/2 × 7/__1__

adding fractions

you need a common denominator. ex. 4/5 + 6/5= 10/5 =__2__

multiplying fractions

just multiply denominators together and tops together.

when multiplying a whole # and a fraction you multiply it by the denominator and then add it to the top. then simplofy never forget to simplify!

dividing fractions

multiply by reciprocals. NOT THE NEGATIVE RECIPRICALS JUST THE RECIPRICAL.

Factors

Numbers that multiply evenly into the number that is being factored.

factor trees

when you are simplifying a radical u make a factor tree. they are when u write to factors of a number. then the factors factors. ex.45<5,9 okay its really hard to do when typin.

bedmas

b-brackets e-exponants d-division m-multiplication a-addition s- subtraction.

distributive property

ex. 7(x+5) = 7x +35. you can expand the multiplication within the bracket.

collecting algebra skills

you can collect the same variables together. ex. a+c+a=2a+__c__

multiplying binomials

binomial = (y+5) two polynomials.

when you are multiplying two binomials together. ex. (y+5)(y-2) you multiply both numbers in the 1st binomial with each number in tje other binomial but yoi neber multiply the 2 #s in a binomial together.

midpoint

basically the average. formula= (Xa+Xb÷2, Ya+Yb÷2)

solving an algebraic equation

steps

1. isolate the bariable term

2. isolate the variable

ex. 12-3m=2(m+1)

12-3m=2 (m+1)

10=5m} variable term

m=2} __variable__

conjugates

when you have the same terms with different signs. ex. (2x-5)(2x+5) for factorig this would form a answer that is a difference of squares.

difference of squares

when subtracting a perfect square(ex. 25) or a squared nu, ber or variable. (ex. X^2) This is a difference

common factoring

1. find the greatest common factor between the terms

2. work your way back for the other factors ex. 2a^2-4a =2a(a-2) *factoring is the opposite of expanding.

multiply out the fraction

if you hate fractions and you want to get rid of it then u can always multiply out the denominator giving you a whole number.

length of a line equation

formula= (square root) (X1-X2)^2 +(Y1-Y2)^2 * sorry tablet dosent have square root or squared symbols.

you use this formula when you have the points of the endpoints of line that u want to find the length of.

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