Notes

A    =     3x 4 – 9x 3 +5x 2 – 11 B     =      10x 3 – 6x 2 + 24 C     =      B – A =      (10x 3 – 6x 2 + 24) – (3x 4 – 9x 3 +5x 2 – 11) =      10x 3 – 6x 2 + 24 – 3x 4 + 9x 3 – 5x 2 + 11 =      – 3x 4 + 19x 3 – 11x 2 + 35 ORDER DOESN’T MATTER IN ADDITION -2-3=-5 -3-2=-5 2-3=-1 2 steps right, 3 steps left -3+2=-1 3 steps left, 2 steps right

Algebra X= 3p + 2q 2 terms in this expression Y= 2q - r + 4 3 terms in this expression Z= 5q + 17p - pq 3 terms in this expression X+Y= 3p + 4q - r + 4 4 terms Y+Z= 17p + 7q - r - pq + 4 5 terms Z+X= 20p + 7q - pq 3 terms 2(X+Y)= 2(3p + 4q - r + 4) 6p+8q-2r+8 3(Y+Z)= 51p+21q-3r-3pq+12 4(Z+X)= 80p+28q-4pq X-Y= (3p + 2q) - (2q - r + 4) 3p + 2q - 2q + r - 4 3p + r - 4

While performing addition/subtraction on fractions, the key is “making the denominators equal”. While performing addition/subtraction on decimal numbers, the key is “making the number of places equal”. 0.5+0.5=1 0.5–0.25=0.50–0.25=0.25 0.1–0.01=0.10–0.01=0.09 0.1+0.12+0.123=0.343 0.3–0.125=0.175 0.9+0.19+0.99=2.08 1.08–0.54=0.54 1.08–0.81–0.27=0 15.1–1.51–5.551=8.039 (17/10)–(87/100) =1.7– 0.87=0.83 ?–0.05 = 0.05 Answer: 0.1 3.5–? = 3.15 2 = 1+1 Adding 5 on both sides 2+5 = 1+1+5 Subtracting 2 from both sides 2 – 2 = 1 + 1 – 2 6 = 2+4 Dividing by 2 on both sides 6/2 = 2/2 + 4/2 7 = 3+4 Multiplying both sides by 5, 7*5 = 3*5 + 4*5 3.5–x = 3.15 Adding x on both sides, 3.5 – x + x = 3.15 + x (The purpose of this is to make x positive.) 3.5 = 3.15 + x 3.15 + x = 3.5 (It is better to have x on the left side because it is the value of x which we are trying to find.) Subtracting 3.15 from both sides 3.15 + x – 3.15 = 3.5 – 3.15 (The purpose of this is to remove 3.15 from the LHS so that only ...

1.5+1.05+1.005=? =1.500+1.050+1.005 1.500 1.050 1.005 3.555 1.5 1.05 1.005 3.555 1500 1050 1005 3555 0.1=1/10 1.1=11/10=11/10 1.2=12/10=11/5 3.04=304/100=34/100=31/25 3/10=0.3 3/20=3*5/20*5=15/100=0.15 1/2=5/10=0.5 1/4=25/100=0.25 3/4=25/100=0.25 2/4=1/2=0.5 11/2=3/2=half of 3=1.5 3/20=half of 3/half of 20=1.5/10=0.15 9/25=36/100=0.36 1/2=0.5 3/2=1.5 5/2=2.5 7/2=3.5 9/2=4.5 1/4=0.25 3/4=0.75 2/4=0.5 5/4=1.25 7/4=1.75 9/4=2.25 11/4=2.75 1/5=0.2 (1 dollar divided into 5 parts; each part 20 cents) 1/5=2/10=0.2 2/5=0.4 3/5=0.6 4/5=0.8 6/5=12/10=1.2 7/5=1.4 1/20=5/100=0.05 (1 dollar into 20 parts; each part 5 cents) 21/20=1.05 23/20=1.15 27/20=1.35 1/50=0.02 37/50=0.74

1/3=0.333… 2/3=0.666… 4/3=11/3=1+1/3 =1+0.333…=1.333… 5/3=12/3=1.666… 7/3=21/3=2.333… 8/3=2.666… 10/3=3.333… 3/10=0.3 3.333….*0.3=1 10/3*3/10=30/30=1 10/3 and 3/10 are reciprocals. When reciprocals are multiplied, the result will be 1. 1.666…*0.6= 12/3*6/10 =5/3*3/5 =15/15=1 1/6=0.1666… 0.1666…*0.6= 1/6*6/10=6/60=3/30=1/10=0.1 1/9=0.111… 0.222…=2/9 0.333…=3/9=1/3 0.444…=4/9 0.555…=5/9 0.666…=6/9=2/3 0.777…=7/9 0.888…=8/9 0.999…=1 1/7=0.142857142857142857…

0.1/10=0.01 0.1*10=1.0 or 1 12.34/10=1.234 1.234*10000=12340 0.05/100=0.0005 0.0005*1000=0.5 Half of 5000=2500.0 Half of 500=250.0 Half of 50=25.0 Half of 5=2.5 Half of 0.5=0.25 Half of 0.05=0.025 Half of 0.5= Half of 0.50 =0.25 Half of 1200=600.0 Half of 120=60.0 Half of 12=6.0 Half of 1.2=0.6 Half of 0.12=0.06 Half of 2500=1250 Half of 250=125 Half of 25=12.5 Half of 2.5=1.25 Half of 0.25=0.125 Half of 0.250=0.125 Half of 1.5=0.75 $1.5 is shared between A and B. How much will each get? 37+26=63 I have 37 cookies. You have 26 cookies. How many cookies do we have together? 37–26=11 You have 37 pencils. You give away 26 of them to your friends. How many are you left with? 12*15=180 I brought 15 bags. Each bag has 12 books. What is the total number of books? 154/14=11 I have 154 books. 14 books are arranged in each rack. How many racks are used to arrange all the books? 1/3=2/? 1 : 3 :: 2 : ? 1 pen costs $3. What will be the cost of 2 pens? 1/3=?/12 1 notebook costs $3. How many notebook...