Adding/Subtracting Decimals
0.64 + 0.89
***Remember to LINE UP the decimals! The order doesn't matter when adding so you can put either addend on top.
What is the sum of 1.53?
13 + (-5)
***The signs are DIFFERENT, so you take the difference (subtract) to get 8. Since you have more positives than negatives, 8 is positive.
What is 8?
Solve: I -22 I
***This symbol means what is the ABSOLUTE VALUE (distance from zero) of -22. They look like football touch down posts. Remember this means if you were standing on a number line at -22, how many steps would it take to get to zero? Absolute value, as it is distance is NEVER negative.
What is 22?
Find the GCF of 100 and 50
***Remember GCF is finding the GREATEST (largest) number (factor) that goes into BOTH 50 and 100. I always start with listing the factors of the smaller number as they have less factors and seeing (starting with the larger end) which is also a factor of 100.
factors of 50: 1, 2, 5, 10, 25, 50
Is 50 a factor of 100? yes, so that is the GCF of 50 and 100.
What is 50?
2.348 - 0.8
***Remember to LINE UP the decimals! The order DOES matter when SUBTRACTING, so you HAVE to put the first subtrahend, 2.348, on top.
What is the difference 1.548?
-10 - (-5)
***KFC (Keep Flip Change) to make it easier and into an addition problem so -10 - (-5) KFC'd becomes -10 + 5. Now apply the rules of adding. ***The signs are DIFFERENT, so you take the difference (subtract) to get 5. Since you have more negatives than positives in your REWRITTEN expression, 5 is negative.
What is -5?
The additive inverse of -3?
***ADDITIVE INVERSE is just a fancy word for the OPPOSITE of the integer -3. The opposite is the integer that is ALSO 3 steps away from 0 on the other side of the number line.
What is -3?
Find the LCM of 28 and 49.
***To find the LCM, I list the first 6 multiples of the larger number, then I list multiples of the smaller number to find the SMALLEST (least) number (multiple) on (common to both) lists.
multiples of 49: 49, 98, 147, 196, 245, 294
When I list multiples of 28, I find 196 is SMALLEST (least) number on BOTH lists.
What is 196 as the LCM?
1.9 + 8.759
***Remember to LINE UP the decimals! The order doesn't matter when adding so you can put either addend on top.
What is the sum 10.659?
The three steps when subtracting integers to make it EASIER (by turning it into an addition problem).
What is KFC (Keep, Flip, Change)?
***KEEP the FIRST integer the same
FLIP the subtraction sign to an addition sign
CHANGE the second integer to the opposite integer
Then, apply your addition rules.
The greatest number that is a factor of two or more numbers is called the _____________ ______________ ________________________.
***This is helpful to know when you simplify fractions in simplest form so their ONLY common factor in the numerator and denominator is 1. When you simply by the GCF, you get right to simplest form. If you simply by just a common factor, you have to keep simplifying.
What is the Greatest Common Factor?
Find the GCF and LCM of 120 and 30.
***GCF: I start by listing ALL the factors of 30 as it is the smaller number and has less to list.
Factors of 30: 1, 2, 3, 5, 6, 10 15, 30
Now, I start on the right side of the factor list and see what is the largest (GREATEST) number (factor) that also goes into 120 (common). Since, I can count by 30's and get to 120, I know 30 is also a factor of 120.
***LCM: I know that 120 is the FIRST multiple of 120 and I know I can count by 30's to get to it, so that is my LCM.
What is 30 for the GCF of 120 and 30?
What is 120 for my LCM of 120 and 30?
***If someone only got GCF or LCM, you can give partial credit of 150 points.
10.7 + 3.67 - 0.222
***Remember in GEMDAS Adding and Subtraction are done simultaneously LEFT to RIGHT. So, since addition comes first in THIS expression, you'd add 10.7 and 3.67 first (LINE
UP the decimals) and then subtract 0.222 (LINE UP the decimals) to get your answer.
What is 14.148?
-5 + (-20)
***Way 1: Adding Integers Rule: When signs are the SAME, you keep the sign and add the addends. Way 2: Number Line: Start at -5 on the number and move LEFT 20 more spaces since 20 is negative.
What is -25?
Name one strategy that you can use to help you solve addition/subtraction of integer problems (besides a calculator).
***There is NO calculator on the test today. You can only use your mult. chart and your divisibility rules in One Note.
***Remember we are ALL at different places with how we can add and subtract integers. Use the strategy that lets you be 100% accurate, not necessarily the quickest way.
What is (any of the 4-5 strategies mentioned below)?
Number Line
Chips
+'s and -'s
Rules
KFC (for subtraction and then use adding rules)
Soren has a math test every 20 days and a science test every 25 days. In how many days will he have a test again on the same day?
***So, I need to find the LCM of 20 and 25. I start with listing multiples of the larger number and then find the SMALLEST (least) number (multiple) also common to 20.
science: 25, 50, 75, 100, 125
Since I can count by 20's and get to 100 first, that is my least common multiple of 20 and 100.
What is in 100 more days?
1.38 + 3.99 - 1.036 - 0.7 + 2.5555
***2 ways: Way #1) According to GEMDAS you add and subtract simultaneously LEFT to right, so you add the first two decimals, subtract the next one, subtract the next one and add the final decimal. Way #2) you could all ALL your positive decimals, add all your negative decimals and then subtract the negative sum from the positive sum to get the same answer.
What is 6.1895?
-3 - (-8) + (-12)
***FIRST KFC the first part of the expression so -3 - (-8) becomes -3 + 8. You now have the expression -3 + 8 + (-12) so according to GEMDAS, it is ALL addition and the order doesn't matter. I tend to still solve LEFT to RIGHT. Use rules or number line to get 5 and then add -12. Use rules or number line to get your final answer of -7.
What is -7?
More than 1/4 of Ireland lies BELOW sea level. CAley visits a museum located at an elevation of 9 meters and bikes to a town at an elevation of -14 meters. What is her change in elevation for the trip?
***The change in elevation means the difference (which is the math word for the answer when you subtract). Remember order matters in subtraction so you need to start with 9 and subtract -14 which looks like: 9 - (-14). Then KFC it to 9 + 14 which =23.
What is 23 meters?
What is a great resource to use in One Note that helps us find COMMON FACTORS to divide by when simplifying a fraction to simplest form?
***You CAN use this now and on your test. It is in One Note; Content Library; Resources; Divisibility Rules (and your Mult. Chart is ALSO there).
What is the DIVISIBILITY RULES resource?