Adding and Subtracting Integers

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Logan Cobb
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1 Quarterly 1 Review Sheet (NOTE: This may not include everything you need to know for tomorrow about every topic. It is student created and I am just sharing it in case you find it helpful) Page 1: Adding and subtracting integers Page 3: Multiplying, Dividing, Adding, Subtracting Fractions Page 5: Word Problems Page 6 & 9: Converting decimals and fractions Page 10 & 11: Distributing and Fatoring Adding and Subtracting Integers Rules to add and subtract integers: 1. Rid any double signs 2. If the signs are the same, then it will be addition. 3. If the signs are different, then it will be subtraction. Examples: = = = =

2 = Common Mistakes Wrong =- 15 Right = - 9 When there are different signs you have to subtract. So in the first example the person added and got the wrong answer. It will be negative because the 12 is bigger than 3.

3 Adding, Subtracting, Multiplying, and Dividing Fractions. 1 st quarter outline Steps: adding and subtracting 1. Get rid of double signs *If the signs are the same, change them to a positive. For example, would be If the signs are opposite, make them into a negative. For example, would be Convert all mixed numbers into improper fractions. * 4 5/9 would be 41/9 3. Find the common denominators. 4. Then add or subtract the numerator, but keep the denominator. 5. Simplify your answer into a Mixed # Examples: adding and subtracting Common mistakes: adding and subtracting Some people might make the mistake of forgetting to find their common denominator and just adding the denominators. If you forget to, your work will look like this + =. This is wrong because the numerators are not proportionate to each other, so the two sums will not be equal. Steps: multiplying 1. Change mixed numbers into improper fractions 2. Multiply numerator by numerator and denominator by denominator 3. Simplify if necessary Examples: multiplying Common mistakes: multiplying Some people might make the mistake of multiplying the numerators but not the denominators. This will change your answer because the denominators will not be changed, so the product of the fractions will not have the correct ratio

4 Steps: dividing 1. change all mixed numbers into fractions 2. Rewrite first fraction 3. Change the division sign to multiplication 4. Write the reciprocal of the second fraction 5. Multiply and simplify your answer Common Mistakes: dividing A common mistake when dividing is forgetting to find the reciprocal of the second fraction. If you forget to do this, then your answer will be wrong because when you use the reciprocal, it makes up for changing the sign to multiplication. Examples: dividing 1. (no mixed # s) , 3, 4. 6.

5 Word Problems: Strategies: Underline the important words red is mistakes that you could make Figure out the problem it is asking you black is tips and steps Make a plan to solve blue is questions Use a graph (number lines,and pictures) Show all work Check answer Examples: 1. John had 11 cookies and bob has 17 cookies. John eats 1 cookie and steals 5 cookies from bob. Bobs mom decides to make bob 2 times more cookies than john. How much do both of them have? 2. A bunny is flying at 15 meters. It sees a hawk and decreases his height by 8.5 meters to catch it. He decided that it was ugly and increased his height by 1.5 times more than his height after he dived. What is the difference of his original height and his new height? 3. Andy has dollars in his bank. He deposits dollars. He withdraws dollars. Then he adds 4x more money than he had after his withdrawal and deposit. How much money does he have? Words That You Should Look For: Addition Division Subtraction Multiplication Add Divide Change times Plus Half Decrease product Sum quotient Take away repeat add Together separate Subtract factor More part of minus group Increase fraction Difference multiply Possible mistakes You need to read what they are telling you to do. If you don t read it carefully then you could make a mistake Don t forget to add your decimals (if needed) Don t forget to add negative signs (if needed) Don t forget to check work Make sure all work is readable and organize

Learn How to Convert: Fractions to Decimals and/or Decimals to Fractions To convert Fractions to Decimals: You simply divide the numerator value (top) into the denominator value (bottom).

6 Learn How to Convert: Fractions to Decimals and/or Decimals to Fractions To convert Fractions to Decimals: You simply divide the numerator value (top) into the denominator value (bottom). Below are several examples with step by step instruction how this can be accomplished: 1) What is the equivalent of in decimal? 3 is the numerator value (top) (quotient) 4 is the denominator value (bottom), => (divisor) (dividend) =.7 5 <= answer Common Mistake: Placement of the decimal point In our example above, 3 is divided by 4. How many times does 4 go into 3? If 3 is too small than you add a 0 after 3 to make it 30. When you add you must place a decimal point in the quotient indicating that a 0 was added. Now you can proceed with the division problem. 2) What is the equivalent of 2 in decimal? For mixed number first it must change to an 2 = Improper fraction => 10 is the numerator value (top) is the denominator value (bottom) = => = 2. 5 <= answer

7 Common Mistake: Beside the placement of the decimal point, one needs to also make sure the whole number that is in front of the fraction needs appear in front of the decimal value too. To convert Decimals to Fractions: Converting decimal to fraction depends on the place value of the decimal. If you put the number as the numerator of the fractions and use the place value as the denominator. And if the number is: The value of the decimal has one digit after the decimal point (tenth) then use 10 as the denominator. ie..1 = The value of the decimal has two digits after the decimal point (hundredth) then use 100 as the denominator. ie..01 = " The value of the decimal has three digits after the decimal point (thousandth) then use 1000 was the denominator. ie..001 = "" Below are several examples with step by step instruction how this can be accomplished: 1) Find the fractions equivalent of this decimals value of.36? The decimal value has 2 digits after the decimal point so the place value is in the hundredth place, the denominator. 3 6 = Needed is: 100 = " To simply: " = ". 3 6 = <= answer Common Mistake: To reduce to simplest form it is possible that one forgets to simply the fraction after solved it. 2) Find the fraction equivalent of.068? The decimal has 3 digits after decimal point so the place value = Is in the thousandths place, then use 1000 as the denominator needed is: 1000 = To simply: "" "" = "" # = # <= answer

8 Common Mistake: Besides to reduce to simplest form it is possible that one forgets to simply the fraction after solved it. Another common mistake is when converting fraction to decimal is the placement of the decimal point.

9 Steps to Convert Fractions to Decimals (two people did this) 1- Covert fractions to decimals (vice- versa). 2- Perform appropriate operations (following PEMDAS.) 3- Express answer in simplest form. Steps to Convert Decimals to Fractions 1- Write down the decimal divided by 1, like decimal/1. 2- Multiply both top and bottom by ten for every number after the decimal point. 3- Simplify or reduce the fraction. Examples to convert fractions to decimals: 7/8=87.5 I got that answer by dividing 7 by 8 to get the answer /5=8.4 I got that answer by dividing the 42 by 5 to get the mixed number 8 2/5. I would simplify that to a fraction by keeping the whole number which is eight but converting the 2/5. So, if I divide 2 over the 5 which is the problem 2/5 then I would get.4. Since I already know that the whole number is eight, I would add the.4 after the 8 since 2/5 equals.4. Therefore, my answer would be 8.4. Examples to convert decimals to fractions: Convert.625 to a decimal.625=5/8 I got that answer by first putting the decimal.625 over 1. Then, I would keep multiplying the top and bottom number by ten until the top number is a whole number to 625/1000. Finally, I would simplify the fraction 625/1000 to 5/8. Therefore, my answer would be 5/8. Common mistakes made by converting fractions to decimals and decimals to fractions: Always reduce the fractions all the way. Common mistakes made by converting fractions to decimals: Divide the numerator by the denominator not the denominator by the numerator.

10 Changing an Expression from Factored Form to Expanded Form Steps: 1. Find a common factor or the GCF (highest number that goes into both) of each term 2. Divide each term by the common factor or the GCF 3. Write the common factor of the GCF outside the parentheses and the answer to step two inside the parentheses Example one: (2-5) Example two: (4+6) Common Mistakes: Only finding the common factor but not the greatest common factor is a mistake. For example, some people put 2(12+18) instead of 6(2+3). Another common mistake is adding instead of subtracting or subtracting instead of adding. For example, some people would add 6 and 15 instead of subtracting. Changing an Expression from Expanded form to Factored Form Steps: 1. Find the GCF of the terms in the expression 2. Write the GCF on the outside of the Parentheses 3. Inside the parentheses, write each term divided by GCF Example one: 6(5+3) Example two: 3(4-3) 12-9 Common Mistakes: Some people can multiply the numbers wrong. For example, instead of multiplying 6 and 5 you might multiply 6 and 4. Another common mistake is you can add the inside numbers instead of subtracting or subtracting instead of adding. For example, you might add 6 and 15 instead of subtracting.

11 Using the Distributive Property to Factor Expressions Step 1 Find a common factor >>>> OR the GCF (Greatest Common Factor) Step 2 Divide each term by the common factor/gcf Step 3 Write the common factor OUTSIDE of the PARENTHESIS AND the ANSWER to step 2 INSIDE the PARENTHESIS EXAMPLES STEP 1>>>>>>The GCF of 10 and 14 is 2>>>WHY? 2 IS THE LARGEST NUMBER THAT CAN BE DIVIDED EVENLY INTO 14 AND 10 STEP 2>>>>>>WHEN YOU DIVIDE 10 BY 2 YOU GET 5.LIKEWISE WHEN YOU DIVIDE 14 BY 2 YOU GET 7 >>>> 5 and 7 STEP 3>>>>>>The new expression is 2(5 + 7) COMMON MISTAKES.OOPS DON T MIX UP WHICH NUMBER GOES OUT THE PARENTHESIS AND WHICH GOES INSIDE MAKE SURE YOU HAVE THE GREATEST COMMON FACTOR BE SURE TO CHECK YOUR WORK FOR COMPUTATION ERRORS

HOW TO DIVIDE: MCC6.NS.2 Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE

HOW TO DIVIDE: MCC6.NS.2 Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE MCC6.NS. Fluently divide multi-digit numbers using the standard algorithm. WORD DEFINITION IN YOUR WORDS EXAMPLE Dividend A number that is divided by another number. Divisor A number by which another number