Elementary Mathematics Mind Map By: Angela Costa

When the least common denominator is used in adding and subtracting fractions, is the result always a fraction in its simplest form? Explain by giving examples. By using the least common denominator, the fractions do not always have to be in simplest form because we are trying to find equivalent fractions. 

Adding- Unlike denominators: Find a common denominator Add the numerators (keep the denominator) Simplify the fraction By using pattern blocks to represent parts of a whole, we avoid 26+36=512Like denominators:Add straight across

Subtracting- Unlike denominators:Take the LCM of the denominator Convert to the LCM value by multiplying the numerator and denominator by the same number Once the denominator becomes equal, then subtract the numberSimplify if neededLike denominators:Subtract straight across

Multiplying- Multiply the numerators and denominators straight across. Draw a picture!!! The product gets smaller*

Dividing- Find the reciprocal (reverse the numerator and denominator) of the second fractionMultiply the two numbers Multiply the denominators Simplify the fraction if needed See attached notes for in depth explanation To put it in simpler terms, all #s are over 1, so we need to make the denominator 1 in order to invert and multiplyWe will not teach this way for our students, more so important for us to know why it works. 

Addition/Subtraction of Decimals- Same process for whole numbers Problem with the part and whole, so pay attention to place value. Why do we line up our decimals? Because of place valueWe can help our students visualize this concept by flipping our papers horizontally to emphasize place value. It is difficult for students to subtract decimals (with grouping) because we still have numbers left over in the tenths and hundredths place. Addition example: Given: 27.35 + 2.30 Solution: 29.65 See class notes for more information.

Addition/Subtraction of Decimals- Same process for whole numbers Problem with the part and whole, so pay attention to place value. Why do we line up our decimals? Because of place valueWe can help our students visualize this concept by flipping our papers horizontally to emphasize place value. It is difficult for students to subtract decimals (with grouping) because we still have numbers left over in the tenths and hundredths place. Addition example: Given: 27.35 + 2.30 Solution: 29.65 See class notes for more information.

Addition/Subtraction of Decimals- Same process for whole numbers Problem with the part and whole, so pay attention to place value. Why do we line up our decimals? Because of place valueWe can help our students visualize this concept by flipping our papers horizontally to emphasize place value. It is difficult for students to subtract decimals (with grouping) because we still have numbers left over in the tenths and hundredths place. Subtraction example: Given: 5.00 -1.37 Solution: 3.63See class notes for more information.

Multiplication/ Division of Decimals- Multiplicaticapation steps: Estimate- estimate where we place the decimal point; ask yourself, “where does it make sense?”Explain- explain the rule of place value and connect it to fractions. Multiplication example: Given: 32.53 x 2.1 Don't need to always line the decimals up unless they are the same number of digits. Estimate by taking the whole numbers and multiplying them; for example, 32 x 2 = 64, so we know that our answer will be around there. Explain the numbers after the decimal point and connect it to fractions; for example, in 32.53 would be 5/10 and 3/100. In 2.1, it would be 1/10. We must talk about the rule of place value because when we multiply 1/10 x 3/100, we get 3/1000. The zeros explain how many times we need to move the decimal to the left. The rule of moving decimal after how many digits are after the decimal is NOT helpful. Solution: 68.313 

Division steps: If the divisor is a whole number- bring the decimal point up and solve. If divisor is not a whole number- multiply the decimal by a number to make it a whole number and then solve. 3.1 would be multiplied by 10 to make it a whole number 3.12 would be multiplied by 100 to make it a whole number

Addition (put together, join): a. Identity Property- for any #, when you add zero to the #, the identity is the same. Example- a + 0 = a ; 4 + 0 = 4 b. Commutative Property- when you add two #s, the order of when you add them, doesn’t matter/ change. Example- a + b = b + a ; 4 + 3 = 3 + 4c. Associative Property- when you have #s in a ( ), you can group them together. Example- (a + b) + c = a + (b+c) ; (3+4) + 2 = 3 + (4+2)Class notes: https://docs.google.com/document/d/16z-XuWEVj-cxsXrTPPh34f52I-hxgttsHTCebuVb-V0/edit?usp=sharing

Multiplication (repeated addition, skip counting, combining items to one group to another): a. Identity Property- for any #, when you multiply by 1, its identity remains the same. Example- a x 1 = a ; 3 x 1 = 3 b. Commutative Property- the order of how we multiply stays the same/ doesn't matter. Example- a x b = b x a ; 3 x 4 = 4 x 3 c. Associative Property-  the grouping stays the same Example- (a x b) * c = a * (b x c) ; (3 x 2) * 5 = 3 x (2 x 5) d. Zero Property- when you multiply any # by zero, it remains zero. Example- a x 0 = 0 ; 3 x 0 = 0 e. Distributive Property- FOIL; multiplying the # outside of the ( ) to all of the #s inside the ( ). Example- a x (b + c) = (a x b) + (a x c) Sum is the (b + c) Partial products is (a x b) + (a x c) Class notes: https://docs.google.com/document/d/16jKp-en4PlK34qBrKyObOZNPJECc0IzMg79Ddp-CiGI/edit?usp=sharing

Subtraction (take away): a. Take away- Example: 7 - 3 = b. Compare? D. has 5 books P. has 7 books How many more books does P. have than D.? c. Missed Addend?? 5+ = 73+ = 7*How a 6 year old will solve the problem* Class notes: https://docs.google.com/document/d/15znhv8Qea1KLlmqGrncmtlh0lHLal7Wv1TaWIMMKdT0/edit?usp=sharing

https://docs.google.com/document/d/17D62T51Y0t9Wl3CT-ghCj3W0cFz9rAXWG0fh7eax7Ws/edit?usp=sharing

American Standard: One we are comfortable with; however, this algorithm must be taught last. Possible Errors: R -> L No reference to place value Regrouping errors Picture of class notes for examples are located in the Title.

Partial Sum: Set vertical columns in between digits. Solve by putting the regrouping (tens) into the correct line. Possible Errors: R-> L No reference to place value Not lining up digits properly Picture of class notes for examples are located in the Title.

Partial Sum w/ Place Value: Set vertical columns in between digits. Then solve by putting the regrouping (tens) into the correct line. However, we are solving L->R unlike the "Partial Sum" since there is place value reference. Possible Errors: Not lining up digits properly Picture of class notes for examples are located in the Title. Link to Partial Sum YouTube video: https://youtu.be/jzoPVm7WteM

Left-to-Right: Instead of solving upwards like how we did in Partial Sum w/ Place Value, we are going downwards with our place value. We like this because we are solving from L->R and there is place value reference.Possible Errors: Not lining up digits properly Picture of class notes for examples are located in the Title. Link to Left-to-Right Addition YouTube video: https://youtu.be/6cWd585cZPQ

Expanded Notation: Set up problem like American Standard, then create horizontal arrows to the next set up to show expanded form. Each digit should be explained by their place value.Add all of the numbers, then do American Standard on the right side to show your explanation/ meaning. We like this method because there is reference to place value. Possible Errors: Not knowing place value rules Picture of class notes for examples are located in the Title.

Lattice: Create a square, then create a lattice pattern in the squares, the number of squares describe the number of digits. Picture of class notes for examples are located in the Title.

https://docs.google.com/document/d/17nD4asmUcfGs5wVtQwh7-TxLo9VOcuS41g7vsgllVdk/edit?usp=sharing

American Standard: One we are comfortable with; however, this algorithm must be taught last. Possible Errors: R -> L No reference to place value Regrouping errorsPicture of class notes for examples are located in the Title.

European/Mexican: Usually taught in different countries. Typical regroup; however, with the bottom number, we are increasing by 1 each time we add a ten to the other number. Possible Errors: Not knowing to increase digit R->LPicture of class notes for examples are located in the Title. Link to European/Mexican Subtraction Algorithm YouTube video: https://youtu.be/6RKK5BP8WL4

Reverse Indian: We like this method because we are solving from L->RSimilar to the Left-to-Right method, explained more in depth. Possible Errors: No reference to place value Picture of class notes for examples are located in the Title.

Left-to-Right:We like this method because we are solving from L->RThere is place value referenceEach time we bring a ten over to the right, we are subtracting another ten (if the next digit needs a ten). Possible Errors: Not knowing place value Picture of class notes for examples are located in the Title. Link to Left-to-Right Subtraction YouTube video: https://youtu.be/CvQx6i1biTE

Expanded Notation: Same set up in Addition; however, instead of adding the numbers up in the expanded form, we are subtracting them. Make sure to explain the meaning behind why it is reasonable. Possible Errors: Not knowing place value rules Picture of class notes for examples are located in the Title. Link to Expanded Notation Subtraction YouTube video: https://youtu.be/fqFXmsrv8tQ

Integer Method: Solving from down to up. The farthest digit (on left) will be adding the number (if it can be subtracted), then subtracting each time you move up. Make sure you have arrow showing that you are moving down to up. Possible Errors: Regrouping errors (forgetting to subtract)Picture of class notes for examples are located in the Title.

Class notes of Multiplication Algorithms: https://docs.google.com/document/d/1ChKxFPA1fhbsfuSfcHc1xqUD4aH1EDcpUzF0bG9Z37E/edit?usp=sharingYouTube video of Lattice method: https://youtu.be/Z3T_NhFlpB0

Class notes of Division Algorithms: https://docs.google.com/document/d/16xneRwHxJQvrCGF9FNL-7FhZYMpW_e8rJm4zDD6VU_A/edit?usp=sharing

Percentages: %- per cent, per 100, out of 100. $300 dress in the store and the sign says 30% sale. This would mean 30% off of every hundred dollars. NOT EVERYTHING WILL BE OVER 100. For example, “shade in ⅗”; if the denominator is not over 100, then you have to look and find equivalent fractions by finding factors of 100. ⅗ = 60/100 3 x 20 = 60 5 x 20 = 100Converted ⅗ to 60/100  Convert fraction into decimal- 0.60 Convert decimal into percent- 60%Class Notes: https://docs.google.com/document/d/1AM_WD_mSxz16jDIx86rQzvHEGi5faYwveCqWNLvMd98/edit?usp=sharing

Problem-Solving with Percents: 3 types of problems: Each one answers a different question. Meanings of problems- Is: = Of: x (multiplication) What?: unknown variable (n) 8% or %: write as a decimal 0.08 = 8/100 8 is what % of 22? 8% of 22 is what number? 8% of what number is 22? *Problems represented in Class Notes. Finding a Percent of a Number Videos: https://youtu.be/AL0-0f9azNohttps://youtu.be/AL0-0f9azNo

Integers: Integers- positive and negative numbers Students work with positive numbers all of the time; however, they do not know this because there is no indication of the sign in the beginning of the number. Students may see negative numbers on a number line (horizontal model); therefore, they may know that they are less than zero. Bring real-life examples into the lesson, such as temperature. Use a vertical model to represent the number line of degrees shown with temperature. Helps students understand place value better when we provide  them with vertical models like the one mentioned above. It also helps students understand operations like understanding an elevator analogy. We use the Chip Method. Our manipulative/ model is chips. Two different colored sides on the chips. The yellow is for positive numbers. The red is for negative numbers. We draw a picture to represent how many positive and negative numbers we have. In order to solve the problem, we must write the positive and negative signs smaller to help us understand what operation we are using. In addition, we need to stay clear of the ‘rules’ we were taught considering it is NOT helpful. Zero pair- when you have  a + and - chip(s) together in your picture, this is a zero pair- meaning when there is a positive and negative pair, it cancels out. Noted in the class notes.Class Notes: https://docs.google.com/document/d/1KVlOMzuNXhDkISZkSFcjI3lSZlg_6aaBzSQ84-onjys/edit?usp=sharing Intergers videos: Adding Integers with Chip Method https://youtu.be/KQwvjE7eypESubtracting Integers with Chip Method https://youtu.be/KQwvjE7eypEMultiplying Integers with Chip Method https://youtu.be/Yhoz1g35alwDividing Integers https://youtu.be/DR8LBKSdI20

In Subtraction, we may have a problem like -2 - (-3) When we see this, we make a zero pair but DO NOT cancel them out because we have already -2 in the -3. So we take away two negatives and then another, so we are left with +1. In Multiplication, we may have a problem like -3 x +2 When we see this, we need to remember the commutative property of Multiplication tells us that the order does not matter in how we arrange our numbers. We need to take the opposite of the number. For example, the opposite of -3 is +3. This is only applicable for multiplication problems that have a negative as the first number. In Division, we will split our division problem into two computations because multiplication and division are inverse operations. Remember Fact Families!!For example, +3 x +2 = +6 +3: +6 / +2 = +3 +2: +6 / +3 = +2 … For example, +3 x -2 = -6 +3: -6 / -2 = +3 -2: -6 / +3 = -2 

Problem Solving with Fractions: See attached notes. Corresponds with Four Operations of Fractions; application to adding, subtracting, multiplying, and dividing fractions.

George Polya: first mathematician to write a book on Problem Solving. Created 4 steps to Problem Solving since we go through the same processes to solve one. Understand the problem: What are you asked to find out or show?How can you restate the problem in your own words? Can you draw a picture or diagram to help you understand the problem? Devise a plan: What problem solving strategy are you going to use? Guess and check/ trial and error picture or diagram make a table act it out make it simpler Look for a pattern work backwards make a list Carry out the plan: easier than devising the plan be patient because most problems aren't solved on the first attempt if a problem doesn't work out, be persistent and do not let yourself get discouraged. If one strategy doesn't work out, try another!Look back (reflect):Does your answer make sense? Is it reasonable? Did you answer all of the questions? What did you learn from this? Could you have solved this problem in a different way? Maybe an easier way?Picture of class notes over Problem Solving section: https://docs.google.com/document/d/1DIz22cMvE9FCQo1tviU3c0AmANlO0rCc7FfjcWd-sjc/edit?usp=sharing

Stamps Problem Explained: Given- 5      2-cent stamps 7      4-cent stamps Multiply how many possibilities there are 7*5 = 35  Then add the possibilities (5+7)47 combinations Pictures of problem: https://docs.google.com/document/d/15nU8IKo53CMCvD3pmGEJ8anPtWv4REQeNMeVauSJzAA/edit?usp=sharing

What is a numeration system? A numeration system is a system we use to record quantity. In America, we use a Base-10 system. A Base-10 system is 10 of something to create something else; for example, like in the decimal system. Base-10 Digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 910^0 -Ones 10^1 -Tens 10^2 -Hundreds 10^3 -Thousands Given: $377.52 We need to separate the units. Dollars and cents are given. The dollars would represent 3 in the hundreds place, 7 in the tens place, and 7 in the ones place. In terms of the cents, they would represent 5 dimes and 2 pennies. This is shown as 5- 1/10 of a dime; 1/10 * 1/10 = 1/100 2- 2/100 Base-10 positional system is where the numbers get their place value from. Shown in Expanded Notation for ALL bases or could work BACKWARDS. However, not all countries use the same system to record quantities. For instance, in Australia, they use a Base-5 system. Each system changes based on the relationship. Base-5 Digits: 0, 1, 2, 3, 4 5^0 -Ones 5^1 -Fives 5^2 -25s 5^3 -125s Base_ in Expanded Notation Picture Example: https://docs.google.com/document/d/1Q94c8Un78bF5Ih-Cw3ZJSUZprQUwvuECE8q-aZKp7Z0/edit?usp=sharing

Spot the problem? *focus on digits* :For example: 10= 23   Base-3 The first number (10) is in Base-10, so the digits 1 and 0 would be fine; however, the 24 in Base-3 only uses the digits 0, 1, 2, and 3. 4 cannot be in there because of the Base-3 digits. Comparing Base_ to another Base_ :If there is no base shown on one of the numbers, then it is in Base-10. If there is a bigger base shown, then it will be greater than the other number because of how the base is greater. Working backwards with Base- :Draw a picture to make the number of groups that can go into the Base. For example, if it says, “Write 45 in Base-7”, we would need to draw 45 Xs. Next, we need to circle the amount of groups that make up 7. This would be 6 and the first number to be shown. Then, we would count the Xs that are not in the circles. This would be 3. Lastly, we need to write our answer as 45 = 63    Base-7 IF THERE ARE NONE THAT CAN GO IN A BASE, THEN IT WILL BE ZERO. For example, 45 in Base-3 would be 1200   Base-3. There would be 1 group of 27, 2 groups of 9It cannot  go into 3s or 1s since we have circled all that we can, so it would be zeros for the 3s and 1s place.Examples of topics noted above: https://docs.google.com/document/d/14SCPL4qKE4m0TuaghQlU-GQ5T0wU7GZ9j9AP_87Hsyw/edit?usp=sharing Base_ in Expanded Notation picture example: https://docs.google.com/document/d/1w96xQeTLQOTtHhsB9wRVvGFCBjWKcDPg25HN6810EzA/edit?usp=sharing

Divisibility and Number Theory: Divisibility- a number a is divisible by a number b IF there is another number c that meets this requirement of c * b = a No remainders 10 is divisible by 5 because 2 * 5 = 10. (more information in under “Number Theory”)Broken up into three groups… Ending- By 2: 0, 2, 4, 6, 8 By 5: 0, 5 By 10: 0 Example- the number 2, 760 is divisible by 2, 5, and 10. Sum of digits- By 3: the sum of the digits is divisible by 3 By 9: the sum of the digits is divisible by 9 Example- 12, 735 is divisible by 3, 5, and 9. 1 + 2 + 7 +3 + 5= 18 Ending & Sum of digits- By 6: the number is divisible by 6 if it is divisible by BOTH 2 and 3. Last digits- By 4: look at the last 2 digits 12,735 x 12, 740 ✓By 8: look at the last 3 digits and divide them by 8 905, 256 ✓256 / 8 = 32 By 7: double the last digit, subtract the # from remaining #, and then see if it is divisible. 826; 2 * 6= 12; 82 - 12 = 70 ✓By 11: “chop off method”; chop off the last 2 digits, add 2 remaining #s, and see if it is divisible. 29,194; 291+ 94 = 385; 85+ 3= 88 ✓On Test: *will be given a # and you will see if it's divisible by all #s covered above *Given: 770 Divisible by 2, 5, 10, 7, and 11Number Theory- end goal to learning/ teaching fractions Divisibility rules Types of numbers Factors and multiplesGetting us to fractions!Example- 2 * 5 = 10; 2 is a factor of 10 5 is a factor of 10 10 is divisible by 5 10 is divisible by 2 10 is a multiple of 5 10 is a multiple of 2 5 is a divisor of 10 2 is a divisor of 10 

Factors and Multiples Day 1: Composite #s: more than two factors 28- 1, 2, 4, 7, 14, 28Factors of #s can use divisibility rules28 is divisible by 2 and 4, but not 8 30- 1, 2, 3, 4, 5, 6, 10, 15, 3042- 1, 2, 3, 6, 7, 14, 21, 4251- 1, 3, 17, 51 NOT PRIME! WILL BE ON TEST84- 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 8491- 1, 7, 13, 91NOT PRIME! WILL BE ON TEST 56- 1, 2, 4, 7, 8, 14, 28, 56 Write all prime #s from 0-60: 2 35711131719232931374143475359How about 0 and 1? 0 and 1 are not prime numbers because… 0 is the additive identity element 1 is the multiplicative identity element 0 and 1 are not prime nor composite; they are very special #s in the number system. 

Factors and Multiples Day 2: Review from previous day: 24: 1, 2, 3, 4, 6, 8, 12, 24 All factors of 24 Expressed by using composite numbers Prime Factorization: when you take all of the prime #s in a number like 24 (represented above), you break it up into the prime #s. 24; make a factor tree; expressed by using prime #s ⇩2 & 12          ⇩        2 & 6                ⇩            2 & 3 24 = 2 * 2 * 2 * 3- how it needs to be expressed on the test 24 = 2^3 * 3 Always stays the same, does not change Greatest Common Factor (GCF): used when we simplify fractions  25 100 55 = 520 55 =14 25 100 2525 = 1425 is the greatest common factorExample: 25: 1, 5, 25100: 1, 2, 4, 5, 10, 20, 25, 50, 10025 is the greatest common  factor Least Common Multiple (LCM): used to find a common denominator to create equivalent fractions. LCM also known as skip counting; 2, 4, 6, 8, 10, 12 and so on… It is best to use LCM for smaller #s, less likely to make errors. Used to simplify fractions, adding with unlike denominators Example: Find LCM first 4: 4, 8, 12, 16, 20, 24 6: 6, 12, 18, 24, 30 LCM = 12 GCF = 24 Find GCF next 1466 +16 44624 + 424 = 10241024 is equivalent to 512 Two methods used to find GCF and LCM: List method- preferred method Prime factorization- need to find GCF first, then LCM; takes longer and more errors could be made. Picture of examples using the list and prime factorization methods attached to this note. 

Fractions (a little discussion): Fraction: A fraction is a symbol… can be represented in 3 ways A part of a whole- a representation of a part and a whole 0.75 is not a whole ¾ is a fraction; symbol Quotient- an answer to a division problem24/4 = 6 24/4 =6Ratio- conceptually different because not all are fractions; therefore, we need to be careful! Example: we have 20 students, 15 are girls and 5 are boys. Given the information which ones are represented as a fraction and represented NOT as a fraction. boys/students = 5/20 girls/students = 15/20 Yes, because part/whole ratio is a fraction. boys/girls= 515girls/boys =155The above information are NOT fractions because they only show a relationship of a part and a part. No, because part/part ratio is NOT a fraction. Types of Models/ Manipulatives: Surface area; using pattern blocks, shading a box or pie Length; a long piece of paper or # line Sets (groups of things); 3 groups of 5 kids Why is it important to use models/ manipulatives? We need to use manipulatives like paper or pie dishes even in older classrooms. Yes, kids get older, but content gets harder.Need to show manipulatives at any grade level. 1 whole: 1 whole is when the numerator and denominator are the same 33 = 1Fractional parts are equivalent parts: When we cut into a pie, it gets smaller The more pieces the whole is divided into, the smaller the pieces Use the size of the whole get their worth from the whole; portions Numerator- the missing part from the whole (top #)Denominator- the whole part (bottom #)Attached classnotesReasoning strategies for comparing fractions: Same-sized parts (same denominator) 5/10 > 3/10 Same number, but different-sized parts (same numerator)⅖ > 2/9 More/less than one-half or one whole (comparison to benchmarks)⅞ < 8/73/7 < ⅝ Closeness to one-half or one whole (distance from benchmarks)¾ < 9/10 Benchmarks: Picture of # line example we did in class. The smaller the #, the bigger the pieces34 < 910 use percents 34 is 75% whereas 910 is 90%37 >17 same denominator 45 > 49  same numerator 37 < 58 use half benchmark 

Decimals: One-to-ten relationship (review from previous learning concepts) 555 The 5 in the ones place is 5 The 5 in the tens place is 50 The 5 in the hundredths place is 500Decimals- separates the whole from the part; a symbol ¾ = 0.75 “The point”- stands to the right of what unit separates the wholes/parts. The point explains the part of the unit and/or the function of the decimal. When we are looking at the examples below, we can see this is a one-to-ten relationship. For example, if we have $375.10 The fractions represented after the decimal point would be… 1= 1 dime; 0.10 or 1/10 0= 0 pennies 0.00 or 0/100 For example, if we have $375.11 The fractions represented after the decimal point would be… 1= 1 dime; 0.10 or 1/101= 1 penny; 0.01 or 1/100 Shading and Student Misconceptions- Students make the same mistakes with comparing fractions and decimals. We need to help students in both areas. One way we can do this is by shading. 1st misconception: With $ and surface area They don't look at the part of the whole; ex: 0.75 and 0.9We need to look at the value, not the digits! 2nd misconception:With decimals and number lines They don't know that numbers are in between the numbers represented on the number line; does not understand decimals We need to look at the numbers as a base for what is in the middle of the current number and next number.  Practice comparing decimals: Place the following in order from least to greatest. Given- 0.02, 0.2, 0.022, 0.002, 2.02, and 0.22 Solution- 0.002, 0.02, 0.022, 0.2, 0.22, and 2.02 Comparing Decimals video:https://youtu.be/trTS_KfkqtIExpressing Fractions as Terminating vs. Repeating Decimals: Divide the numerator by the denominator. ⅛ = 1 8 Terminating decimals- if you end up with a remainder of 0, then it is a terminating decimal. Use Bar Notation to show which numbers repeat, may want to try dividing a couple of times to see if there is a pattern. For example: ⅛  Solution- 0.125 with the bar over the 2 and 5 because they both repeat in that pattern. Repeating decimals- if the remainders keep continuing, then it is a terminating decimal. For example: ⅚ Solution- 0.833333The 3 is clearly repeating. Repeating and Terminating Decimals video: https://youtu.be/Jf_-FfaMMZM

Converting Fractions -> Decimals -> Percents: Percents to Decimals- Divide by 100 and remove the % sign. Move the decimal point two places to the left. For example: 75% to 0.75 Decimals to Percents- Multiply by 100 Move the decimal point two places to the right. For example: 0.125 to 12.5% Fraction to Decimal- Divide the top number by the bottom number. For example: ⅖ to get 0.4 Fraction to Percent- Divide the top number by the bottom number, and then multiply that number by 100 to get the percent. Percent to Fraction- Convert the percent to a decimal using the method “Percent to Decimal.” Then, use the same method for converting a decimal to a fraction.Class Notes: https://docs.google.com/document/d/1APSLiGEKkIF3Kvia40k-LXhtcDZSx9BTtKuKO1LJTKo/edit?usp=sharing Converting Fractions to Decimals https://youtu.be/guBVW5PiHLsConverting Decimals to Percents https://youtu.be/NJ31kZey01I