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Fraction Guide Page 1 Page 2 Page 3 Page 3 Page 4 Page 4 Page 5 Page 6 Page 7 Page 8 Page 9 Page 10 Page 11 Page 12 Page 13 Intro to Fractions Three types of Fractions: Improper, proper, and mixed. Changing Fractions Making whole numbers into fractions Equivalent Fractions Comparing Fractions Adding fractions with like denominators Subtracting fractions with like denominators Adding fractions with unlike denominators Subtracting fractions with unlike denominators How to reduce or simply fractions Adding/subtracting mixed numbers Changing a fraction to a percent or decimal Multiplying fractions Dividing fractions Intro to Fractions A fraction is a part of a whole Slice a pizza, and you will have fractions: 1 1 /2 (One-Half) /4 (One-Quarter) 3 /8 (Three-Eighths) The top number tells how many slices you have and the bottom number tells how many slices the pizza was cut into. Here are some examples: Numerator / Denominator Top number = Numerator, it is the number of parts you have. Bottom number = Denominator, it is the number of parts the whole is divided into. numerator denominator Page 1 Three Types of Fractions There are three types of fractions: Examples of Proper Fractions (Bottom # is bigger than top #) Examples of Improper Fractions (Top # is bigger than bottom #) Examples of Mixed Numbers (A whole # and a fraction) 2 3 1 2 3 4 5 3 7 2 9 4 1 23 2 45 8 79 Page 2 Changing Fractions Change a mixed number to an improper fraction: Multiply the bottom number by the big number, then add the top number. Keep the bottom number the same. Example: Change an improper fraction to a mixed number: 3x2+1=7 1 23 7 3 Answer: Ask a question. How many times can the bottom number go into the top number without going over? Your answer will be the big number. Put your remainder on top, and the bottom remains the same. Example: 17 3 How many times can 3 go into 17 without going over? (5 times) Then, there is 2 left over, which goes on the top, and 3 stays on the bottom. 2 53 Change a whole number into a fraction: Example: Any whole number can be made into a fraction by putting it over 1. 12 = 12 1 Page 3 Equivalent Fractions Equivalent fractions are fractions that are equal, but use different numbers. How to find an equivalent fraction: Multiply both the top and bottom number by another number. Example: I am going to multiply it by 2. 2 3 Remember: 4 6 = What you do to the top of the fraction you must also do to the bottom of the fraction ! You can use any number you want to multiply it by, but it is usually easier to do low numbers. Comparing Fractions When comparing fractions, use the < , > , or = sign. Cross multiply at an upwards angle and write the number at the top. Do the same for the other side. 8 9 2 3 3 4 Since 9 is bigger, that means the fraction on that side is bigger. 2 3 < 3 4 Page 4 Adding fractions with like denominators 1. Add the top numbers. 2. Put the answer over the same bottom number. 1 4 1 4 + = 2 4 3. When you are done, you may need to reduce the fraction or change it to a mixed number. Example: 3 4 + 2 4 = 5 4 Now, since it is an improper fraction, I have to change it to a mixed number. 5 4 = 11 4 Page 5 Subtracting fractions with like denominators 1. Subtract the top numbers. 2. Put the answer over the same bottom number. - 3 4 1 4 = 2 4 3. When you are done, you may need to reduce the fraction or change it to a mixed number. Example: 7 4 - 2 4 = 5 4 Now, since it is an improper fraction, I have to change it to a mixed number. 5 4 = 11 4 Page 6 Adding fractions with unlike denominators When adding fractions that have unlike denominators, your first step is to get the denominators the same. 2 3 + 3 4 Multiply by the opposite bottom number. = x4 x3 + 4x2 4x3 8 12 + 3x3 4x3 9 12 = 17 12 = Now you can add the top numbers. Your last step is to reduce or change it to a mixed number. In this case, since it is an improper fraction, you have to change it to a mixed number. 17 12 5 = 112 Shortcut: If you have a bottom number that goes evenly into the other bottom number, you only have to multiply one side. Example: x2 1 3 2 6 + 3 6 + 3 6 3 can go into six evenly if I multiply it by 2 = 5 6 Page 7 Subtracting fractions with unlike denominators When subtracting fractions that have unlike denominators, your first step is to get the denominators the same. - 3 4 2 3 Multiply by the opposite bottom number. = x 3 x4 3x3 4x3 9 12 - 4x2 4x3 - 8 12 = 1 12 = Now you can subtract the top numbers. Your last step is to reduce or change it to a mixed number. In this case, you cannot reduce it any further. 1 12 Shortcut: If you have a bottom number that goes evenly into the other bottom number, you only have to multiply one side. Example: x2 3 6 - 1 3 3 6 - 2 6 3 can go into six evenly if I multiply it by 2 = 1 6 Page 8 Reducing or Simplifying Fractions * Can also be called “lowest terms” When you are ready to put your final answer on paper, you must ask yourself, “Can this fraction be reduced?” Your answer will not be correct unless you reduce the fraction first. What that means is making the fraction look as small as it can, while still keeping the same value of the fraction. Steps: 1. Ask: What can both the top and bottom number be divided by? 9 12 Example: In this case, the number that both can be divided by is 3. 2. Do the division. 9 12 3 3 = 3 4 Once you do your division, check to see if it can be reduced again. Page 9 Adding and Subtracting Mixed Numbers When subtracting fractions that are mixed numbers, the same rules apply as when you are adding and subtracting regular fractions. If you forgot how to add and subtract fractions, look at pages 5, 6, 7 and 8 for more help. Adding Example: (like denominator) 5 112 + 2 112 7 = 212 1. Add the whole numbers. 2. Then add the fraction. Adding Example: (unlike denominator) 1 13 + = 3 16 5 1 = 6 1. Get the denominators the same by multiplying. 2. Add the whole numbers. 3. Then add the fractions. When you are subtracting mixed numbers you can do it exactly the same as adding, EXCEPT WHEN THE FIRST FRACTION IS SMALLER THAN THE SECOND FRACTION. Then, there is a different way. If you are not sure if it is smaller or not, you can do this way and still get the correct answer. Subtracting Example: 5 310 - 7 110 1. Change both numbers to an improper fraction. (page 3) 2. Subtract the numbers. 3. Change back to a mixed number. 35 10 - 17 10 = 18 10 Change back to mixed # 8 110 Reduce 4 15 Page 10 Changing Fractions to a Percent or Decimal Change a fraction to a decimal In order to change a fraction into a decimal, you must divide. The top number must go on the INSIDE of the division problem Example: 3 4 = 4)3 Last, DO the long division. Change a decimal to a percent Example: 4) 3 In order to change a decimal into a percent, you must move the decimal point. .75 Move the decimal point TWO places to the right. = 75% No matter what, you always move it TWO places! Examples: 1.75 = 175% .485 = 48.5% .5826 = 58.26% 25 = 2500% Page 11 Multiplying Fractions When you multiply fractions, you DO NOT need to have the same denominator. Step 1: Multiply across 2x4 x 2 3 4 5 = 8 15 3x5 Step 2: Reduce or simplify if needed. If you have a mixed number, you should change the mixed number to an improper fraction before starting. (If you forgot how to change a mixed number into an improper fraction, go to page 3.) Example: 5 310 x 35 10 x = 1 2 1 2 = 35 20 Now you must change it back to a mixed number. (If you forgot how to do that, look at page 3.) 15 120 Now reduce it. 3 14 Page 12 Dividing Fractions When you divide fractions, you DO NOT need to have the same denominator. Dividing is the same as multiplying, but with some extra steps in the beginning. 2 3 4 5 Step 1: Get the reciprocal of the SECOND number. A reciprocal is when you flip the fraction upside down. The reciprocal of = 4 5 5 4 Step 2: Change the division sign to a multiplication sign. 2 3 x 5 4 Step 3: Multiply the fraction. (If you forgot how to multiply, see page 12) 2 3 x 5 4 = 10 12 Step 4: Reduce or simplify if needed. 5 6 If you have a mixed number, you should change the mixed number to an improper fraction before starting. (If you forgot how to change a mixed number into a fraction, go to page 3.) Page 13