Objectives related to Common Core Standards:



Parent HandbookAdding and Subtracting Fraction and Mixed NumbersObjectives related to Common Core Standards:Use equivalent fractions as a strategy to add and subtract fractions.Add fractions with unlike denominators.Add mixed numbers with unlike denominators.Subtract fractions with unlike denominators.Subtract mixed numbers with unlike denominators.Solve word problems involving addition of fractions.Solve word problems involving subtraction of fractions. Unit vocabularyPrime numberComposite numberBenchmark fractionPrime factorizationFactor treeCommon denominatorLeast Common denominatorProper fractionMixed numberImproper fractionConcept GuideConcept 1: Prime Factorization This concept involves expressing whole numbers as a product of prime numbers. According to The Fundamental Theorem of Arithmetic, a whole number can be factored into prime factors. (Prime numbers have exactly two factors, 1 and the number itself. For example, 5 is a prime number because the only factors that result in a product of 5 are 1 x 5. The inverse is also true: 5 has exactly two divisors, 1 and 5. In other words, only 1 and 5 can divide into 5.)Using factor trees for locating the prime factors of any given whole number:Let’s find the prime factors for the whole number 12.Place the number 12 at the top of your paper.Write a factor pair for 12 below the 12 you have written; for example (2 x 6)If one of the numbers in the pair is a prime number, circle it. (The 2 is a prime number, so circle it and keep factoring the 6.)Next, continue factoring the composite number 6. (2x3 may be written below the 6)HandCircle any prime factors (both the 2 and 3 are circle and you are done)Here is the result:Concept 2: Finding Equal Fractions:Students must understand that all fractions may be named in different ways. By multiplying both numerator and denominator by the same number, you are able to find equivalent fractions for an original fraction. For example, if I begin with 2/4 and multiply both the numerator (top number) and denominator (bottom number) by 2, the resulting equivalent would be 4/10. If I begin with the original fraction 3/10, and multiplied both numerator by 2, I would get 6/20. If I multiplied both numerators and denominators of the original fractions by 3, I would get the equivalents 6/15 and 9/30 etc.2/4 = 4/10 = 6/15 = 8/203/10 = 6/20 = 9/30 = 12/40*In order to add or subtract fractions, fractions must have common denominators. 2/4 and 3/10 cannot be added together because they have different denominators. Therefore, I would need to find equivalent fractions for each that had matching denominators.Concept 3: Finding Common Denominators The simplest way to find a common denominator for two fractions is to multiply the denominators of each fraction together. A common denominator for 2/4 and 3/10 would be 40 because when you multiply the denominators 4 and 10 together, you get 40. (4 x 10 =40.) The numerators would have to be adjusted in this case.2/4 = ?/40 (Since the denominator or 4 had to be multiplied by 10 in order to arrive at 40, then the numerator must also be multiplied by 10. The equivalent would be 20/40.) 3/10 = ?/40 (Since the denominator would be multiplied by 4 to arrive at 40, the numerator would have to be multiplied by 4. Therefore the equivalent for 3/10 would be 12/40.)2/4 + 3/10 may be changed to 20/40 + 12/40 so that the student is able to add them together. Concept 4: Finding Least Common Denominator (LCD): The smallest denominator that two or more fractions have in common is called the Least Common Denominator (LCD). Using the LCD is helpful because it makes fractions more manageable to work with and makes simplifying fractions much easier. The LCD by easily be determined by finding the multiples of the denominators of the given fractions. So, in 2/4 the denominator is 4; in 3/10, the denominator is 10. If I find the multiples of 4 and 10 like this:4, 8, 12, 16 ,20 ….10, 20, 30,40…I notice that the first multiple in common on both lists is 20. 20 is therefore the Least Common Multiple for 4 and 10 and therefore, the Least Common Denominator for 2/4 and 3/10. These fractions would be renamed in twentieths. (see equivalent fractions).2/4 = 4/20 3/10 = 6/20. Once the denominators are the same the fractions with the LCD may be added together: 4/20 + 6/20 = 10/20 or 1/2 (when simplified)Concept 5: How to subtract two fractions with unlike denominators:2/6 – 1/5 =First find a Common Denominator for the fractionsSince the denominators are 6 and 5, multiply them together.The common denominator for these fractions is 30Change the numerators accordingly:2/6 = ?/30 Since the denominator 6 must be multiplied by 5 to arrive at 30, the numerator must be multiplied by 5 as well.Therefore, 2/6 = 10/301/5 = ?/30 Since the denominator 5 must be multiplied by 6 to arrive at 30, then the numerator 1 must be multiplied by 6, as well. Therefore, 1/5 = 6/3010/30 – 6/30 = 4/ 30 or 2/15 (when simplified)Students will be learning how to use visual models to enable them to add or subtract fractions with unlike denominators. Here is an example: 1/4 + 2/3 =By combining these two diagrams, it is easy to see that each can be turned into twelfths: (four vertical sections, combined with 3 horizontal sections)1/4 is equivalent to 3/12 and 2/3 is equivalent to 8/123/12 + 8/12 = 11/12Concept 5: How do we estimate if a fraction is closer to 0, 1/2, or 1?Use a number line.Is 1/6 closer to 0, 1/2, or 1?Since the unit fraction I am rounding has 6 as a denominator, I would break my number line into 6 equal pieces between 0 and 1. I would mark of each section with a line and place 1/6 at its location. I would evaluate the position of 1/6 and determine if it is closer to 0, ?, or 1._________________________________________011/6 is closest to 0, therefore, when estimating I would round it to 0.If I was asked to estimate the sum of 3/4 + 1/7, I would round each fraction to either 0, ?, or 1, then add.Since ? is closest to 1 on a number line and 1/7 is closest to 0 on a number line, I would estimate the sum to be 1, because 1 + 0 = 1.The same process is used in estimating differences (subtraction).Concept 6 –Adding or subtracting mixed numberA mixed number is made up of a whole number and a fraction. For example 3 1/4 and 2 1/5 are mixed number. To add them or subtract them, it is important to first find common denominators. Ignore the whole numbers until you are ready to add or subtract. For example: To add 31/4 + 21/5Find a common denominator for the fractions in the mixed numbers 1/2 and 1/5.It’s easiest to multiply the denominators together: 4 x 5 = 20 and change each fraction to twentieths. 1/4 = 5/20 1/5 = 2/20Make sure to include the original whole numbers back in your addition problem: 3 1/4 = 3 5/20+ 2 1/5 = + 2 4/203 5/20 + 2 4/20= 5 9/20Concept 7: Improper fractions must be converted to whole numbers or mixed numbers:Improper fractions equal one whole or more. They have numerators that are equal to or greater than the denominator. Since fractions are really division problems, you would simplify the improper fraction by dividing the numerator (top) by the denominator (bottom) or as students like to say: “bottom into top.” Here are some examples of improper fractions and how to simplify them:6/6 = 1 (6 divided by 6 = 1)4/3 = 1 1/3 (4 divided by 3 = 1 and 1/3 remaining)10/5 = 2 (10 divided by 5 = 2)9/4 = 2 ? (9 divided by 4 = 2 and ?)If a sum or difference contains an improper fraction, the answer must be simplified. 1 2/3 + 3 4/5 = 1 10/15 + 3 12/15 = 4 22/15 = 4 + 22/15 = 4 + 1 17/15 = 5 7/15Concept 8: Subtracting fractions from whole numbersWhen subtracting a fraction from a whole number, rename the whole number as a fraction with the same denominator as the fraction you are subtracting from it and then find the difference.For example: 1 – 1/5 First rename 1 as 5/5 then subtract 1/5 from 5/5. 5/5 – 1/5 = 4/5When you subtract a fraction from a whole number greater than one, borrow “1” from the whole number and rewrite it with the same denominator as the fraction you are subtracting from it. The whole number should be recorded as one less than it was. For example: 5 – 2/3 (borrow one from the 5 and rename it 3/3… since we borrowed one from the 5, the renamed amount 1s 4 3/3 )4 3/3 – 2/3 = 4 1/33 – 1/6 (borrow one from the 3 and rename it, 6/6…the amount has been renamed 2 6/6.)2 6/6 – 1/6 = 2 5/6Here is a vertical presentation: ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download