Adding Fractions And Mixed Numbers

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Adding Fractions and Mixed NumbersI. Adding Fractions with the Same Denominator562 3 5 6 6 626 3656REMEMBER the denominator tells how many parts are in one rectangle. It tells ussomething about the size of the parts. The numerator tells how many of these parts are beingadded.EXAMINE THE STATEMENT263656NOTICE:The denominators are the same in both addends.The denominator of the sum is also this same number.(Denominators are NOT ADDED.)The numerators of the addends are added to get the numerator of the sum.The answer is simplified. (1 is the only factor of 5 and of 6.)THINK: If you add 2 dimes to 7 dimes, you'll have 9 dimes (the kind of coin can be like adenominator - we keep it; the numbers of coins are added just as numerators are).Isn't a dime1of a dollar?102 dimes 7 dimes is the same as279dollar dollar dollar101010Understanding the meanings of the numerator and denominator makes addition of fractionseasier to understand.This instructional aid was prepared by the Tallahassee Community College Learning Commons.

1–4. ADD and SIMPLIFY the answers:1.49292.58383.7124124.5123126125. Write a rule for adding fractions with the same denominator.II. Adding Fractions with Unlike DenominatorsIf you have 3 nickels 4 dimes, you have 7 coins but that doesn't tell the value. To get thetotal value, you will probably think of 3 nickels as 15 cents and 4 dimes as 40 cents. Then you add1dollar. (Doesn't it take 100 cents to make one15 40 to find the value is 55 cents. A cent is100dollar?)13Let's look at the addition problem.12We have 2 parts but they are not thesame size, so we don't know howmuch of a rectangle this sum is.13121213Let's think of asandas . (Look up writing equivalent fractions in your text.)3626113226 36Once the fractions have the same denominator, we know how to add them, but how do wedecide what denominator we should use? We use the LCM of the denominators.Complete the Rule:To add fractions with unlike denominators:1. Find the of the denominators.2. Build fractions having the of the denominators as thedenominator of each fraction.3. Add the ; keep the of these new fractions.4. Simplify the answer if .This instructional aid was prepared by the Tallahassee Community College Learning Commons.

EXAMPLE:5856291. Find the LCM of denominators869LCM 2 2 22 33 32 2 2 3 3 722. Build equivalent fractions5845725660722916723. Add numerators; keep denominator45 60 1672121724. Simplify (see your text)11 4972(There is no common factor other than 1 in the numerator and denominator)7 72 2 2 3 3II. 5–7 Add and Simplify:5.5127246.3856116237.2314III. Adding Mixed Numbers and FractionsWe know that a mixed number is a short way of writing addition.33115 is 5 and 3 is 38844To add 531and 3 , we apply the Commutative and Associative Properties of Addition.84This instructional aid was prepared by the Tallahassee Community College Learning Commons.

38THINK: 5313is 548314Because this is all addition we can use the Commutative and Associative Properties ofAddition to group the whole number addends and the fraction addends.5 31438Now add inside each parentheses (REMEMBER the denominators of the fractions must be thesame!)2 388 858 858 (Simplified form)8Sometimes the fraction is an improper fraction and must be simplified. Then the whole numbers canbe added.5EXAMPLE:53427 9127 19127 1834256You may add the fractions, then add the wholenumbers, then simplify.56This is a shorter way to do theproblem on the left. You mustunderstand why this short wayworks!101234526591210212197125712712III. 8–11 Add and Simplify:8. 3568122239. 634412This instructional aid was prepared by the Tallahassee Community College Learning Commons.

III. 8–11. Add and Simplify (continued):10. 9157 5161211. 825361412. Tell how to add mixed numbers. Include the rules for the fraction parts and simplifyinganswers.ANSWERS:I.6 21.9 314124.12.8813.1611125. Add the numerators; keep thedenominator. Write the answer in simplestform.II. Rule for Adding Fractions:1.2.3.4.5.LCMEquivalent, LCMNumerators, denominatorThere is a common factor and/or if it is an improper fraction.17246. 115167.1112III.8. 1512.9. 111410. 15254811. 171320Add the fractions (be sure to build equivalent fractions so that the denominators are all thesame). Add the whole numbers. If the fraction is an improper fraction, write it as a mixednumber, then add its whole number to the whole number part of the answer. Get rid ofcommon factors in the fractions' numerator and denominator.This instructional aid was prepared by the Tallahassee Community College Learning Commons.

II. Adding Fractions with Unlike Denominators If you have 3 nickels 4 dimes, you have 7 coins but that doesn't tell the value. To get the total value, you will probably think of 3 nickels as 15 cents and 4 dimes as 40 cents. Then you add 15 40 to find the value is 55 cents. A cent is

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