Adding Fractions with Unlike Denominators
- 1. Adding Fractions With Unlike Denominators Fourth Grade Math Mr. Mitchell
- 2. Adding Fractions with Unlike Denominators • When adding fractions with unlike denominators it is a little different than fractions with like denominators. • Unlike denominators means that the denominators of the fractions are different. 2 1 1 2 3 1 3 5 6 9 12 6 The fractions above have different denominators, called unlike denominators.
- 3. Adding Fractions with Unlike Denominators • The goal of adding fractions with unlike denominators is to get the denominators to be the same. • When the denominators are the same the fraction is easier to add. • As you have learned before, adding fractions with like denominators are easier, because you will just add the numerators. • Our focus for this lesson is: To make our denominators the same.
- 4. Adding Fractions with Unlike Denominators • The following are the steps to adding fractions with unlike denominators. • Example: 2 1 5 3 As you can see, our fractions have unlike denominators. To make them the same we need to find the Least Common Denominator or LCD.
- 5. Adding Fractions with Unlike Denominators • To find our LCD we need to first find the multiples of both of our denominators, and then identify the Least Common Multiple, or LCM. • The LCM will become our LCD. • A multiple is the answer to a multiplication problem. Example: multiples of 4 are: 4,8,12,16,20 and so on. Multiples of 7 are: 7,14,21,28,35 and so on
- 6. Adding Fractions with Unlike Denominators 2 1 5 3 •Step 1 •Find the multiples of the denominators, 5 and 3. •Start with the lowest valued number, because at times your larger number may be a multiple of your smaller number. •Multiples of 3: •3,6,9,12,15,18,21,24 •Multiples of 5: •5,10,15 •Stop finding multiples when you have found one they both have in common.
- 7. Adding Fractions with Unlike Denominators 2 1 5 3 •Step 2 •Identify the LCM •The multiples are: 3: 3,6,9,12,15,18,24 5: 5,10,15 The Least Common Multiple is 15
- 8. Adding Fractions with Unlike Denominators 2 1 5 3 •Step 3 •Create equivalent fractions to your current fractions, using your LCM as your new denominator 2 ? 1 ? 5 15 3 15
- 9. Adding Fractions with Unlike Denominators 2 1 5 3 •To find an equivalent fraction, you will need to find out what you multiplied each of the original denominators by to get the new denominator. •First look at your multiples: •3,6,9,12,15 •5,10,15 •You can count the number of multiples of 3 by counting how many multiples it takes to get to 15 •Do the same for your multiples of 15
- 10. Adding Fractions with Unlike Denominators 2 1 5 3 •Step 3 continued: •Remember, to find equivalent fractions, whatever you do to the denominator you must do the same to the numerator. • For the fraction 2/5, you multiplied the denominator by 3 so you need to multiply the numerator by 3 as well. •The equivalent fraction will become: 2 6 5 15
- 11. Adding Fractions with Unlike Denominators 2 1 5 3 •Step 3 continued: •Remember, to find equivalent fractions, whatever you do to the denominator you must do the same to the numerator. • For the fraction 1/3, you multiplied the denominator by 5 so you need to multiply the numerator by 5 as well. •The equivalent fraction will become: 1 5 3 15
- 12. Adding Fractions with Unlike Denominators 2 1 5 3 •The fractions in the addition problem then become: 6 5 15 15
- 13. Adding Fractions with Unlike Denominators 2 1 5 3 •Our goal was to convert our fractions into fractions with the same denominators. Following the steps you have ended up with the following fractions. 6 5 15 15
- 14. Adding Fractions with Unlike Denominators 2 1 5 3 Step 4 •Add the numerators of the fraction together. •6+5=11 •Eleven will be the numerator of your answer. 6 5 11 15 15 ?
- 15. Adding Fractions with Unlike Denominators 2 1 5 3 Step 5 •The denominators are not added together. The denominator tells us the equal number of pieces all together so this number does not change. •Remember the following: •If the denominators are the same, keep them the same. If they are not the same, make them the same. 6 5 11 15 15 15
- 16. Adding Fractions with Unlike Denominators 2 1 5 3 6 5 11 15 15 15 The final step is to reduce the fraction if needed. This fraction is already in the simplest form, so reducing is not needed.
- 17. Adding Fractions with Unlike Denominators • For further practice of adding fractions with unlike denominators you can visit the following websites: http://www.mathplayground.com/fractions_add.ht ml http://www.aaamath.com/fra66kx2.htm http://www.math.com/school/subject1/practice/S 1U4L3/S1U4L3Pract.html Template for presentation provided by Microsoft PowerPoint 07