FRACTIONS Adding Subtracting Fractions with Different Denominators By

FRACTIONS Adding & Subtracting Fractions with Different Denominators By Timothy Leonard

Fractions with Same (Common) Denominators n It's easy to add and subtract like fractions, or fractions with the same denominator. l You just add or subtract the numerators and keep the same denominator. 1/ 3/ 1/ 2 + 4 4 = /4 (or ½) 5 - 1/ = 5 2/ 5

Denominators that are multiples of another n To Add and Subtract Fractions with different denominators, you need to know how to find the least common denominator (LCD). l To find the least common denominator find the least common multiple of the denominators. 1/ l 2/ = ? + 5 3 In the above addition problem the multiples of each denominator are: Multiples of 5 5, 10, 15, 20, 25 3, 6, 9, 12, 15, 18, 21 l Multiples of 3 15 is the least common multiple (lowest shared number) between the two sets of multiples and is your least common denominator (LCD).

Adding Fractions with Different Denominators (cont’d) n Now that you’ve found your least common denominator (15), ask yourself how many times does each starting denominator go into 15. 1/ n 5+ 2/ ? 3= + ? 15 15÷ 5 = 3 and 15÷ 3 = 5 Now multiply each result times the corresponding numerator. 3 x 1 = 3 and 5 x 2 = 10 n Answer: 3 + 10 15 = 13 15

Subtracting Fractions with Different Denominators 1 3 - 1 4 = ? n It’s difficult to determine the exact answer using this animation of 1/3 – 1/4. Now attempt to solve using least common denominator method. Lets take a look at the next slide.

Subtracting Fractions with Different Denominators (cont’d) 1 3 - 1 4 ? = Multiples of 3: 3, 6, 9, 12, 15 Multiples of 4: 4, 8, 12, 16 Least common multiple: 12 WHOLE Now we have twelfths Multiply numerators by 12÷ 3=4 and 12÷ 4=3, respectively 4 12 - 3 12 = 1 12

Denominators that are multiples of each other n To Add and Subtract Fractions with different denominators which are multiples of each other, you have fewer steps to find the least common denominator (LCD). l To find the least common denominator in this instance the greater of the 2 denominators becomes the LCD. 1/ 2/ =? + 5 10 5, 10, 15, 20, 25 l 10 is a multiple of 5, and 10 is also a multiple Now only 1 division and 1 multiplication operation is required:

Give It a Try Let’s Practice Adding Fractions Number 1 Number 2 Number 3 Number 4 2/6 + 2/3 = ? a) 1/3 b) 1 c) 2/6 + 1/6 = ? a) 4/6 b) 3/5 c) 1/2 3/8 + 2/8 = ? a) 5/8 b) 3/8 c) 1/8 3/8 + 2/6 = ? a) 5/14 b) 6/24 c) 17/24

What Has Been Given, We Now Have to Take Away. It’s Time to Practice Subtracting Fractions Number 1 Number 2 Number 3 Number 4 2/3 - 2/6 = ? a) 2/3 b) 1/3 c) 1/2 2/6 - 1/6 = ? a) 3/6 b) 1/2 c) 1/6 3/8 - 1/8 = ? a) 1/8 b) 3/8 c) 1/4 3/8 - 2/6 = ? a) 1/24 b) 5/14 c) 1/6

Incorrect n Did you forget to make them equivalent fractions?

Correct n Great Job, move to the next question.

Incorrect n Did you forget to subtract or did you forget to make them equivalent?

Correct n Great Job, move to the next question.

Correct—Done w/Adding, Now Let’s Try Something New… n Great Job, move to the next question.

Excellent Job n For further practice or explanations on adding and subtracting fractions, here are some suggested websites.

For Further Study n http: //www. visualfractions. com/ n http: //www. shodor. org/interactiv ate/activities/Fraction. Sorter/? ver sion=skip 1&browser=unknown n http: //www. funbrain. com/