Transcript lesson
Fractions Any fraction can be written in many ways and still have the same value… 4 2 1 or or 8 4 2 …are all the same… 0.5 Equivalent Fractions Fractions are equivalent (equal) if they have the same value We could change them to decimals to see if they are equal or leave them as fractions How would we use this? 1. We might want the fraction to look “simpler” like ½ instead of 44/88 2. We might want to compare fractions to see which is bigger or smaller (it’s easy if they have the same denominator) 3. We might want to add or subtract fractions We know that we can multiply or divide by 1 and the number stays the same Since… 3 2 5 or or 3 2 5 =1 We can multiply or divide any fraction by these and the fraction keeps its value 4 5 3 3 6 8 = ÷ 12 15 2 2 = 3 4 What if we have 2 fractions like… 3 5 5 8 Why might we want them to have the same denominator? to compare to add or subtract We need to find a common denominator 3 8 8 5 5 8 5 5 There are many common denominators, but only one is the smallest 5 8 8 6 7 8 6 6 Is there a smaller denominator we could use? Yes, 24! What we are doing is looking at the multiples of numbers… The multiples of 6 are: 6, 12, 18, 24, 30, 36, 42, 48 and so on The multiples of 8 are: 8, 16, 24, 32, 40, 48 and so on Both 24 and 48 are common, but 24 is the least Remember! You CAN’T have a Greatest Common Multiple! Why not? Let’s compare some fractions Which is larger, 5 12 3 8 What is the LCD? Yes, 24 Compare these: 9 16 7 12 The multiples of 16 are: 16, 32, 48, 64, 80 … The multiples of 12 are: 12, 24, 36, 48, 60… 36 96 Would this fraction be easier to “understand” if the numbers were smaller? 36 96 We know we can divide both the numerator and denominator by the same number and get an equivalent fraction… Sure, there 3 36 ÷ 6 ÷ are many, =but = let’s try 6 2 6 96 ÷ 16 ÷ Now 8 2… 2 6 What number goes into both 36 and 96? could have 3 done this in 36 ÷We12 =if we had used one step the GCF of 36 and 96… 8 ÷ 12 96 The GCF of 36 and 96 is… 12 Practice… 18 24 25 40 42 102 We can also multiply the numerator and denominator by the same number… 3 4 2 6 = 2 8 Why would we want to do that? 7 2 14 5 3 15 = = 12 2 24 8 3 24 Can you think of a reason besides comparing that we might want the same denominators? More on this next lesson To summarize... We use common factors or GCF to... simplify a fraction (lowest terms) We use common multiples or LCM to... find common denominators