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Sixers Guide to Ordering Fractions I love ordering fractions! Sixers Guide to Ordering Fractions You have 30 seconds to do the following: Write the title “Ordering Fractions” with today’s date Do “Belly Taps, Belly Rubs” when finished Ordering fractions We can order numbers fairly easily. For example: 7 14 6 19 50 Ordering fractions This becomes: 6 < 7 < 14 < 19 < 50 (if ordered smallest to largest) Ordering fractions Fractions are ordered the same way. For example- Order these fractions from smallest to greatest 3 8 5 8 4 8 1 8 2 8 Ordering fractions If the DENOMINATOR is the same, look at the NUMERATORS, and put the fractions in order. Remember: DENOMINATOR = the BOTTOM number NUMERATOR= the TOP number 3 5 4 1 2 8 8 8 becomes 8 8 1 8 < 2 8 < 3 8 < 4 8 < 5 8 But what if the denominators are different? For example: Mr. Meldrum has 3/4 of a dollar. Mr. Slater has 3/5 of a dollar. Who has more money? Ordering fractions Mr. Meldrum has 3/4 of a dollar. How much is 3/4 of a dollar? One quarter is 25 cents Therefore, 3 quarters is 75 cents Mr. Meldrum has 75 cents Ordering fractions Mr. Slater has 3/5 of a dollar. How much is 3/5 of a dollar? 1 dollar = 100 cents To find one fifth of a dollar, divide 100 by 5 100 divided by 5 = 20 20 cents is 1/5 of a dollar Therefore, 3/5 of a dollar= 20 x 3 Mr. Slater has 60 cents Ordering fractions Therefore, 3/4 (75 cents) is greater than 3/5 (60 cents) 3 Qui ckTi me™ and a decompresso r are ne ede d to see thi s pi cture. 4 > 3 5 QuickTime™ and a decompressor are needed to see this picture. Therefore, Mr. Meldrum has more money! Ordering fractions How else can we compare 3/4 to 3/5? Both fractions have the same numerator Fourths are bigger than fifths So, three-quarters are bigger than three-fifths * If the numerators are the same, the fraction with the smallest denominator is greater Ordering fractions How else can we compare 3/4 to 3/5? 3 3 4 5 Ordering fractions Look at the denominators. We must look for a COMMON MULTIPLE. 3 3 4 5 This means that we check to see which numbers are in the 4 times table, and the 5 times table. We need a number that appears in both lists. Ordering fractions Look at the denominators. We must look for a COMMON MULTIPLE. 3 3 4 Multiples of 4 are 5 4, 8, 12, 16, 20, 24, 28, 32, 36, 40…… Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50…… Ordering fractions COMMON MULTIPLES are: 3 3 4 Multiples of 4 are 5 4, 8, 12, 16, 20, 24, 28, 32, 36, 40…… Multiples of 5 are 5, 10, 15, 20, 25, 30, 35, 40, 45, 50…… Ordering fractions COMMON MULTIPLES of 4 and 5 are 20 and 40 3 3 4 5 There are others that are higher, but we only look at smaller numbers. Remember: Smaller numbers are SIMPLER. 20 is the smallest number that is common, so we’ll use this. * This is called the Lowest Common Denominator or LCD Ordering fractions We need to convert these fractions so they have the same denominator. 3 3 4 3 4 x5 x5 ? 20 5 Ordering fractions We need to convert these fractions so they have the same denominator. 3 3 4 3 4 x5 x5 15 20 5 Ordering fractions We need to convert these fractions so they have the same denominator. 3 3 4 3 4 x5 x5 15 20 5 3 5 x4 x4 ? 20 Ordering fractions We need to convert these fractions so they have the same denominator. 3 3 4 3 4 x5 x5 15 20 5 3 5 x4 x4 12 20 Ordering fractions So these fractions: 3 4 3 5 Are EQUIVALENT to these ones: 15 20 12 20 Ordering fractions So this is the correct answer: 3 4 Because: 15 20 > > 3 5 12 20 Ordering fractions Keys to putting fractions in order: If the denominators are the same, the fraction with the bigger numerator is greater If numerators are the same, the fraction smaller denominator is greater. If neither the numerator or denominator are the same, you must change both fractions into equivalent fractions with a common denominator. Ordering fractions Try this one… 4 7 6 9 Which fraction is bigger? (Explain your thinking to a neighbour in 30 seconds or less) Ordering fractions Look at the denominators. We must look for a COMMON MULTIPLE. 4 7 6 9 This means that we check to see which numbers are in the 6 times table, and the 9 times table. We need a number that appears in both lists. Ordering fractions Look at the denominators. We must look for a COMMON MULTIPLE. 4 7 6 Multiples of 6 are 9 6, 12, 18, 24, 30, 36, 42, 48, 54, 60…… Multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90…… Ordering fractions COMMON MULTIPLES are: 4 7 6 Multiples of 6 are 9 6, 12, 18, 24, 30, 36, 42, 48, 54, 60…… Multiples of 9 are 9, 18, 27, 36, 45, 54, 63, 72, 81, 90…… Ordering fractions COMMON MULTIPLES of 6 and 9 are 18, 36 and 54 4 7 6 9 There are others that are higher, but we only look at smaller numbers. Remember: Smaller numbers are SIMPLER. 18 is the smallest number that is common, so we’ll use this. * This is called the Lowest Common Denominator or LCD Ordering fractions We need to convert these fractions so they have the same denominator. 4 7 6 4 6 x3 x3 ? 18 9 Ordering fractions We need to convert these fractions so they have the same denominator. 4 7 6 4 6 x3 x3 12 18 9 Ordering fractions We need to convert these fractions so they have the same denominator. 4 7 6 4 6 x3 x3 12 18 9 7 9 x2 x2 ? 18 Ordering fractions We need to convert these fractions so they have the same denominator. 4 7 6 4 6 x3 x3 12 18 9 7 9 x2 x2 14 18 Ordering fractions So these fractions: 4 6 7 9 Are EQUIVALENT to these ones: 12 18 14 18 Ordering fractions So this is the correct answer: 4 6 Because: 12 18 < < 7 9 14 18 Ordering fractions Your homework: Which fraction is bigger? Use < or > 1. 5 7 3 4 2. 2 3 6 8 3. 4 5 7 9 Ordering fractions Here’s one for you to try: 4 3 5 4 Which fraction is bigger? Ordering fractions Here’s one for you to try: 4 5 4 1) Find the Lowest Common Denominator 20 2) Rewrite the fractions with 20 as the denominator 16 > 3 20 > 15 20 Ordering fractions If the DENOMINATOR is the different, we have a problem that must be dealt with differently. 3 6 7 8 4 4 1 3 2 4 We need to convert our fractions to EQUIVALENT fractions of the same DENOMINATOR. We will come back to this example. Ordering fractions Remember our example 3 6 7 8 4 4 1 3 2 4 1) Find the Lowest Common Denominator of 6, 8, 4 & 3 24 Ordering fractions Convert to 24ths 3 7 4 1 2 6 12 24 8 21 24 4 24 24 3 8 24 4 12 24 The LOWEST COMMON DENOMINATOR is 24 – check for all the multiples of the DENOMINATORS. 24 is the first number to appear in all the lists. Ordering fractions Convert to 24ths 3 7 4 1 2 6 2nd 12 24 8 4th 21 24 4 5th 24 24 3 1st 8 24 4 3rd 12 24 Now put the fractions in order from smallest to largest. Ordering fractions Convert to 24ths 3 7 4 1 2 6 2nd 12 8 4th 21 4 5th 24 3 1st 8 4 3rd 12 24 24 24 24 24 Now put the fractions in order from smallest to largest. 1 3 3 6 2 4 7 8 4 4 Ordering fractions Now it’s your turn: Put the following fractions in order from smallest to largest 5 7 3 3 9 12 6 4 REMEMBER THE FOLLOWING STEPS: 1) We look for a COMMON DENOMINATOR. 2) Rewrite the fractions as equivalent fractions using the LCD 3) Order the fractions from smallest to largest Ordering fractions 5 9 7 12 3 6 3 4 Look at the DENOMINATORS. What are the MULTIPLES? Ordering fractions 5 9 7 12 3 6 3 4 Look at the DENOMINATORS. What are the MULTIPLES? 9: 9, 18, 27, 36, 45, 54, … 12: 12, 24, 36, 48, 60, … 6: 6, 12, 18, 24, 30, 36, 48, … 4: 4, 8, 12, 16, 20, 24, 28, 32, 36,… Ordering fractions 5 9 7 12 3 6 3 4 Use 36 as the COMMON DENOMINATOR. Ordering fractions 5 9 7 12 3 6 3 4 36 36 36 36 Ordering fractions 5 9 x 4 7 12 x 3 3 6 x 6 3 4 x 9 Find the number that you need to multiply the DENOMINATORS by to get 36. 36 36 36 36 Ordering fractions 5 9 x 4 7 12 x 3 3 6 x 6 3 4 x 9 Multiply the NUMERATORS by the same amount as you multiplied the DENOMINATORS 36 36 36 36 Ordering fractions 5 9 x 4 7 12 x 3 3 6 x 6 3 4 x 9 20 36 21 36 18 36 27 36 Ordering fractions 5 9 x 4 7 12 x 3 3 6 x 6 3 4 x 9 Decide which order the fractions need to be in. 20 36 2nd 21 36 3rd 18 36 1st 27 36 4th Ordering fractions 5 9 x 4 7 12 x 3 3 6 x 6 3 4 x 9 putting them in order… 20 36 2 21 36 3 18 36 1 27 36 4 18 36 20 36 21 36 27 36 Ordering fractions 5 9 x 4 7 12 x 3 3 6 x 6 3 4 x 9 Now convert them back… 20 36 2 21 36 3 18 36 1 27 36 4 18 36 20 36 21 36 27 36 3 5 7 3 6 9 12 4 Ordering fractions 5 9 x 4 7 12 x 3 3 6 x 6 3 4 x 9 and the final answer… 20 36 2 21 36 3 18 36 1 27 36 4 18 36 20 36 21 36 27 36 3 5 7 3 6 9 12 4

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