3 Simplified Fractions To simplify a fraction, we find an equivalent fraction which uses the smallest numbers possible. We do this by dividing. We need to know our tables for this! Ask yourself, what can I divide both 2 and 0 by? 8 is the biggest number we can divide both by and 3/5 uses the smallest possible numbers as we cannot divide them by anything else.
4 Look at this one The first thing I notice is that 28 and 56 are both in the 7 times table. So I m going to divide both numbers by = 7= 8 Is this simplified? NO! I can still divide both numbers by. = 8 = 8
5 Let s work through this together. 8 60
6 Try this one with a partner 2 63
7 Try this one with a partner 5 90
8 Try this one with a partner 32 56
9 OMA Round Decimal numbers to the nearest 0 th or 00 th
10 Learning Objective Consolidate recognition of equivalent fractions.
11 Equivalent fractions We are learning about equivalent fractions whole / 2 / 2 / / / /
12 whole ½ ½ ¼ ¼ ¼ ¼ We can see that / = 2 / 2 = / = 8 They are equivalent fractions
13 whole / 2 / 2 / / / / We can see that 2 is the same length as / So 2 = / They are equivalent fractions
14 Which fractions are equivalent to ½? whole ½ ¼ ¼ / 2 = 2 / =
15 whole / 2 / 2 / / / / Which of these fractions is equivalent to /? / 2 2
18 whole / 2 / 2 / / / / Which of these fractions is equivalent to? 2 / /
21 whole / 3 / 3 / 3 / 6 / 6 / 6 / 6 / 6 / 6 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 2 / 3 = 2 / 6 = / 2 Look at the equivalent fractions each time the numerators double, the denominators also double. Which other fraction will be equivalent? 8 / 2 6 / 2 / 2
23 Equivalent Fractions
24 We can see that ½ is the same as 2/, 3/6, /8 and 5/0. These are EQUIVALENT FRACTIONS. Find me an equivalent of: 2/8 3/9 8/0 9/9 /6
25 How do we know that two fractions are the same? We cannot tell whether two fractions are the same until we simplify them to their lowest terms. A fraction is in its lowest terms (simplified) if we cannot find a whole number (other than ) that can divide into both its numerator and denominator (A common factor). Examples: is not reduced because 2 can divide into both 6 and 0. is not reduced because 5 divides into both 35 and 0.
26 How do we know that two fractions are the same? More examples: is not reduced because 0 can divide into both 0 and 260. is reduced. is reduced To find out whether two fraction are equal, we need to reduce them to their lowest terms.
27 How do we know that two fractions are the same? Examples: Are and 2 30 equal? 5 reduce reduce reduce Now we know that these two fractions are actually the same!
28 How do we know that two fractions are the same? Another example: Are and equal? 2 0 reduce reduce reduce This shows that these two fractions are not the same!
29 Simplify the following Fractions
30 Ordering fractions If the DENOMINATOR is the same, look at the NUMERATORS, and put the fractions in order (if ordered smallest largest)
31 Ordering fractions If the DENOMINATOR is different, we have a problem that must be dealt with differently We need to convert our fractions to EQUIVALENT fractions of the same DENOMINATOR. We will come back to this example.
32 Ordering fractions If the DENOMINATOR is the different, we have a problem that must be dealt with differently Here s an easier example, with just 2 fractions to start us off.
33 Ordering fractions Look at the denominators. We must look for a COMMON MULTIPLE 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.
34 Ordering fractions Look at the denominators. We must look for a COMMON MULTIPLE. Multiples of 6 are 6, 2, 8, 2, 30, 36, 2, 8, 5, 60 Multiples of 9 are 9, 8, 27, 36, 5, 5, 63, 72, 8, 90
35 Ordering fractions COMMON MULTIPLES are: Multiples of 6 are 6, 2, 8, 2, 30, 36, 2, 8, 5, 60 Multiples of 9 are 9, 8, 27, 36, 5, 5
36 Ordering fractions COMMON MULTIPLES are: 8, 36 and 5. There are others that are higher, but we only look at smaller numbers. Remember: Smaller numbers are SIMPLER. 8 is the smallest number that is common, so we ll use this.
37 Ordering fractions We need to convert these fractions so they have the same denominator. 6 x 3 x 3? 8
38 Ordering fractions We need to convert these fractions so they have the same denominator. 6 x 3 x 3 2 8
39 Ordering fractions We need to convert these fractions so they have the same denominator. 3 9 x 2 x 2? 8
40 Ordering fractions We need to convert these fractions so they have the same denominator. 3 9 x 2 x 2 6 8
41 Ordering fractions So these fractions: Are EQUIVALENT to these ones:
42 Ordering fractions And this is the correct order Because these EQUIVALENT FRACTIONS are in order 2 8 8
43 Ordering fractions Remember our example The LOWEST COMMON DENOMINATOR is 2 check for all the multiples of the DENOMINATORS. 2 is the first number to appear in all the lists.
44 Ordering fractions Convert to 2ths The LOWEST COMMON DENOMINATOR is 2 check for all the multiples of the DENOMINATORS. 2 is the first number to appear in all the lists.
45 Ordering fractions Convert to 2ths 2 nd th 5 th st 3 rd This tells you how large our fractions are. Check which order they go in.
46 Ordering fractions Convert to 2ths 2 nd th 5 th st 3 rd This tells you how large our fractions are. Check which order they go in.
47 Ordering fractions So this is the correct order
48 Ordering Fractions 2 If we want to order fractions, we need to make sure our working out is clear. For every question, please use the following method We look for a COMMON MULTIPLE.
49 Ordering Fractions Look at the DENOMINATORS. What are the MULTIPLES?
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