Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
John Wallis wikipedia , lookup
Mathematics of radio engineering wikipedia , lookup
Positional notation wikipedia , lookup
Mathematics and art wikipedia , lookup
Mathematics and architecture wikipedia , lookup
List of works designed with the golden ratio wikipedia , lookup
STRAND: Measurement TOPIC: Ratio & rates Ratios involving fractions To express two fractions as a ratio in simplest form, follow the steps below: 1. convert mixed number(s) into improper fraction(s) 2. change both fractions to the equivalent fractions with the same denominator 3. omit denominators and write numerators as a ratio 4. simplify the ratio by dividing both numbers by the highest common factor. WORKED Example Express each of the following as a ratio in its simplest form. 2 11 2 3 4 1 - -----a ----b 2 --5- : 1 --5c 1 --7- : 1 --313 : 13 Solution 2 11 a Both ------ and ------ are proper fractions with the same denominator, so omit the denominators and write the 13 13 numerators as a ratio. The ratio is 2 : 11 2 3 12 8 b 2 --- : 1 --- = ------ : --(Change mixed numbers into improper fractions.) 5 5 5 5 Since denominators are the same, write the numerators as a ratio and simplify. The ratio is 12 : 8 or 3:2 (Divide both numbers by 4 — the HCF of 12 and 8.) 4 1 11 4 c 1 --- : 1 --- = ------ : --(Change the mixed numbers into improper fractions.) 7 3 7 3 33 28 = ------ : -----(Change both fractions to the lowest common denominator.) 21 21 Since the denominators are the same, write the numerators as a ratio. The ratio is 33 : 28 Try these Express each of the following as a ratio in its simplest form. 2 3 1 --- : --5 5 1 1 2 1 --- : --2 2 2 5 3 4 --- : 2 --9 9 3 7 4 2 ------ : 3 -----11 11 3 1 5 6 --- : 2 --4 3 3 3 6 1 --- : 2 --7 5 2 2 7 5 --- : 7 --3 9 5 4 8 2 --- : 3 --9 9 5 3 9 1 ------ : 6 --12 8 3 1 10 7 --- : 11 --4 9 2 1 11 3 ------ : 4 --11 3 5 7 12 9 --- : 2 -----6 15 15 3 13 1 ------ : 1 --16 8 3 1 14 1 ------ : -----17 51 2 1 15 3 --- : 4 --7 8 1 1 16 12 --- : 1 -----3 13 John Wiley & Sons Australia, Ltd 2001