Tuesday 29 September 2015

Unit 1 sec 3.2

Although decimal numbers are used in everyday situation, there are occasions when fractions are appropriate. Fractions are also important in mathematics, particularly in Algebra.  
        A fraction is a number that describes the relationship between part of something and the whole. The top number in a fraction is called the numerator and the bottom number is called the denominator. 
        When u divide the top and bottom number of a fraction by the whole number larger than one, you get an equivalent fraction with a smaller numerator and denominator. This is called cancelling the fraction. When a fraction has been cancelled to give the smallest possible numerator and denominator, it is said to be in its simplest form or lowest terms. 
     However, the fractions and percentages in the headlines can sometimes be misled. How many people were included in the survey? Are the people in the survey representative of the overall population? Mixed numbers and improper fraction A proper fraction is a fraction in which the numerator is smaller than the denominator such as 2/3 A fraction in which the numerator is larger than the denominator. 
     An improper fraction is also known as a top-heavy fraction

Example 9 Converting between mixed numbers and top- heavy fractions.

Write 25/8 as a top- heavy fraction.
        Write 13/4 as a mixed number Solution There are eight eighths in one whole, so 25/8 can be written as two lots of eighths plus five eigthths. 25/8 = (2×8+5)/8 =21/8 b) Divide 4 into 13. The answer is 3, remainder 1 13/4 = 31/4
          Activity 18 Converting between mixed numbers and top- heavy fractions. Write 52/3 as a top heavy fraction. Answer 52/3 = (5×2+3)/3 = 17/3 Write 18/5 as a mixed number.    

Answer 18/3 = 33/5

Fractions of quantities Sometimes you need to calculate fractions in quantities. Example 10 Scaling a recipe A recipe for eight people specifies 750g of strawberries. What quantity of strawberries would be needed for 3 people? 
    Solution First method Work out the quantity of strawberries needed for one person use this to find the quantity of strawberries needed for 3 people. The quantity of strawberries needed for one person 750÷8= 93.75g So the quantity of strawberries needed for 3 people is 3×93.75g=281.25g=280g (to 2 s.f). 
       The second method Find the fraction of the original quantity that is needed, and use this to calculate the quantity of strawberries needed Three-eighths of the original quantity is required. So the quantity of strawberries needed for three people is 3/8× 750g= 3÷8×750= 281.25g= 280g (to 2 s.f) 
     There are different ways to solve a problem, so you may sometimes find that you have used a method different from the one in the unit or suggested by someone else. However, it is a good idea to look at any model solution provided, as it may suggest an alternative and possibly quicker method that you could use to solve a similar problem in the future.

ACTITITY 19 Work out the following fraction of quantity.  (a1) 4/5 of 60ml 
(A2)5/8 of 20kg
            (B)A recipe for potato curry for 6 people uses 900g of potatoes. If you are making a the curry for 20 people, what quantity of potatoes do you need?
    Answer
(A1) 4÷5×60=48ml 
(A2) 5÷8×20=12.5kg 
(b) 20÷6×900=380g=3kg
    you can scale any cater for a group of any size, but in practice you may wish to adjust your answers a little. In a large group it is most likely that few people will eat only small portions or none at all, so caters often use guidelines such as the following. Allow 150g of potatoes per person for up to 10 people; for more than 10 people, allow 125g per person. When you are using maths to make practical decision, it is important to think about whether your calculation are appropriate for the situation.

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