Maths Workshop for Parents 2. Fractions and Algebra

Transcription

1 Maths Workshop for Parents 2 Fractions and Algebra

2 What is a fraction? A fraction is a part of a whole. There are two numbers to every fraction: 2 7 Numerator Denominator

3 2 7 This is a proper (or common) fraction

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5 Improper and mixed fractions An improper fraction has a numerator that is bigger than its denominator, for example 10/7 9/4 is also an improper fraction. It means nine quarters. If you think of this as cakes, nine quarters are more than two whole cakes. It is 2 1/4 cakes.

6 Changing a mixed number to an improper fraction To change a mixed number to an improper fraction, multiply the whole number by the denominator and add the numerator. This gives you the new numerator; the denominator stays the same e.g. 2 ¼ 2 x 4 = = 9 9/4

7 Changing an improper fraction to a mixed number To change an improper fraction into a mixed number, divide the numerator by the denominator. e.g. 9/2 = 9 2 = 4 ½ 2 goes into 9 four times, with a half left over.

8 ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ 2 1/4 is a mixed fraction because it has a whole number and a fraction together.

9 Fractions of quantities To find a fraction of a quantity: Divide the quantity by the denominator Multiply the answer you get by the numerator To find 2/ 5 of 15, for example: Divide 15 by 5 (the denominator): 15 5 = 3 Multiply the answer 3 by 2 (the numerator): 3 x 2 = 6 So 2/ 5 of 15 is 6

10 Equivalent Fractions Equivalent fractions are fractions that look different but show exactly the same amount. 1/3, 2/6, 4/12

11 You can make equivalent fractions by multiplying or dividing the numerator and denominator by the same number. You can simplify fractions by dividing the numerator and denominator by the same number. This is called cancelling. Sometimes fractions will cancel more than once.

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14 Ordering and comparing fractions To compare fractions, you must first change them so they have the same denominator. Compare 2/3 and 3/5 and find out which fraction is bigger. First look at the denominators (the bottom numbers). Find a new number that both denominators go into: Try 9 - you can divide 9 by 3 but you can't divide 9 by 5. Try 10 - you can divide 10 by 5 but not by 3, so that isn't right either. Try 15 - you can divide 15 by 5 (which equals 3) and you can also divide 15 by 3 (which equals 5), so 15 is the new denominator.

15 Ordering and comparing fractions Now you have found a new denominator that is divisible by both numbers, you need to change the numerators (the top numbers). To change the numerators, simply multiply them by the number of times the denominator goes into 15. So for 2/3-3 goes into 15 five times, so you must multiply the numerator (2) by 5 which equals 10. And for 3/5-5 goes into 15 three times, so you must multiply the numerator (3) by 3 which equals 9.

16 Common Denominators You can compare fractions by writing them over their lowest common denominator. This is the lowest number that is a multiple of both denominators.

17 Converting fractions to decimals You can use a calculator to turn a fraction into a decimal. Just divide the numerator by the denominator. ¾ = 3 4 = 0.75

18 Adding or Subtracting Fractions Change any whole or mixed numbers into improper fractions. If the fractions have different denominators find a common denominator. Add or subtract the numerators and cancel answer down to its simplest form. 1 2/3 + ½ = 5/3 + ½ = 10/6 + 3/6 = 13/6 = 2 1/6

19 Multiplying Fractions Change any whole or mixed numbers into improper fractions. Multiply the numerators then multiply the denominators. Cancel down the answer to its simplest form. 2 2/3 x ½ = 8/3 x ½ = 8/6 = 1 2/6 = 1 1/3

20 Dividing Fractions Change any whole or mixed numbers into improper fractions. Turn the second fraction upside down and multiply the fractions together. Cancel answer to its simplest form. 2 2/3 ½ = 8/3 x 2/1 = 16/3 = 5 1/3

21 Fractions, Decimals and Percentages ½ = 0.5 = 50% ¼ = 0.25 = 25% ¾ = 0.75 = 75% 1/1 = 1 = 100%

22 Algebra Algebra is about seeing mathematical patterns, understanding the patterns and describing them using words and symbols. You use algebra every day without even noticing: e.g. A box of 4 doughnuts costs 6 4d = 6 2d = 3 d = 1.50

23 Think of a number Double it: Double it again: Add the number you first thought of: Divide by 5, and you get the number you first thought of:

24 Word formulae and equations Alice sells candles for 50p each. So if she sells 2 candles, she earns 1. 3 candles will cost 1.50 and so on. She can sell 80 candles for 40 and 120 candles for 60. As a word formula, the total cost is the cost for one item multiplied by how many items are bought or sold

25 Equations Much the same as word formulae, except symbols like X and = are used, and instead of words, letters are used. The rule for total cost becomes: T = n x P Which is just a short way of writing: Total cost = number of items X price per item

26 What s my number? I m thinking of a number: n I subtract 1: n 1 I multiply it by 3: 3 (n 1) = 15 The answer is 15. What s my number? You can work backwards and undo the operations to find out:

27 Patterns in sequences Algebra can help you to find terms in number sequences. e.g. here are the first few terms in the sequence of even numbers. The rule for finding the nth term is 2n: n ? 2n

28 Here are the first few terms in the sequence of odd numbers. The rule for finding the nth term is 2n n ? 2n 1

29 Tips for writing algebra A number, letter or combination of numbers and letters multiplied together is called a term. The terms are separated by + and signs, and each + or is joined to the term that follows it. Any term that does not have a + or sign is always positive: e.g. 3a + 2ab 5

30 Tips for writing algebra A collection of terms is called an expression. So 3a + 2ab 5 is an expression. Write single letters on their own: a not 1a Avoid using multiplication signs: ab = a x b Write divisions as fractions: a / b When you multiply numbers and letters, always write the number first: 2ab = a x 2 x b

31 Useful websites: