Parent and student guide book for year 7 mathematics in term 4.

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1 Parent and student guide book for year 7 mathematics in term 4. Dear Parent/Carer, Please use the following booklet so you and your child can work together to help aid their progression in maths over their time here at the Academy. After looking at the guide go to the back of the booklet to find practice questions to try out. Homework is completed on website They can also use the website for help videos. Example of login details for Mangahigh: Username d.hooker Password Hastings School ID Thank you in advance for helping us move your child forward in maths here at the Academy. If you have any issues or feedback please me at de.hooker@hasla.org.uk Yours Sincerely, Dean Hooker Subject Leader of KS3 Mathematics

2 What is included in this booklet? Understanding what a fraction is Equivalent fractions Simplifying fractions Improper fractions and mixed numbers Calculating fractional amounts Multiplying fractions Dividing fractions Converting decimals to equivalent fractions Converting fractions to percentages Converting decimals to percentages Ordering fraction, decimals and percentages

3 Understanding what a fraction is: A fraction is part of whole. For example below is a pizza that has been cut into 5 slices: This is a whole pizza which is the same as 1 or 100%. We can also say as this shows we have 5 slices of pizza out of the 5 pieces that have been cut. This picture now shows us that we do not have a whole pizza as two slices have been taken away. The slices taken away can be written as 2 5 and the slices left can be written as 3 5.

4 Equivalent fractions: Equivalent fractions are fractions that look different but are equal. For instance the picture below shows us that a, and are exactly the same amount. " If you wanted to create equivalent fractions all you need to do is multiply or divide the numerator and denominator by the same number. For example, if I multiply 1 4 by 4 I would get 3 12 Simplifying fractions: Simplifying a fraction means when we take a fraction such as and we divide it by the highest common factor (i.e. what is the biggest number that goes into 4 and 8?) This is the most efficient ways. However, if you get stuck you can always divide both the numerator and denominator by 2 or 3 and do this as many times needed to simplify your fraction. 1 2

5 Improper fractions and mixed numbers: An improper fraction is whereby the numerator (top number) is bigger than the denominator (bottom number). E.g. would like A mixed number is whereby we have a whole number and a fraction together. E.g. 1 ¾. This would be like the picture above. So now all we need to do is learn to convert between the two To convert an improper fraction to a mixed number the following steps must be taken: Step 1 Divide the numerator by the denominator Step 2 Write down the whole number answer Step 3 Then write down the remainder over the denominator. E.g. 7 4 = 1 with 3 remaining. So my answer is 1 ¾ To convert a mixed number into an improper fraction the following steps must be taken: Step 1 Multiply the whole number and denominator together Step 2 Add the numerator to the previous answer Step 3 The write down the answer on top of the denominator E.g. 1 x 4 = 4, I then add 3 to get 7. So my answer is 7 4.

6 Calculating fractional amounts: How do we find a fraction of any given amount? For example how do we find of 20? One method would be to find 1 and then multiply this answer by 3. 5 To find 1 we divide 20 by = 4. 5 We now do 4 x 3 = 12. So, 3 is equal to Here is a picture example: To find 3 of 20 I could shade in 3 squares out of 5 until I get to The second method would be to do 3 x 20 (more detail in the 5 multiplying fractions section). It would look like 3 x 20 = This would then simplify to 12 which is equal to 12. 1

7 Multiplying fractions: In order to multiply fractions you just simply multiply the numerators of the question together and the denominators together. E.g. 3 5 x 7 9 = However, we need to be confident in all aspects. In order to multiply a whole number by a fraction we need to know how to write the whole number as a fraction. For instance how do we multiply by 5? In order to write 5 as a fraction it need to be put over 1. E.g. 3 5 x 5 1 = 15 5 You can then go onto simplify this by converting this back into a mixed number which you were shown earlier in the booklet. How do we multiply mixed numbers? In order to multiply mixed numbers we need to be able to covert these into improper fractions first (you were shown earlier in the booklet). For example 1 3 x 5 21 would be turned into 8 x 5 = We can then convert this back into a mixed number which would then be 4.

8 Dividing fractions: In order to divide fractions we must do the following steps: Step 1 Keep the first fraction as it is Step 2 Change the divide sign for a multiply sign Step 3 Change the second fraction into its reciprocal by turning it upside down. E.g. 3 3 turns into 3 x 4 = This can then be simplified to 4. 5 Below is a real good example to show how certain dividing questions may come up with bigger answers: is asking us how many sixths go into a half. The pizzas below can show this. How many slices fit into a ½ slice?

9 What do we do if we have a whole number in the question? We follow the same steps from the previous question it just depends whether the whole number is the dividend or divisor. E.g. 4 would become x = " This would then give an answer of 24 4 would become x = 1 24 This would give an answer of 1 24 Converting decimals to equivalent fractions: One straight forward way to convert a decimal to a fraction is to do the following: Step 1 Write down the decimal divided by one E.g. if I have 0.18 it would become." Step 2 Multiply the numerator (top number) by a power of a 10 so it becomes a whole number. E.g x 100 = 18. I then do exactly the same to the denominator (bottom number) x = Step 3 Simplify the fraction if you can = 9 50

10 Converting fractions to percentages: Converting a fraction to a percentage without a calculator: Convert into a percentage " Step 1 We need to think if our denominator (bottom number) is a factor (goes into) of 100. If it is we can multiply by the factor pair to make a 100. If it is not we may be able to simplify the fraction to create a factor that is 100. Step 2 20 is a factor of 100. Therefore, I multiply the numerator (top number) and denominator by 5 7 x 5 = Step 3 I then write the numerator as the percentage (as percent means out of 100). So, my answer is 35% Converting a fraction to a percentage with a calculator: In order to do this you need to simply divide the numerator by the denominator and multiply the answer by 100. E.g. would become 5 8 = x 100 = 62.5 So, the answer is 62.5%

11 Converting decimals to percentages: In order to convert a decimal to a percentage all you need to do is multiply by 100. See the examples below: 0.1 x 100 = 10. This becomes 10% 0.67 x 100 = 67. This becomes 67% 0.04 x 100 = 4. This becomes 4% x 100 = This comes 9.12%

12 Ordering fraction, decimals and percentages: In order to place a mixture of fractions, decimals and percentages in ascending/descending order we need to covert all of them to the same units. E.g. all into decimals. Here s an example I need to place the following in ascending order: 0.45 " 74.5% " % I will choose to change all of them into percentages from what I have learnt in the previous sections x 100 = 45. This is equal to 45% " " " multiplied all by 5 equals. This is the same as 35% "" I would need to multiply both the numerator and denominator by 10. This gives me ". This is the same as 80% "" x 100 = This is equal to 45.6%. I can now put them in ascending order: 35%, 43%, 45%, 45.6%, 74.5%, 80% I can now put them back into their original forms to get full mark in an exam question: 7 20, 43%, 0.45, 0.456, 74.5%, 8 10

13 Year 7 Module 4 - Practice Questions Part 1 Understand and use fraction notation in a variety of contexts Q1) What fraction of the shape is shaded?... (1) Q2) Give, as a fraction, the value of the number the arrow is indicating on the number line below. Q3) Which of these shapes show shaded? a) b) c) d) e)... (1)... and... (2)

14 Q4) What number is represented by this diagram, if each full circle represents one whole? Give your answer as an improper fraction and a mixed number. Improper fraction.... Mixed number... (2) Part 2 Compare and order fractions, decimals and mixed numbers Q5) a) Change " to a mixed number b) Change 2 to an improper fraction (1) (1) Q6) Circle two fractions that are equivalent (1) Q7) Which of the following decimal numbers is equivalent to """? (1)

15 Q8) Give the decimal 0.35, as a fraction in its simplest form (2) Q9) Write each number above the corresponding arrow on the number line Part 3 Multiply and divide with fractions (2) Q10) a) Janine is saving to buy a handbag which costs 15. After one week she has saved of the amount she needs. How much is this?.. (1) b) A train runs late on of the journeys it takes. If Jason takes the train 20 times, how many times will he expect it to be late? (2)

16 Q11) Calculate: a)... (1) b)... (1) c) 6... (1) Q12) Find the answers to the following: a) (2)

17 b) (2) Part 4 Mixed Questions Q13) Write as a percentage. "... (1) Q14) Which of the following is the largest? 15% (1)

18 Q15) Karim achieved 29 out of 40 marks on his English test. Laura said that this means he got over of the total marks. Is she correct? Explain why (2) Q16) Which of these is the odd one out? You must give a reason for your answer. 3 5, 60%, (2)