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GCSE Maths Starter 13 1. Write down the reciprocal of 3 2. Write 42 as a product of its prime factors 3. Find the perimeter and the shaded area of the shape below. 4. Expand: 5a(3a+2) 5. 123 × 26 Lesson 13 Ratio Mathswatch clip (61/94). • To simplify a ratio (Grade D ) • To solve ratio problems using the unitary method (Grade D) I like simple cakes madeisonly But now my cake 4 : 2out !!!of flour and sugar . I mix it using a ratio of 2 : 1 Both ratios are equivalent. But the cake tastes Two goes into both 4 But the cake will notin be They can be simplified Repeat the process exactly the same !! the and 2 big enough ! same way as fractions are simplified. Flour 2 2 4 : :: 1 Sugar 21 I’m going to try a cake using flour and But now my cake has used a ratio of 4 : 6 !!! sugar in a ratio of 2 : 3 But will be But 2 :the 3thecake iscake a simplified willnot taste Repeat the process. Two goes into 44 and big enough !: 6 !6 exactly version the of same Flour 2 24 : 3 63 Sugar Lesson 13 Ratio Mathswatch clip (61/94). 1) 4) 7) 10) 1:2 4:8 2:3 6:9 1:4 2:8 1:3 7 : 21 Write the following ratios in their simplest form. 2:3 1:3 2) 8 : 12 3) 4 : 12 1:2 4:5 5) 10 : 20 6) 8 : 10 7:3 3:2 8) 14 : 6 9) 30 : 20 4 : 11 3:2 11) 8 : 22 12) 9:6 Lesson 13 Ratio Mathswatch clip (61/94). 1. Helen has 16 DVDs and 24 videos. Write down the ratio of the number of DVDs to the number of videos. Give your ratio in its simplest form. 2. There are 40 students on a school trip. 12 of the students are girls. The rest are boys. Find the ratio of the number of girls to the number of boys. Give your ratio in its simplest form. 3. There are 50 sweets in a packet. 24 of the sweets are mints. The rest of the sweets are toffees. Write down the ratio of the number of mints to the number of toffees. Give your ratio in its simplest form. Lesson 13 Ratio Mathswatch clip (61/94). 1. Helen has 16 DVDs and 24 videos. Write down the ratio of the number of DVDs to the number of videos. Give your ratio in its simplest form. 16:24 = 2:3 2. There are 40 students on a school trip. 12 of the students are girls. The rest are boys. Find the ratio of the number of girls to the number of boys. Give your ratio in its simplest form. 12:28 = 3:7 3. There are 50 sweets in a packet. 24 of the sweets are mints. The rest of the sweets are toffees. Write down the ratio of the number of mints to the number of toffees. Give your ratio in its simplest form. 24:26 = 12:13 Dividing in a given ratio Divide £40 in the ratio 2 : 3. A ratio is made up of parts. We can write the ratio 2 : 3 as 2 parts : 3 parts The total number of parts is 2 parts + 3 parts = 5 parts We need to divide £40 by the total number of parts. £40 ÷ 5 = £8 8 of 67 © Boardworks Ltd 2005 Dividing in a given ratio Divide £40 in the ratio 2 : 3. Each part is worth £8 so 2 parts = 2 × £8 = £16 and 3 parts = 3 × £8 = £24 £40 divided in the ratio 2 : 3 is £16 : £24 Always check that the parts add up to the original amount. £16 + £24 = £40 9 of 67 © Boardworks Ltd 2005 Dividing in a given ratio A citrus twist cocktail contains orange juice, lemon juice and lime juice in the ratio 6 : 3 : 1. How much of each type of juice is contained in 750 ml of the cocktail? First, find the total number of parts in the ratio. 6 parts + 3 parts + 1 part = 10 parts Next, divide 750 ml by the total number of parts. 750 ml ÷ 10 = 75 ml 10 of 67 © Boardworks Ltd 2005 Dividing in a given ratio A citrus twist cocktail contains orange juice, lemon juice and lime juice in the ratio 6 : 3 : 1. How much of each type of juice is contained in 750 ml of the cocktail? Each part is worth 75 ml so, 6 parts of orange juice = 6 × 75 ml = 450 ml 3 parts of lemon juice = 3 × 75 ml = 225 ml 1 part of lime juice = 75 ml Check that the parts add up to 750 ml. 450 ml + 225 ml + 75 ml = 750 ml 11 of 67 © Boardworks Ltd 2005 Lesson 13 Ratio Mathswatch clip (61/94). Share in the given ratios 1. Share £400 between Courtney and Adele in the ratio 2:3 2. Share £280 between April and Jack in the ratio 2:5 3. Share £500 between Molly and Toni in the ratio 3:7 Extension work 1. Share £240 between Brad and Emma and Louis in the ratio 3:5:12 2. Share £600 between Kera, Chloe and Raven in the ratio 1:5:6 3. Share £5 between Jake, Adele and Lucretia in the ratio 7:10:8 Lesson 13 Ratio Mathswatch clip (61/94). Answers 1. Courtney = £160 and Adele = £240 2. April = £80 and Jack = £200 3. Molly =£150 and Toni = £350 Extension work 1. Brad = £36 Emma = £60 2. Kera = £50 Chloe = £250 3. Jake = £1.40 Adele = £2.00 £1.60 Louis = £144 Raven = £300 Lucretia = Lesson 13 Ratio Mathswatch clip (61/94). Exam questions