RATIO Ratio says how much of one thing

RATIO Ratio says how much of one thing there is compared to another

RATIO • Ratio tells us how many equal parts of a whole one thing has compared to another The ratio 3: 2 can be expressed visually as: Equal sizes You can see there are 5 parts altogether

RATIO • You can find equivalent ratio: 3: 2 = 6: 4 = 9: 6

Equivalent Ratio • On whiteboards, show me any equivalent ratio to: 1: 4 42: 35 5: 3 3: 2 12: 4 3: 5 7: 1. 5

Sharing ratio into a given quantity • Share £ 20 into the ratio 3: 2 1 part is £ 4 So ratio is £ 12: £ 8 £ 20 4 4 4

Your turn • • • Share £ 21 into the ratio 3: 4 £ 9: £ 12 Share £ 121 into the ratio 4: 7 £ 44: £ 77 Share £ 36 into the ratio 3. 5: 2. 5 £ 21: £ 15 Share £ 12. 50 into the ratio 2: 3 £ 5: £ 7. 50 Share £ 44. 25 into the ratio 1: 2 £ 14. 75: £ 29. 50

• Scott and Megan share some money in the ratio 3: 2. Scott gets £ 12. How much does Megan get? £ 12 1 part is £ 4 So Megan gets 2 x £ 4 =£ 8

• The ratio of the number of Cara’s CDs to the number of Tahlia’s CDs is 3: 5. If Tahlia has 45 CDs, how many does Cara have? 45 1 part is 9 CDs So Cara has 3 x 9= 27 CDs

Your turn • Aidan and Matt have football stickers in the ratio 2: 3. Altogether they have 25 stickers. If Aidan gives half his stickers to Matt, how many will Matt have? 25 5 Aidan 5 5 Matt 5 5

Your turn • Aidan and Matt have football stickers in the ratio 2: 3. Altogether they have 25 stickers. If Aidan gives half his stickers to Matt, how many will Matt have? 5 5 Aidan Matt now has 20 CDs 5 5 Matt 5 5

• The ratio of Brook’s pencils to Beth’s pencils was 7: 3. When Brook gave 20 pencils to Beth, they each had the same amount. How many pencils did they have altogether?

• The ratio of Brook’s pencils to Beth’s pencils was 7: 3. When Brook gave 20 pencils to Beth, they each had the same amount. How many pencils did they have altogether? Brook Beth 20 10 blocks altogether. Still have 10 blocks – but same amount each So one block = 10 pencils 10 blocks = 100 pencils

Solving more complicated Ratio problems…. • The ratio of books owned by Scott and Matthew is 3: 5. If Scott gives Matthew 2 of his books, then the ratio will be 1: 3 • How many books do they each have initially?

• The ratio of books owned by Scott and Matthew is 3: 5. If Scott gives Matthew 2 of his books, then the ratio will be 1: 3 • How many books do they each have initially? Scott Matthew We can see that if we move two of the blocks from Scott, to Matthew, the new ratio isn’t going to be 1: 3, but 1: 7………

• The ratio of books owned by Scott and Matthew is 3: 5. If Scott gives Matthew 2 of his books, then the ratio will be 1: 3 • How many books do they each have initially? Let’s look for some equivalent ratios – starting by doubling Scott Matthew …. . however, ratio shows the comparison of two quantities, so could be in simplified version…… 3: 5 = 6: 10

• The ratio of books owned by Scott and Matthew is 3: 5. If Scott gives Matthew 2 of his books, then the ratio will be 1: 3 • How many books do they each have initially? Scott Matthew We can now see that if we take 2 books away from Scott and give them to Matthew, our new ratio would be…… 4: 12 = 1: 3

• The ratio of books owned by Scott and Matthew is 3: 5. If Scott gives Matthew 2 of his books, then the ratio will be 1: 3 • How many books do they each have initially? Scott Matthew So the initial amount of books they each had was 6 for Scott and 10 for Matthew

• Jess and Faye own a number of marbles that are in the ratio 5: 6. Jess gains 2 more marbles and the ratio is now 7: 8. How many marbles did they own originally? 2 11 parts + 2 = 13 divisions cannot be split into 15 parts so we must look for equivalent ratios of 5: 6

• Jess and Faye own a number of marbles that are in the ratio 5: 6. Jess gains 2 more marbles and the ratio is now 7: 8. How many marbles did they own originally? 2 5: 6 = 10: 12 22 parts + 2 = 24 divisions which cannot be split into 15 parts

• Jess and Faye own a number of marbles that are in the ratio 5: 6. Jess gains 2 more marbles and the ratio is now 7: 8. How many marbles did they own originally? 2 5: 6 = 40: 48 88 parts + 2 = 90 divisions which can be split into 15 parts

• Jess and Faye own a number of marbles that are in the ratio 5: 6. Jess gains 2 more marbles and the ratio is now 7: 8. How many marbles did they own originally? 2 So, originally, Jess had 40 marbles and Faye had 48

Could we have done this without using bars?

• Jess and Faye own a number of marbles that are in the ratio 5: 6. Jess gains 2 more marbles and the ratio is now 7: 8. How many marbles did they own originally? Hint 1: equivalent ratios. . . Hint 2: you’ll need an equivalent ratio of 5: 6 that if you add ‘ 2’ to the ‘ 5’ equivalent, will generate a ratio that can be SIMPLIFIED to a ratio of 7: 8…. Hint 3: your second ratio will have to be a multiple of 8 so find the LCM of both 6 and 8 as these are the two parts that won’t change …

• Jess and Faye own a number of marbles that are in the ratio 5: 6. Jess gains 2 more marbles and the ratio is now 7: 8. How many marbles did they own originally? Add 2 to Jess 5: 6 = 10: 12 7: 6 12: 12 We could continue looking for equivalent ratio that will generate the correct simplification in this way, or we could try to reduce our workload by thinking about LCMs…

• Jess and Faye own a number of marbles that are in the ratio 5: 6. Jess gains 2 more marbles and the ratio is now 7: 8. How many marbles did they own originally? Add 2 to Jess SIMPLIFY 5: 6 = 40: 48 42: 48 7: 8 The LCM of 6 and 8 is 48 Faye’s marbles are going to have to simplify to 8 so we actually need to find a multiple of 6 that is also a multiple of 8……. .

• The ratio of cockles to winkles in a bag of seashells is 1: 2 • When 6 winkles are accidentally spilt from the bag, the ratio is 3: 5 • How many of each shell were there originally?

The ratio of Ann’s age to Bob’s age is 3: 4. In 7 years’ time, this ratio will be 4: 5 i. what are their ages now? ii. after how many years from now will the ratio be 5: 6?