Because a ratio is a fraction b can not be zero Ratios are expressed in simplest form 4 How to Use Ratios
The ratio of boys and girls in the class is 12 to11.
This means for every 12 boys you can find 11 girls to match.
There could be just 12 boys 11 girls.
There could be 24 boys 22 girls.
There could be 120 boys 110 girlsa huge class
How many dogs and cats do I have We dont know all we know is if theyd start a fight each dog has to fight 2 cats.
The ratio of length and width of this rectangle
is 4 to 1.
4cm 1cm What is the ratio if the rectangle is 8cm long and 2cm wide Still 4 to 1 because for every 4cm you can find 1cm to match
The ratio of cats and dogs at my home is 2 to 1
5 How to simplify ratios
The ratios we saw on lastwere all simplified. How was it done
The ratio of boys and girls in the class is The ratio of the rectangle is The ratio of cats and dogs in my house is Ratios can be expressed in fraction form This allows us to do math on them. 6 How to simplify ratios
Now I tell you I have 12 cats and 6 dogs. Can you simplify the ratio of cats and dogs to 2 to 1
Divide both numerator and denominator by their Greatest Common Factor 6. 7 How to simplify ratios
A persons arm is 80cm he is 2m tall.
Find the ratio of the length of his arm to his total height
To compare them we need to convert both numbers into the same unit either cm or m.
Lets try cm first!
Once we have the same units we can simplify them. 8 How to simplify ratios
Lets try m now!
Once we have the same units they simplify to 1. To make both numbers integers we multiplied both numerator and denominator by 10 9 How to simplify ratios
If the numerator and denominator do not have the same units it may be easier to convert to the smaller unit so we dont have to work with decimals
3cm/12m 3cm/1200cm 1/400 2kg/15g 2000g/15g 400/3 5ft/70in (512)in / 70 in 60in/70in 6/7 Of course if they are already in the same units we dont have to worry about converting. Good deal 2g/8g 1/4 10 More examples
11 Now on to proportions! What is a proportion A proportion is an equation that equates two ratios The ratio of dogs and cats was 3/2 The ratio of dogs and cats now is 6/43/2 So we have a proportion 12 Properties of a proportion Cross Product Property 3x4 12 2x612 3x4 2x6 13 Properties of a proportion
Cross Product Property
ad bc means extremes 14 Properties of a proportion Lets make sense of the Cross Product Property For any numbers a b c d 15 Properties of a proportion
If Can you see it If yes can you think of why it works Then 16 How about an example Solve for x 7(6) 2x 42 2x 21 x Cross Product Property 17 How about another example Solve for x 7x 2(12) 7x 24 x Cross Product Property Can you solve it using Reciprocal Property If yes would it be easier 18 Can you solve this one Solve for x 7x (x-1)3 7x 3x 3 4x -3 x Cross Product Property Again Reciprocal Property 19 Now you know enough about properties lets solve the Mysterious problems! If your car gets 30 miles/gallon how many gallons of gas do you need to commute to school everyday 5 miles to home 5 miles to school Let x be the number gallons we need for a day Can you solve it from here x Gal 20 5 miles to home 5 miles to school So you use up 1/3 gallon a day. How many gallons would you use for a week Let t be the number of gallons we need for a week What property is this Gal 21 So you use up 5/3 gallons a week (which is about 1.67 gallons). Consider if the price of gas is 3.69 dollars/gal how much would it cost for a week Let s be the sum of cost for a week 3.69(1.67) 1s s 6.16 dollars 5 miles to home 5 miles to school 22 So what do you think 5 miles 10 miles You pay about 6 bucks a week just to get to school! What about weekends If you travel twice as much on weekends say drive 10 miles to the Mall and 10 miles back how many gallons do you need now How much would it cost totally How much would it cost for a month Think proportionally! . . . Its all about proportions! 23 (No Transcript)
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