What Is A 32 Out Of 40 – A) 12% b) 18% of $ c) 5% of 320 m d) 21.5% of 2500 e) 4.5% of 20 kg f) 7.5% of 360˚ g) 90% of 45 d h) 36% of $5.50
5 Word Problem Fred earned $325 last year working at Pizza Boat. He spent $165. What percentage of his money did he spend? The school has 1,970 students, of which 550 are 9th graders. What percentage of students are in 9th standard. What percentage of students do not study in 9th standard.
What Is A 32 Out Of 40
How to use ratios? How to simplify? Proportion! What is the ratio? Properties of proportions? How to use proportion? Mysterious problems…
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Coefficients can be written in three different ways: a to b Since the ratio a:b is a fraction, b cannot be zero Coefficients are expressed in simple form.
How to use ratios? The ratio of boys to girls in the class is 12 to 11. This means that for every 12 boys you can get 11 girls. There can be only 12 boys, 11 girls. There can be 24 boys, 22 girls. There could be 120 boys, 110 girls… a huge class. How many dogs and cats do I have? We don’t know, all we know is that if they start a fight, each dog will have to fight 2 cats. The ratio of length to width of this rectangle is 4 to 1. 4 cm 1 cm If the length of a rectangle is 8 cm and the width is 2 cm, what is the ratio? Still 4 to 1 because for every 4 cm you can find 1 cm to match the 2 to 1 ratio of cats and dogs in my house
How to simplify 13 coefficients? The ratio we saw on the previous slide has been simplified. How was it done? The ratio of boys and girls in the class is equal. The ratio in the rectangle is the same. My house has an equal ratio of cats to dogs. Ratios can be expressed as fractions… This allows us to do math with them.
Now I tell you that I have 12 cats and 6 dogs. Can you simplify the cat to dog ratio to 2 to 1? == Divide the numerator and denominator by the greatest common divisor of 6.
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A man’s hand is 80 cm, height 2 meters. Find the ratio of his arm length to his total height. To compare them, we need to convert both numbers to the same unit… cm or m. Let’s try cm first! If we have the same units, we can simplify it.
If we have the same units, it simplifies to 1. To make both numbers perfect, we multiply the numerator and denominator by 10.
How to simplify 17 coefficients? If the numerator and denominator have different units, it may be easier to convert to a smaller unit so we don’t have to deal with decimals… 3 cm/12 m = 3 cm/1200 cm = 1/400 2 kg/ 15 g = 2000 g /15 g = 400/3 5 ft/70 in = (5*12) in / 70 in = 60 in/70 in = 6/7 Of course, if they’re already in the same units, we don’t have to worry about the conversion. No need to. Good deal 2g/8g = 1/4
A proportion is an equation that equates two ratios. The ratio of dogs to cats was 3/2. Now the ratio of dog to cat is 6/4=3/2. Thus, we have the ratio:
Solve for x: 7x = 2(12) 7x = 24 x = Cross Product Property. Can you solve this using the reciprocal property? If so, would it be easy?
Can you solve this? Solve for x: 7x = (x-1)3 7x = 3x – 3 4x = -3 x = Cross Product Property Reciprocity Property Again?
Now that you know enough about properties, let’s solve the mystery problems! If your car goes 30 mpg, how many gallons of gas will you need each day to drive to school? 5 miles from home 5 miles to school x = gal
28 5 miles from home to 5 miles to school so you use 1/3 gallon per day. How many gallons do you use per week? Let us look at the number of gallons required per week: What is this property? gal
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So you use 5/3 of a gallon per week (that’s about 1.67 gallons). Think about it, if gas costs $3.69 a gallon, how much will it cost in a week? Let’s sum up the cost per week: 3.69(1.67) = 1s s = $6.16 5 miles from home to 5 miles to school
30 So what do you think? 5 miles 10 miles you pay about 6 bucks a week to go to school! What about the weekend? If you make a double trip on the weekend, say 10 miles to the mall and 10 miles back, how many gallons do you need now? How much will it cost in total? How much will it cost per month? Think proportionally! It’s all about proportion!
32 Classification of Polygons A polygon is a closed figure formed by three or more line segments. A regular polygon has all sides equal and all angles equal. A regular quadrilateral is a square. An irregular quadrilateral can be a rectangle, rhombus, parallelogram, or trapezoid.
42 An interior angle is an angle formed by two sides inside a polygon that meet at a vertex.
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Exterior Angle – An angle formed outside of a geometric figure by extending one of the back sides of the vertex.
Adjoint – adjacent or complementary – adding up to 180 degrees Transversal – a line that crosses two or more lines
A convex polygon is a polygon that does not have a segment connecting two points on the outside of the polygon. A concave polygon is a polygon in which some segment segments connect two points on the polygon outside the polygon.
Hexagon – Polygon with six sides Heptagon – Polygon with seven sides Octagon – Polygon with eight sides Regular Polygon – Polygon with equal sides and interior angles Sum of interior angles = 180(n-2)
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