Ratio 11/12 My bike’s fuel has a ratio of oil to gas 1 : 25

The comparison of two or more numbers Can be written three ways 2/3 2:3 2 to 3 ratios notation

Count the number of red and green hearts Red : Green 4 : 8 4 RED and 8 GREEN Writing Ratios

Red : Green 4 : 8 You know how to simplify fractions, simplifying with a colon works the same way Divide ÷ by 2 2 : 4 1 : 2 Simplifying ratios

The ratio of red to green is Red : Green 1 : 2 This tells you that there are 2 green hearts for every red heart

Copy and complete this chart RatioSimplest terms 12 / : / to 40 You try

Copy and complete this chart RatioSimplest terms 12 : 16 3 : 4 24 / 32 3 / 4 27 to 36 3 to 4 28 / 40 7 / 10

Workbook P 79 # all You try

Unit Rate and Proportional Reasoning11/13 rate A ratio that compares two numbers with different units Miles per hour mph The rate for one unit Unit rate mph is usually expressed as a unit rate

1. It takes 2 hours to get to a friends house in Atlanta, 124 miles away. What would the mph be? Examples Unit Rate 2. You can solve 76 math problems in 3 hours and 42 minutes. How many problems do you solve per minute?

1. 20 pieces of candy cost $2.40, what does one piece of candy cost? Examples Unit price 2. Kaleigh’s dog food is $1.15 per pound. How much does a 40lb bag of food cost?

Workbook P 81 # all You try

Turn in homework Get your workbook Sharpen pencil Sit down Get ready for notes

Turn in homework Sharpen Pencils Grab a workbook Sit down and get ready for notes

Proportions11/16 Proportions = 1:3 = 3:9 - If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar figures.

If the ratios form a proportion, then the simplified forms of the ratios will equal. Simplest Form Determine if the ratios form a proportion by writing each ratio in simplest form. 4/8, 10/20 15/20, 10/12 24/30, 9/15 Examples

If the ratios form a proportion, then the numerator and denominator will share a multiplier. Common Multiplier Determine if the ratios form a proportion by finding a common multiplier 8/15, 32/40 60/140, 3/7 10/24, 30/70 Examples

a c b d Cross Multiplying If a/b = c/d then ad = bc ad = = Determine if the ratios form a proportion by cross multiplying 2/3, 4/5 10/5, 6/3 5/6, 50/72 Examples bc If the ratios form a proportion, then the cross products are equal

Workbook Page 85 # all You Try

Solving Proportions 11/18 Proportions = 1:3 = 3:9 - If two ratios are equal, they form a proportion. Proportions can be used in geometry when working with similar figures. Similar - Similar describes things which have the same shape but are not the same size.

a c b d Cross Multiplying If a/b = c/d then ad = bc ad = = 1.2/3 = 4/6 2.10/x = 6/3 3.5/6 = x/72 Examples bc

A proportion can be made relating the height and the width of the smaller figure to the larger figure: The ratio of the smaller figure to the larger figure is 1:2 (said “one to two”). This can also be written as a fraction of ½. Ratio 2 ft 4 ft 8 ft 4 ft 2 ft = 8 ft 4 ft Proportion

Solving Proportion Problems First, designate the unknown side as x. Then, set up an equation using proportions. What does the numerator represent? What does the denominator represent? 2 feet 6 feet 18 feet ? feet 6 ft 2 ft = 18 ft x ft 6x = 2 ∙ 18 6x = 36 x = 6 Then solve for x by cross multiplying: height width

Workbook P 87 start at # 6 You try

Binder Check 1.What was the topic for the notes given on 11/18? 2.What was the answer to number 1 from the homework assigned 11/16, p , 1-23 odd. 3.Write the calculator policy from the Classroom Guidelines and Procedures handout.

Similar Shapes11/20 Similar shapes are very important because if we know the dimensions of one shape and one of the dimensions of another shape similar to it, we can figure out the unknown dimensions.

Figures are similar if the ratio between each side make a proportion Write each example off the white board Similar figures

You Try 1.Write a proportion relating the similar shapes. 2.Find the missing width. 3 feet 8 feet 12 feet x feet These two stick figures are similar.

You Try These two trapezoids are similar. 1.Write a proportion relating the similar shapes. 2.Find the missing sides. 15 x a

Leonardo da Vinci

The average adult human figure is about 7 to 7.5 heads tall. The arms' wingspan (measured from the tips of the middle fingers) is about equal to the body height. The length of the foot is about equal to the length of the forearm. Write a ratio that represents each statement. 7 head heights 1 body height 1 wingspan 1 body height 1 foot length 1 forearm length

Head Height Estimated total height Wingspan Estimated total height Actual height Foot length Estimated forearm length Actual forearm length da Vinci Proportions Activity Measure in inches

The eyes are at the mid-height of the head. The head also can be divided into thirds top of the head to the bottom of the forehead bottom of the forehead to bottom of the nose bottom of nose to the bottom of the chin. Width of head is between four and five eyes wide. Height of the face is about equal to length of hand. Eyes are apart by a distance of one eye width. Bottom of the nose to the corner of the eye is equal to the height of the ear. Width of base of nose is equal to width of the eye. The width of the mouth is equal to the distance between pupils, or the width of two eyes. Draw like da Vinci Use these proportions to draw a head.

Maps and Scale Drawings 11/30 Scale Drawing An enlarged or reduced drawing of an object that is similar to the actual object A small picture of Kaleigh is similar to Kaleigh

Scale The ratio that compares a length in a drawing to the corresponding length of the actual object. The scale of this picture is 2 in : 1 foot. What is Kaleigh’s real height? 6 in Drawing Real ScaleValues =

You Try 1.The scale of a drawing is 1in : 6 ft. Find the actual length for a drawing length of 4.5 inches. The scale of a map is 1 inch : 10 miles. Find the actual distance given the distance on the map inches 3. 1 foot inches

Scale Kaleigh’s actual length is 3.5 feet. Her length in the drawing is 7 inches. Find the scale. 7 in Drawing Real Values = Scale Plug in the values and simplify to find the scale

You Try 5. The actual length between the wheels of a mountain bike is 260cm. The length between the wheels in the scale drawing is 4cm. Find the scale of the drawing.

You Try Workbook p 91 # all p 92 # all