DO NOW (not later): Compare the number of boys to girls in the class. Free powerpoints at http://www.worldofteaching.com

The number of boys = The number of girls = If we compare boys to girls we get boys to girls.

What do we call a comparison between two or more quantities? We just found the RATIO of boys to girls. RATIO Is the ratio of girls to boys the same ? No, when writing a ratio, ORDER matters.

AIM: What is a ratio?

It’s Friday night and your friends are having a party…… The ratio of girls to guys is 2 to 12. Would you want to attend the party?

How many basketballs to footballs are there? For every 4 basketballs there are 6 footballs. The ratio is 4 to 6.

What are some other ways we can write the ratio of basketball to footballs? Every ratio can be written in 3 ways: 4 to 6 4 : 6 4 6 First quantity to Second quantity Careful!! Order matters in a ratio. 4 to 6 Is NOT the same as 6 to 4 First quantity : Second quantity First quantity divided by the second quantity (as a fraction).

Write the ratio of sandwiches to coke bottles 3 different ways. 6:8 , 6 to 8, and 6 8 Since a fraction can be simplified, We can simplify the ratio 6/8 to 3/4. The ratio of sandwiches to coke bottles can also be expressed as 3 : 4 or 3 to 4. In other words, ratios can be simplified to form equivalent ratios.

Equivalent Ratios Simplify the following ratios: 4 to 8 10 to 8 8 8 / 4 2 GCF = 4 Step 1 – Write the ratio as a fraction Step 2 – Simplify the fraction (Find the greatest common factor (GCF) of both numbers and divide the numerator and denominator by the GCF). Step 3 – Write the equivalent ratio in the same form as the question

The ratio 2 : 3 can be expressed as Equivalent Ratios can be formed by multiplying the ratio by any number. For example, the ratio 2 : 3 can also be written as 4 : 6 (multiply original ratio by by 2) 6 : 9 (multiply original ratio by by 3) 8 : 12 (multiply original ratio by by 4) The ratio 2 : 3 can be expressed as 2x to 3x (multiply the original ratio by any number x)

Practice problem # 1 (1) You have 100 different shirts. The ratio of blue to black shirts is 20 . 30 a) Write the ratio of blue to black shirts 3 different ways. b) Write the ratio in simplest form. c) Explain what this ratio tells us. d) How many black shirts do you have?

Solution - # 1  You have 100 different shirts. The ratio of blue to black shirts is 20 / 30 a) Write the ratio of blue to black shirts 3 different ways. 20 to 30 , 20 : 30, 20 30 b) Write the ratio in simplest form. 2 3

Practice Word Problems You go to a party where the ratio of boys to girls is 28 to 56. Express the ratio of boys to girls in simplest form. Explain what this ratio tells us. 28 / 56 = 1 / 2 The ratio of boys to girls is 1 to 2 (2) For every 1 boy there are 2 girls at the party.

5-1 Objective: Solving proportions

A ratio is the comparison of two numbers written as a fraction. An equation in which two ratios are equal is called a proportion. A proportion can be written using colon notation like this a:b::c:d Or as the more recognizable (and useable) equivalence of two fractions.

Proportions To set up a proportion think part/whole part ______ part = whole whole If you can travel 120 miles on 6 gallons of gas, how far can you drive on 8 gallons of gas? (6)gas (8)gas ______ ______ 6x=960 x=160 = 120miles (x) miles

RATIOS & PROPORTIONS Are the following proportions? FALSE – Not a proportion FALSE – Not a proportion TRUE – this is a proportion TRUE – this is a proportion

RATIOS & PROPORTIONS Find the missing numbers to make the following proportions. 10 10 9 9