Warm UpWrite each fraction in simplest form.

1. 2.

3. 4.

26__ 1

3__ 4

16__ 1

4__

25 70___ 5

14__ 6

52__ 3

26__

10-27-14 Ratios and rates

DO NOW (not later):

Compare the number of boys to girls in the class.

The number of boys =

The number of girls =

If we compare boys to girls we get

___ boys to _____ girls.

Unit 5 Ratio and Proportionality

Vocabulary:

Ratio-

What do we call a comparison between two or more quantities?

RATIOWe just found the RATIO of boys to girls.

Is the ratio of girls to boys the same ?

No, when writing a ratio, ORDER matters.

How many basketballs to footballs are there?

For every 4 basketballs there are 6 footballs.

The ratio is 4 to 6.

P: What are some other ways we can write the ratio of basketball to footballs?

4 to 6

4 : 6

4 6

First quantity to Second quantity

First quantity : Second quantity

First quantity divided by the second quantity (as a fraction).

Every ratio can be written in 3 ways:

Careful!!

Order matters in a ratio.

4 to 6

Is NOT the same as

6 to 4

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 to 10

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

4 = 4 / 4 = 1 = 1 to 2

8 8 / 4 2

GCF = 4

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)

You can compare the different groups by using ratios. A ratio is a comparison of two quantities using division.

For a time, the Boston Symphony Orchestra was made up of 95 musicians.

Violins 29 Violas 12

Cellos 10 Basses 9

Flutes 5 Trumpets 3

Double reeds 8 Percussion 5

Clarinets 4 Harp 1

Horns 6 Trombones 3

For example, you can use a ratio to compare the number of violins (29) with the number of violas (12). This ratio can be written in three ways.

Notice that the ratio of violins to violas, is

different from the ratio of violas to violins, . The order of the terms is important.

29 12___

29 12___

12 29___

29 to 12 29:12Terms

Ratios can be written to compare a part to a part, a part to the whole, or the whole to a part.

Turn to page 276 Guided Practice

Write as a fraction in simplest form and as a decimal. Round to nearest hundredth. Explain it’s meaning.

1. Candles to Matches

Turn to page 276 Guided Practice

Write as a fraction in simplest form and as a decimal. Round to nearest hundredth. Explain it’s meaning.

1. Candles to Matches

; .57; For every 4 candles, there are 7

mmatches

Turn to page 276 Guided Practice

Write as a fraction in simplest form and as a decimal. Round to nearest hundredth. Explain it’s meaning.

2. Lemons: Limes

Turn to page 276 Guided Practice

Write as a fraction in simplest form and as a decimal. Round to nearest hundredth. Explain it’s meaning.

2. Lemons: Limes

; .33; For every 1 lemon, there are 3 limes.

Last week, William ate 15 grapes, 2 bananas, and 3 apples. Determine the ratio of grapes to the total number of fruit in simplest form. Use a multiplicative comparison to explain the meaning.

***MAKE A TABLE

______, ____ to ____, __:__ ; There are ____ or ____ as many _____ as total _____

Fruit Quantity

Grapes

Bananas

ApplesTOTAL FRUIT=

1. Create the correct ratio.

2. Divide the fraction to make a multiplicative comparison.

In your groups work on the Ratios Matching Cards.

***Remember to simplify and pay attention the ratio it asks.

Homework:-Test Corrections and signature!-Pg. 277 1-5-Converting Table Wednesday!