L8 Comparing Ratios (5.7).notebook February 09, 2016

Lesson 8 5.7 Comparing Ratios

Example 1: Mr King makes his coffee with 2 scoops of coffee to 5 cups of water. Mr. Marsh makes his coffee with 3 scoops of water to 7 cups of water. Who makes the stronger coffee?

There are many ways to approach this question, we will look at a few of them below.

Method 1: Express one of the terms of the ratio as one.In this case we will write an equivalent ration so that the first term (# of scoops of coffee) is one.

We can write the ratio of coffee to water for each teacher...

Mr. King 2 : 5 Mr. Marsh 3 : 7

For Mr. King, divide both terms by 2 to get a ration of coffee to water of 1 :

For Mr. Marsh, divide both terms by 3 to get a ration of coffee to water of 1 :

is less than . This means Mr. Marsh is using less water for the same amount of coffee. Mr. Marsh's coffee is stronger.

Answer Answer

?

?

Answer

?

?

Method 2: We can use equivalent ratios to compare the strength of the coffee.

The first numbers in each ratio are 2 and 3. A common multiple for 2 and 3 is 6. We can rewrite each ratio with 6 as the first term.

Mr. King 2 : 5 = 6 : 15 .... Multiply both terms by 3

Mr. Marsh 3 : 7 = 6 : 14 .... Multiply both terms by 2

For the same amount of coffee, 6 scoops, Mr. Marsh used less water than Mr. King. Mr. Marsh's coffee is stronger.

ORThe second numbers in each ratio are 5 and 7. A common multiple for 5 and 7 is 35. We can rewrite each ratio with 35 as the second term.

Mr. King 2 : 5 = 14 : 35 .... Multiply both terms by 7

Mr. Marsh 3 : 7 = 15 : 35 .... Multiply both terms by 5

For the same amount of water, 35, Mr. Marsh used more coffee than Mr. King. Mr. Marsh's coffee is stronger.

Mr. King 2 : 5 Mr. Marsh 3 : 7

?

?

Answer

Answer

Answer

Answer

Answer

Answer

L8 Comparing Ratios (5.7).notebook February 09, 2016

Example 2: The directions for mixing hardener in fiberglass resin is 10 drops of hardener for 150 ml of resin. Joshua used 15 drops in 210 ml of resin. Is he using more than, less than, or equal to the recommended amount of hardener?

The correct ratio of hardener to resin is 10 : 150. This can be written with the first term of 1 if we divide both terms by 10.

10 : 150 = 1 : 15

Joshua mixed 15 drops with 210 ml of resin, 15 : 210. This can be written with the first of 1 if we divide both terms by 15.

15 : 210 = 1 : 14

For each drop there should be 15 ml of resin, but Joshua put in a drop for every 14 ml of resin. This is more hardener than he should be using.

OR

We could change the second term to 1

10 : 150 =

15 : 210 =

Divide both terms by 150

Divide both terms by 210

0.714 > 0.0667 therefore Joshua used more drops of harder per ml than the directions indicated should be used.

Answer

Answer

?

Answer

Answer

Answer

Answer

Another Way: There are many ways to do these problems. The fiberglass problem can also be done the same way as our first coffee problem. We can use a common multiple of the first term to answer the question.

The correct ration was 10 : 15 and Joshua used 15 : 210. The lowest common multiple for 10 and 15 is 30, so we will rewrite the first term of both ratios as 30.

10 : 150 = 30 : 450 Multiply both terms by 3

15 : 210 = 30 : 420 Multiply both terms by 2

So, following the directions on the can you would use 450 ml of resin for 30 drops. Joshua only used 420 ml of resin. Again, he is using more than the recommended amount of hardener.

?

Answer

Answer

Answer

L8 Comparing Ratios (5.7).notebook February 09, 2016

Option 1 -- 5 : 3 = 20 : 12 multiply both terms by 4

Option 2 -- 7 : 4 = 21 : 12 multiply both terms by 3

Looking at the options, for equal amounts of white paint (12 cans), option 1 used less yellow for 12 cans of white, so it is the palest.

Example 3: The caretakers at school are getting ready to paint the hallways. They have two options for shades of yellow. Option 1 is made by mixing 5 cans of yellow paint with 3 cans of white paint. Option 2 is made by mixing 7 cans of yellow paint with 4 cans of white paint. Which option will give the palest yellow paint.

As with the other questions, there are several ways to approach this problem, we will complete it with 2 methods.

Method 1: Common term ratios

We will write the ratio as yellow to white

Option 1 -- 5 : 3 Option 2 -- 7 : 4

While we can find a common multiple for yellow or white, in this case we will find a common multiple for white and see which has the least yellow (palest)

A common multiple for 3 and 4 is 12.

Answer Answer

?

Answer

Answer

Answer

Method 2: Percent to whole ratio

The first example (strength of coffee) compared scoops of coffee and cups of water. The second example (fiberglass) compared drops of hardener and ml of resin.

This example is different because we are comparing 2 of the same quantities, cans of paint. This means we can do a part to whole ratio.

Our ratios of cans of yellow to white paint were

Option 1 -- 5 : 3 Option 2 -- 7 : 4

These can be written as part to whole ration

yellow : total cans

Option 1 -- 5 : 8 Option 2 -- 7 : 11

These can be changed to a fraction, decimal and percent.

Option 1 ->

Option 2 ->

Option 2 has the lower percentage of yellow paint and will therefor be the palest.

AnswerAnswer

Answer

Answer

Answer

Questions to complete

Pages 284 - 285

4, 5, 6, 7, 10, 11, 12, 13