Proportions
Video
Recap the Video
What is a ratio?
What is a proportion?
Cross Multiplication
When solving Proportions we use a technique called cross multiplication.
If we have a proportion:
7 = 1
n 2
We can use this cross pattern to determine which 2 numbers to multiply
Cross Multiplication
7 = 1
n 2
Then we can solve for n
7 x 2 = 1 x n
14 = n
Isolating n here is easy because n x 1 = n
But it isn’t always that easy...
Just. One. More. Step.
21 = 3
n 4
21 x 4 = 3 x n
84 = 3n
3 is being multiplied by n here, so we need to divide both sides by 3.
3 3
28 = n
What is on Sale?
It is common practice for grocery stores to put prices in their fliers in price ($) per pound (lb.) but use price per kilogram (kg) when calculating the actual cost.
They usually put the price per kg in small letters below… But seriously… Who can read that?
I Feel Like Chicken Tonight. Chicken Tonight!
Let's say you shop at a store that price matches meat. They charge $8.95/kg for skinless, bone-in chicken.
At another competing store, you see this advertisement.
I Feel Like Chicken Tonight. Chicken Tonight!
Which deal is better?
We need to convert $4/lb to $ per kg.
$4 = price
1 lb 2.2lb
But wait… that video said our units need to be identical. What’s up?
I Feel Like Chicken Tonight. Chicken Tonight!
Well both pounds and kilograms are measures of weight. This makes it acceptable.
4 = p
1 2.2
4 x 2.2 = 1 x p
8.8 = p
So the price is $8.80/kg which is better than the $8.95/kg at the local store.
The Scale of the Universe
In the video we saw that proportion could be used on maps. There are many other ways we can view scale, such as scale drawings/models:
Scale:
1:2800
What is the height of the CN Tower?
Scale:
1:2800
1 = 7.5
2800 h
1 x h = 7.5 x 2800
h = 21,000 in.
Actual number: 21,748 in.
What is the length of the Car?
1 = 10
18 L
1 x L = 18 x 10
L = 180 in.
Solve the Proportion
Remember
To solve the proportion: