Loading...
This Is What We Have Learned 2Loading...
6th Grade AMP 20-21Chapter 5
By: Esteban Rodríguez, Ximena Olivares, and Pablo Leal
RATIOS, RATES, AND PROPORTIONS
RATIOS
UNIT RATES AND PROPORTIONAL REASONING
A ratio is a comparison of two quantities. You can write a ratio in three ways:
a to b a:b or a/b
Two quantities are proportional if they have a constant ratio or unit rate.
The quantities in the ratio are called terms. The first term is a, and the second term is b.
A ratio can compare a part of a whole, a part to another part of the whole, or the whole to a part.
A rate is a ratio that compares two quantities measured in different units. The rate for one unit of a given quantity is the unit rate. To find a unit rate, divide the first quantity by the second quantity.
Proportions
Solving Proportions
When two ratios form a proportion, their cross products yield the same result. What are cross products? Cross products are only possible in fractions, or ratios in the “fractional” form. So to get the cross products, now multiply the denominator of the first fraction by the numerator of the second and viceversa. So, if the two products are the same, you have two proportional ratios.
What do you do when you want to figure out the missing term in a poprotion? Well you would have to divide. So you multiply the first cross terms, and then you divide it by the remaining one. An easy way to do this is to write it in “fractional” form so you can simplify and not have huge numbers.
In this example we multiplied 1x8 and divided it by 2. In the fractional form we simplified 2 and 8 into 1 and 4. So we ended with 1x4 which equals 4.
In this example we multiplied 1x8 and divided it by 2. In the fractional form we simplified 2 and 8 into 1 and 4. So we ended with 1x4 which equals 4.
These two ratios form a proportion as 1x8 equals 8 and 2x4 also equals 8.
Using similar figures
Maps and scale drawings
This topic is about when you have the same figure/shape but in a different scale ( size ).
This topic is about how maps and scale drawings are a different scale/size to the actual place/things they are drawing or the place that is in the map.
Examples:
Examples:
As you may see in the picture the 2 triangles are the same shape but they are not the same size/ scale
How you see from these pictures the drawing is scaled down to fit the paper because if he/she had drawn it real size it will be really big and it wouldn’t fit the page and that’s the same with the map.