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Free proportion videos online (pre-algebra/grade 7)

Find here free online math videos on proportions-related topics: solving proportions, word problems, unit rates, proportional relationships, scaling geometric figures, and maps. These videos match Math Mammoth pre-algebra / grade 7 curriculum, and are aligned to the Common Core standards concerning proportions in 7th grade math.


Solving proportions

Proportion is defined as an equation of the type (ratio) = (ratio). I show three different ways of solving proportions:
1) table
2) thinking of equivalent fractions
3) cross-multiplying

Then I solve several word problems that involve proportions using these methods.




Proportion word problems

I solve three word problems that have to do with equal ratios - therefore, a proportion is involved. However, I don't use a proportion to solve every problem. In the first problem, I use a table of equal ratios. In the second, I write a proportion and solve it by cross-multiplying. And I solve the last problem in two different ways - using proportional thinking and then also with a proportion.




Unit rates and more about proportions

A unit rate is a rate where the second term in the rate is 1 of something, such as $5 per $1 or 65 miles : 1 hour. You can always solve the unit rate from a non-unit rate by dividing. For example, if you have the rate $46 per 6.5 hours, divide $46 by 6.5 to get the rate per 1 hour.

I solve word problems involving unit rates, and also show how unit rate relates to SLOPE in a linear equation. Basically, slope gives you the unit rate!




How to find the unit rate, including with fractions

I explain what is a unit rate, and show how to find the unit rate from a non-unit rate, including when FRACTIONS are involved. For example, I find the unit rate when you walk 1/2 mile in 1/4 hour. Then, I solve a word problem using the unit rate. Lastly, we look at a graphing problem that involves constant speed — the unit rate ends up being the speed, and also the slope of the line.




Proportional relationships / Direct variation

How can we determine if two variables are in a proportional relationship or not? If you write a table of the values of the two variables, when one variable increases by some certain amount, the other should also increase by some certain amount. Another way to know is if you graph the equation that involves the two variables. You should get a straight line through origin, and if that is the case, the slope gives you the unit rate. (Or, just look at the equation that relates the two variables: it should be of the form y = kx.)

I also show an example of a non-proportional relationship, which ends up being an inverse variation. Proportional relationships are also called direct variation.




Scaling figures and the scale ratio

When a figure is enlarged or shrank proportionally, or when two figures are similar, the scale ratio is the ratio of one side of the figure to the corresponding side in the other. When the scale ratio is given, we can solve an unknown side. Or, if a set of corresponding sides is given, we can write a proportion to solve for the unknown side.

This lesson is meant for prealgebra or grade 7 math.




How to calculate distances on the map or in reality using the map scale

Learn basic calculations concerning the scale in maps: how to calculate the distance in reality from the distance on the map, and vice versa.

The scale of a map is actually a ratio, such as 1:200,000 or 1:35,000. A map scale 1:30,000 means that one unit (whether inch or centimeter) on the map corresponds to 30,000 such units in reality. That understanding is the basis for all the calculations we do. Essentially, to go from the map to reality, you would multiply by that number 30,000, and to go from reality to the map you'd divide by it.




These videos match the lessons in my book Math Mammoth Ratios, Proportions, and Problem Solving (Blue Series book), or the lessons in chapter 6 of Math Mammoth Grade 7 curriculum. In either of those, you will get MANY more practice exercises, word problems, and puzzles than what are shown in the videos, and also some lessons that are not in covered in this set of videos.

Math Mammoth Ratios, Proportions & Problem Solving math book cover
72 pages
(includes answers)

Math Mammoth Ratios, Proportions & Problem Solving

Sample pages (PDF)
Contents and Introduction
Solving Problems Using Equivalent Ratios
Scaling Figures 2
Problem Solving with Diagrams, part 1
Ratio Problems & Bar Models 2

PDF download $5.00



By Maria Miller



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