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### Course: Pre-algebra>Unit 3

Lesson 3: Equivalent ratios

# Ratio tables

Learn how to fill out tables of equivalent ratios.
A ratio table gives a bunch of equivalent ratios.
Let's look at an example where we'll build a ratio table.
Ben drinks $1$ glass of milk for every $2$ cookies that he eats:
We can use this ratio to begin a ratio table:
$1$$2$
If Ben drinks $2$ glasses of milk, then he eats $4$ cookies:
Let's use this to continue the ratio table:
$1$$2$
$2$$4$
Notice that both of the ratios in the ratio table are equivalent:
$\frac{1}{2}=\frac{2}{4}$
If Ben drinks $4$ glasses of milk, then he eats $8$ cookies:
Let's use this to continue the ratio table:
$1$$2$
$2$$4$
$4$$8$
Notice that all of the ratios in the ratio table are equivalent:
$\frac{1}{2}=\frac{2}{4}=\frac{4}{8}$

## Let's practice!

### Problem set 1:

Problem 1A
Martha needs $28$ strawberries for every $4$ smoothies she makes.
Complete the table using equivalent ratios.
StrawberriesSmoothies
$28$$4$
$3$
$70$

## Want to join the conversation?

• Do we use ratios in the real world an d if not why are we learning this?
• Ratios are hidden all over the real world. Whether you're measuring the speed of light, the rate of a chemical reaction, or the time it takes for a racecar to reach top speed, ratios are an integral part of quantifying real-life scenarios.
• Can something that is infinite be a ratio?
• Good question! Just to make it clear, value of infinity/infinity can be any number. The ratio can be 0, any finite value or infinity itself. On the other hand, we can say if we going to measure it quantitively, infinity at the numerator may not be equal to infinity at the denominator. So, we can not get any particular value from the ratio.
• Can negative numbers be ratios?
• Yes, ratios can be negative!
For example, you could have -3 / 4 or 5 / -2.
• What is inverse proportion
• Great question for sixth grade!

Two nonzero quantities, x and y, are inversely proportional to each other if and only if their product xy is constant. This means that when x is multiplied by a nonzero factor, y is divided by that factor (for example, when x is doubled, y is halved).

An example from real life involves speed, time, and distance. If the distance is held constant, then speed and time are inversely proportional to each other. For example, if you double your walking speed, then you would take half the amount of time to walk to school.

Inverse proportionality relationships also occur in chemistry and physics. If the temperature of an ideal gas is held constant, then pressure and volume are inversely proportional to each other (Boyle’s Law). If the voltage of an electric circuit is held constant, then the circuit’s current and resistance are inversely proportional to each other (Ohm’s Law).

Have a blessed, wonderful day!
• For the last problem would dividing 32.5 by 3 to get 10.83 then multiplying 10.83 by 6 and 12 be wrong? Because you don't get 65 you get 64.98 and 129.96.
• I multiplied 32 and 1/2 by 2 because that gets me the answer of the 6 lollipops, and we are using fractions here not decimals :D
• the straberry and smoothes problem makes no sence.
• If you have a Hard time understanding it, try reading it again. If you are still stuck, don't worry, they are just questions for practice. Below the "check" button, there is a hyperlink "explain", click on it and it will explain the answer.