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## 6th grade (Illustrative Mathematics)

### Unit 2: Lesson 10

Lesson 11: Representing ratios with tables

# 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 start color #11accd, 1, end color #11accd glass of milk for every start color #e07d10, 2, end color #e07d10 cookies that he eats:
We can use this ratio to begin a ratio table:
Glasses of milkCookies
start color #11accd, 1, end color #11accdstart color #e07d10, 2, end color #e07d10
If Ben drinks start color #11accd, 2, end color #11accd glasses of milk, then he eats start color #e07d10, 4, end color #e07d10 cookies:
Let's use this to continue the ratio table:
Glasses of milkCookies
start color #11accd, 1, end color #11accdstart color #e07d10, 2, end color #e07d10
start color #11accd, 2, end color #11accdstart color #e07d10, 4, end color #e07d10
Notice that both of the ratios in the ratio table are equivalent:
start fraction, start color #11accd, 1, end color #11accd, divided by, start color #e07d10, 2, end color #e07d10, end fraction, equals, start fraction, start color #11accd, 2, end color #11accd, divided by, start color #e07d10, 4, end color #e07d10, end fraction
If Ben drinks start color #11accd, 4, end color #11accd glasses of milk, then he eats start color #e07d10, 8, end color #e07d10 cookies:
Let's use this to continue the ratio table:
Glasses of milkCookies
start color #11accd, 1, end color #11accdstart color #e07d10, 2, end color #e07d10
start color #11accd, 2, end color #11accdstart color #e07d10, 4, end color #e07d10
start color #11accd, 4, end color #11accdstart color #e07d10, 8, end color #e07d10
Notice that all of the ratios in the ratio table are equivalent:
start fraction, start color #11accd, 1, end color #11accd, divided by, start color #e07d10, 2, end color #e07d10, end fraction, equals, start fraction, start color #11accd, 2, end color #11accd, divided by, start color #e07d10, 4, end color #e07d10, end fraction, equals, start fraction, start color #11accd, 4, end color #11accd, divided by, start color #e07d10, 8, end color #e07d10, end fraction

## 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
284
3
70

## Want to join the conversation?

• Do we use ratios in the real world an d if not why are we learning this?
(154 votes)
• 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.
(111 votes)
• Can something that is infinite be a ratio?
(51 votes)
• 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.
(28 votes)
• Can negative numbers be ratios?
(32 votes)
• Yes, ratios can be negative!
For example, you could have -3 / 4 or 5 / -2.
(28 votes)
• we should group up and make a traveling device and go back in time and stop whoever made math from making it so we can have our peace.
(13 votes)
• if you did that computers wouldn't exist or phones or houses or cars or rockets etc.
(26 votes)
• 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.
(12 votes)
• 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
(11 votes)
• What is inverse proportion
(11 votes)
• 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!
(15 votes)
• the straberry and smoothes problem makes no sence.
(14 votes)
• it's easy, 4x7= 28, 3x7=21, & 7x10= 70
(2 votes)
• how often will I see a ratio in the real world?
(8 votes)
• All the time, you drive in ratios (60 miles/hour), every recipe you follow is ratios, people often plan parties with ratios (2 deserts per person, or figuring out how much stuff you need to buy for the number of people you have). This does not even get into the practical uses of science, math, art, etc.
(6 votes)
• This will not allow me to turn in my work its 9pm and it do tomorow. HELP.
(10 votes)
• i dont know da pizza one
(5 votes)
• you have to use decimals look at my post
(6 votes)