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# Ratios with tape diagrams

CCSS.Math:

## Video transcript

we're told Kensi makes quilts with some blue squares and some green squares the ratio of blue squares to green squares is shown in the diagram the table shows the number of blue squares of the number of green squares that Kensi will make on two of her quilts all right this is the table they're talking about based on the ratio complete the missing values in the table so why don't you pause this video and see if you can figure it out well first let's think about the ratio of blue to green squares so for every three blue squares let me do that same a similar color for every three blue squares we are going to have one two three four five green squares so the ratio of blue to green is three to five and so in quilt a she has twenty-one blue squares so she has twenty-one blue squares how many green squares would she have well to go from three to 21 you have to multiply by seven and so you would take five and then multiply that by seven so you'd multiply five times seven to get to thirty-five as long as you multiply both of these by the same number or divide them by the same number you're going to get an equivalent ratio so 21 to 35 is the same thing as three to five now we have a situation quilt B they've given us the number of green squares so that's 20 well how do we get twenty from five well we would multiply by four so if you multiply the number of green squares by four then you would do the same thing for the number of blue squares three times four three times four is going to be equal to twelve twelve blue squares for every twenty green squares is the same ratio as three blue squares for every five green squares let's do another example here we are told the following diagram describes the number of cups of blue and red paint in a mixture what is the ratio of blue paint to red paint in the mixture so try to work it out all right so let's just see we have one two three four five six seven eight nine ten ten cups of blue paint forever one two three four five six cups of red bean so this would be a legitimate ratio a ratio of ten cups of blue paint for every six cups of red paint but this isn't in I guess you could say lowest terms or most simplified terms because we can actually divide both of these numbers by two so if you divide 10 by two you get five blue color and if you divide 6 by 2 you get three so one way to think about is for every blue school every five blue squares you have three red squares in this diagram in this tape diagram that sometimes called or you could say for every five cups of blue paint you have three cups of red paint in our mixture and you could even see that here so three cups of red paint and one two three four five and five cups of blue paint and you see that again right over here let's do another example here we're told Luna and Ginny each cast magic spells the ratio of spells Luna cast spells Ginny casts is represented in this tape diagram all right based on the ratio what is the number of spells Ginny casts when Luna casts 20 spells pause this video see if you can work it out all right so let's just see the ratio here for every one two three four spells that Luna casts Ginny casts one two three four five spells so the ratio is four to five but if Luna casts 20 spells sofa Luna casts 20 spells well to go from four to twenty we had to multiply by five and so we would do the same thing with the number of spells Ginny casts you'd multiply that by five so it's 25 so for Luna spells for every five Ginny spells is the same thing as 20 Luna spells for every 25 Ginny spells and so how many how many spells does Ginny cast when Lulu and Luna cast twenty spells she casts 25 and we're done