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## 6th grade (Illustrative Mathematics)

### Unit 2: Lesson 14

Lesson 16: Solving more ratio problems# Ratios with tape diagrams

Sal uses tape diagrams to visualize equivalent ratios and describe a ratio relationship between two quantities.

## Video transcript

- [Instructor] We're
told Kenzie 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 and the number of green squares that Kenzie
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 or that seem 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 21 blue squares. So she has 21 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 35. 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 in quilt B. They've given us the number of
green squares, so that's 20. Well, how do we get 20 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 12. 12 blue squares for every 20
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, 10... 10 cups of blue paint for every one, two, three,
four, five, six cups of red paint. So this would be a legitimate
ratio, a ratio of 10 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. I'll do that in blue color, and if you divide six
by two, you get three. So one way to think about it
is for every five blue squares, you have three red
squares in this diagram, in this tape diagram
that's 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 casts to 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 to 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... So if a Luna casts 20 spells,
well to go from four to 20, 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 four Luna spells for every five Ginny
spells is the same thing as 20 Luna spells for
every 25 Ginny spells, and so how many spells does Ginny cast when Luna casts 20 spells? She casts 25, and we're done.