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To express a counting problem as a ratio you should divide the number of things before the word "to" by the number of things after the word "to". A ratio can be expressed as a fraction or separating the two numbers with a colon (a:b).

Let's apply this to each one of our problems.

11. Here we have triangles to rectangles, so we are going to divide the number of triangles by the number of rectangles.

We can count 2 triangles and 8 rectangles from our picture, so

Triangles to rectangles = [tex]\frac{NumberofTriangles}{NumberifRectangles} =\frac{2}{8}[/tex]

Notice that both numerator and denominator of our ratio are divisible by 2, so simplify it, we just need to divide them both by 2:

[tex]\frac{2}{8} =\frac{\frac{2}{2} }{\frac{8}{2} } =\frac{1}{4}[/tex]

So the ratio from triangles to rectangles is [tex]\frac{1}{4}[/tex] or [tex]1:4[/tex]

which means that for 1 triangle there are four rectangles.

12. Here we have soccer balls to footballs, so we are going to divide the number of soccer balls to the number of footballs and simplify our resulting fraction. We have 6 soccer balls and 10 footballs in our picture

Soccer balls to footballs = [tex]\frac{NumberofSoccerBalls}{NumberofFootballs} =\frac{6}{10} =\frac{\frac{6}{2} }{\frac{10}{2} } =\frac{3}{5}[/tex]

For every 3 soccer balls there are 5 Footballs.

13. Here we have kittens to puppies or puppies to kittens. We know that there are 36 Kittens and 12 puppies.

- Kittens to puppies = [tex]\frac{NumberofKittens}{NumberofPuppies} =\frac{36}{12} =\frac{\frac{36}{12} }{\frac{12}{12} } =\frac{3}{1}[/tex]

For every 3 kittens there is a puppy.

- Puppies to kittens = [tex]\frac{Number of Puppies}{NumberofKittens} =\frac{12}{36} =\frac{\frac{12}{12} }{\frac{36}{12} } =\frac{1}{3}[/tex]

For each puppy there are 3 kittens.