Reading a ratio as times, film 1 of 2

Adam and Grace tip out all the bottle caps collected in their jars. The number of Adam's caps to Grace's is in the ratio 3 to 5. Draw a bar for each of them. Adam's caps first, 3 blue units. Then Grace's caps, 5 blue units, on the bar below. Now write the two names down. Adam to Grace, 3 to 5. That ratio is a comparison. It compares Adam's units with Grace's units. For every 3 caps Adam has, Grace has 5. And that's all it says. Neither number counts all the caps. Now the question changes. What fraction of all the caps are Adam's? A fraction needs a whole, and this question names it. The whole is all the caps. That's both bars together. Adam's 3 units and Grace's 5 units together. 3 plus 5 is 8 units in the whole. So read the fraction off the bars. Adam's caps are 3 of the 8 units in the whole. That's 3 over 8. Adam's caps are 3 over 8 of all the caps. Careful here. 3 to 5 doesn't make it 3 over 5. The 5 is Grace's units. It isn't the whole. The whole is all 8 units. So the fraction is 3 over 8.

Your turn. What fraction of all the caps are Grace's? Read it off the bars. Try it first. Pause if you like. Grace's caps are 5 units. 5 of the 8 units in the whole. So Grace's caps are 5 over 8 of all the caps. Two bars, drawn once. The ratio compares Adam's units with Grace's. 3 to 5. The fraction compares Adam's units with the whole. 3 over 8. The bars didn't change. The question did.