Three quantities compared

A school library has two thousand six hundred and seventy-four books in English, Chinese and Malay. There are 3 times as many English books as Malay books. There are two hundred and fifty-nine fewer Chinese books than English books. How many Chinese books are there? Try it first. Pause if you like. Malay books are one unit. English books are three units because there are three times as many English books as Malay books. There are two hundred and fifty-nine fewer Chinese books, so this bar is shorter. The dashed part is missing. The Chinese bar is short. Must we add the missing part, or subtract it, to make whole units? Malay is 1 unit. English is 3 units. Chinese is short of 3 units by two hundred and fifty-nine. The dashed part is missing. Add the missing part to make the Chinese bar whole. We must add it to the total too. Now count the whole units: 1 for Malay, 3 for English, and 3 for the completed Chinese bar. That is 7 units. 7 units equal two thousand six hundred and seventy-four plus two hundred and fifty-nine, which is two thousand nine hundred and thirty-three. 1 unit equals two thousand nine hundred and thirty-three divided by 7, which is four hundred and nineteen. 3 units equal 3 times four hundred and nineteen, which is one thousand two hundred and fifty-seven. That is the completed bar. Chinese books are two hundred and fifty-nine fewer. Remove the part we added only to help us calculate. Chinese books equal one thousand two hundred and fifty-seven minus two hundred and fifty-nine, which is nine hundred and ninety-eight books. There are nine hundred and ninety-eight Chinese books. Add the missing part before dividing, then subtract it from the completed Chinese bar.

Boxes A, B and C hold three thousand two hundred and forty paper clips altogether. Box B holds twice as many paper clips as Box A. Box C holds three hundred and fifteen more paper clips than Box B. How many paper clips does Box C hold? Try it first. Pause if you like. This time Box C has an extra part. What must happen to the total before we share the equal units? Box A is 1 unit. Box B is 2 units. Box C is 2 units and three hundred and fifteen more. Set the extra part aside. It is already included in the given total, so subtract it. The whole units are 1 for Box A, 2 for Box B, and 2 for Box C. That is 5 units. 5 units equal three thousand two hundred and forty minus three hundred and fifteen, which is two thousand nine hundred and twenty-five. 1 unit equals two thousand nine hundred and twenty-five divided by 5, which is five hundred and eighty-five. 2 units equal 2 times five hundred and eighty-five, which is one thousand one hundred and seventy. The question asks for Box C. Put its extra three hundred and fifteen back beside the 2 units. Box C equals one thousand one hundred and seventy plus three hundred and fifteen, which is one thousand four hundred and eighty-five paper clips. Make whole units first. Then find the quantity the question asks for.