Reversals with Multiplication and Division

Using Number Properties

Problem: “Snapper costs $13.89 per kilogram. Maru bought some snapper, and it cost him $56.80.When he got home, he wondered what weight of snapper he had bought.”

Discuss the problem and write it on the board as 13.89 x ? = 56.80.Discuss how to solve such problems and how to round the calculator answer sensibly.

(Answer: 13.89 x ? = 56.80 is the same as ? = 56.80 ÷ 13.89 = 4.089272858. As this  is kilograms, it makes no sense to have an answer more accurate than the nearest  gram, that is to say, the nearest 0.001 kilogram. So rounding to 3 decimal places  gives 4.089 kilograms.)

Problem: “Filbert had 7.475 kilograms of olives. He put a set weight of olives in a setof jars and found he had enough for 13 jars. Write this down as a division problem.”(Answer: 7.475 ÷ ? = 13.)

“Later Filbert wanted to add labels showing the weight of olives in each jar, but he had forgotten what this weight was. How would Filbert solve 7.475 ÷ ? = 13?” (Answer: 7.475 ÷ ? = 13 is the same as ? = 7.475 ÷ 13 = 0.575 grams.)

Examples: Worksheet (Material Master 8–2).

Understanding Number Properties:

Choose one answer:

If a
□ = b      □ equals     a ÷ b      b ÷ a      a x b      (Answer: b ÷ a)
If a ÷ □ = b       □ equals     a ÷ b      b ÷ a      a x b      (Answer: a ÷ b)
If □ ÷ a = b       □ equals     a ÷ b      b ÷ a      a x b      (Answer: a x b)
If □
a = b      □ equals     a ÷ b      b ÷ a      a x b      (Answer: b ÷ a)