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“Now, think about 0 ÷ 0,” said Mrs. Dewey.
This time Frank began, “To think about 0 ÷ 0, I try to find the only number that makes the number sentence 0 ? = 0 true. But, any number works. 0 5 = 0 and 0 24 = 0. Zero times any number is zero. Mrs. Dewey, I thought you said there is just one right answer. I remember you said, ‘a unique solution.'”
“That's right, Frank,” Mrs. Dewey replied. “Since there is not a unique solution, mathematicians say that 0 ÷ 0 is undefined as well.”
For each statement below, find one number that will make it true. If there is no such number, say so.
- 8 ÷ 4 =
, since 4 = 8 - 42 ÷ 7 = , since 7 = 42
- 5 ÷ 1 = , since 1 = 5
- 0 ÷ 3 = , since 3 = 0
- 28 ÷ 7 = , since 7 = 28
- 2 ÷ 0 = , since 0 = 2
- 36 ÷ 6 = , since 6 = 36
- 0 ÷ 0 = , since 0 = 0
- Do the division problems in Question 10 on a calculator. Explain what happens.
Check-In: Question 12
Solve the following problems. When necessary, use “undefined.” Justify your reasoning using related multiplication sentences.
- 35 ÷ 7 =
- 0 ÷ 7 =
- 7 ÷ 0 =
- 0 ÷ 0 =
