Fractions and Division

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Write a how many in one group story problem for $1 \div 6$ , and explain how you know your story problem is correct. Then, use our meaning of fractions to explain why the answer to your story problem is $\frac {1}{6}$ .

Why does the previous problem mean that we can use long division to find the decimal representation for $\frac {1}{6}$ ?

Use long division to find the decimal representation for $\frac {1}{25}$ . What happened? Was this a special case or will this happen for all fractions with a terminating decimal representation? Why?

Use long division to find the decimal representation for $\frac {1}{7}$ . What type of pattern occurred? Why did this happen? Was this a special case or will this happen for all fractions with a repeating decimal representation? Why?

Use long division to find the decimal representation for $\frac {1}{9}$ . What type of pattern occurred? Why did this happen? Was this a special case or will this happen for all fractions with a repeating decimal representation? Why?

What do the previous three problems tell us about what the decimal representation of a fraction has to look like? Explain how you know.

Are there any decimals that can’t be written as fractions? Use your work in the previous problem to explain how you know.

Bonus problem! Can you use what you already know about the decimal for $\frac {1}{9}$ to write the decimal for $\frac {4}{9}$ ? What about $\frac {1}{18}$ ?

2026-07-22 02:13:46