IM 6.5.13 Lesson: Dividing Decimals by Decimals

Use long division to find the value of .

Select all of the quotients that have the same value as .

Think of one or more ways to find . Show your reasoning.

Find . Explain your reasoning. If you get stuck, think about what equivalent division expression you could write.

Diego said, “To divide decimals, we can start by moving the decimal point in both the dividend and divisor by the same number of places and in the same direction. Then we find the quotient of the resulting numbers.” Do you agree with Diego? Use the division expression to support your answer.

Can we create an equivalent division expression by multiplying both the dividend and divisor by a number that is not a multiple of 10 (for example: 4, 20, or )? Would doing so produce the same quotient? Explain or show your reasoning.

Here are two calculations of . Work with your partner to answer the following questions. How are the two calculations the same? How are they different?

Look at Calculation A. Explain how you can tell that the 36 means “36 tenths” and the 18 means “18 hundredths.”

Look at Calculation B. What do the 3600 and 1800 mean?

We can think of as saying, “There are 9 groups of 5.42 in 48.78.” We can think of as saying, “There are 900 groups of 5.42 in 4878.” How might we show that both statements are true?

Explain why has the same value as .

Write a division expression that has the same value as  but is easier to use to find the value. Then, find the value using long division.

Mai is making friendship bracelets. Each bracelet is made from 24.3 cm of string. If she has 170.1 cm of string, how many bracelets can she make? Explain or show your reasoning.