# Lesson 13

Dividing Decimals by Decimals

### Lesson Narrative

In the previous lesson, students learned how to divide a decimal by a whole number. They also saw that multiplying both the dividend and the divisor by the same power of 10 does not change the quotient. In this lesson, students integrate these two understandings to find the quotient of two decimals. They see that to divide a number by a decimal, they can simply multiply both the dividend and divisor by a power of 10 so that both numbers are whole numbers. Doing so makes it simpler to use long division, or another method, to find the quotient. Students then practice using this principle to divide decimals in both abstract and contextual situations.

### Learning Goals

Teacher Facing

• Compare and contrast (orally and using other representations) division problems with whole-number and decimal divisors.
• Divide whole numbers or decimals by decimals, and explain the reasoning (orally and using other representations), including choosing to divide a different expression that gets the same quotient.
• Generate another division expression that has the same value as a given expression, and justify (orally) that they are equal.

### Student Facing

Let’s divide decimals by decimals.

### Student Facing

• I can explain how multiplying dividend and divisor by the same power of 10 can help me find a quotient of two decimals.
• I can find the quotient of two decimals.

### CCSS Standards

For example, here is the long division for $$57 \div 4$$.
$$\displaystyle \require{enclose} \begin{array}{r} 14.25 \\[-3pt] 4 \enclose{longdiv}{57.00}\kern-.2ex \\[-3pt] \underline{-4\phantom {0}}\phantom{.00} \\[-3pt] 17\phantom {.00} \\[-3pt]\underline{-16}\phantom {.00}\\[-3pt]{10\phantom{.0}} \\[-3pt]\underline{-8}\phantom{.0}\\ \phantom{0}20 \\[-3pt] \underline{-20} \\[-3pt] \phantom{00}0 \end{array}$$