# Lesson 12

Dividing Decimals by Whole Numbers

### Lesson Narrative

This lesson serves two purposes. The first is to show that we can divide a decimal by a whole number the same way we divide two whole numbers. Students first represent a decimal dividend with base-ten diagrams. They see that, just like the units representing powers of 10, those for powers of 0.1 can also be divided into groups. They then divide using another method—partial quotients or long division—and notice that the principle of placing base-ten units into equal-size groups is likewise applicable.

The second is to uncover the idea that the value of a quotient does not change if both the divisor and dividend are multiplied by the same factor. Students begin exploring this idea in problems where the factor is a multiple of 10 (e.g. $$8\div 1= 80\div 10$$). This work prepares students to divide two decimals in the next lesson.

### Learning Goals

Teacher Facing

• Compare and contrast (orally and using other representations) division problems with whole-number and decimal dividends
• Divide decimals by whole numbers, and explain the reasoning (orally and using other representations).
• Generalize (orally and in writing) that multiplying both the dividend and the divisor by the same factor does not change the quotient.

### Student Facing

Let’s divide decimals by whole numbers.

### Required Preparation

Some students might find it helpful to use graph paper to help them align the digits as they divide using long division and the partial quotients method. Consider having graph paper accessible throughout the lesson.

### Student Facing

• I can divide a decimal by a whole number.
• I can explain the division of a decimal by a whole number in terms of equal-sized groups.
• I know how multiplying both the dividend and the divisor by the same factor affects the quotient.

Building On

Building Towards

### Glossary Entries

• long division

Long division is a way to show the steps for dividing numbers in decimal form. It finds the quotient one digit at a time, from left to right.

For example, here is the long division for $$57 \div 4$$.

$$\displaystyle \require{enclose} \begin{array}{r} 14.25 \\[-3pt] 4 \enclose{longdiv}{57.00}\kern-.2ex \\[-3pt] \underline{-4\phantom {0}}\phantom{.00} \\[-3pt] 17\phantom {.00} \\[-3pt]\underline{-16}\phantom {.00}\\[-3pt]{10\phantom{.0}} \\[-3pt]\underline{-8}\phantom{.0}\\ \phantom{0}20 \\[-3pt] \underline{-20} \\[-3pt] \phantom{00}0 \end{array}$$

### Print Formatted Materials

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