Lesson 17 Fractions as Partial Quotients

- Let’s use fractions to help us divide whole numbers.

Warm-up What Do You Know About …?

What do you know about $\frac{60}{6} + \frac{6}{6}$ ?

Activity 1 Select Expressions

Select all the expressions that are equivalent to $\frac{78}{6}$ . Explain or show your reasoning.
1. $78 \div 6$
2. $\frac{66}{6} + \frac{12}{6}$
3. $\frac{60}{6} + \frac{18}{6}$
4. $(60 \div 6) + (18 \div 6)$
5. $\frac{77}{6} + \frac{8}{6}$
6. $(60 \div 6) + 18$
What is the value of $78 \div 6$ ? Explain or show your thinking.

Activity 2 Choose One Expression

Problem 1

Use each expression to find the value of $165 \div 15$ . Explain or show your thinking.

$\frac{75}{15} + \frac{80}{15} + \frac{10}{15}$
$\frac{30}{15} + \frac{30}{15} + \frac{30}{15} + \frac{60}{15} + \frac{15}{15}$
$\frac{150}{15} + \frac{15}{15}$

Problem 2

Choose one expression and use it to find the value of $540 \div 18$ . Explain or show your thinking.

$\frac{180}{18} + \frac{180}{18} + \frac{180}{18}$
$\frac{500}{18} + \frac{40}{18}$
$\frac{360}{18} + \frac{180}{18}$

Problem 3

Which expressions were most helpful? Which expressions were least helpful? Explain or show your thinking.