Lesson 18 Compare Without Multiplying

- Let’s compare expressions, without evaluating them.

Warm-up Notice and Wonder: Expressions and Number Lines

What do you notice? What do you wonder?

$\frac{2}{3} \times 5$

Activity 1 Approximate Location

Problem 1

Label each expression at its approximate location on the number line.

Partner A
1. $\frac{2}{5} \times 12$
2. $\frac{5}{3} \times 12$
3. $\frac{7}{7} \times 12$
Partner B
1. $\frac{4}{7} \times 12$
2. $\frac{8}{5} \times 12$
3. $\frac{9}{9} \times 12$

Problem 2

Choose a number to put in each box to make the statement true.

$\frac{}{11} \times 12 > 12$
$\frac{}{15} \times 12 = 12$
$\frac{13}{} \times 12 < 12$

Activity 2 An Unknown Number

The number A is shown on the number line. Label the approximate location of the value of each expression. Explain or show your reasoning.
- $\frac{1}{4} \times A$
- $2 \times A$
- $\frac{13}{8} \times A$
- $\frac{2}{3} \times A$
Is $\frac{13}{8} \times \frac{11}{39}$ less than, greater than, or equal to $\frac{11}{39}$ ? Explain or show your reasoning.
Is $\frac{2}{3} \times \frac{17}{53}$ less than, greater than, or equal to $\frac{17}{53}$ ? Explain or show your reasoning.

Practice Problem

Problem 1

The point A is labeled on the number line.

Label each of these points on the number line.

$\frac{2}{5} \times A$
$\frac{13}{10} \times A$
$\frac{7}{4} \times A$

Number line. Tick mark, labeled 0. Point, labeled A to the right.