Lesson 5 Equivalent Multiplication Expressions

Warm-up How Many Do You See?

How many thirds do you see? How do you see them?

Find the number that makes each equation true. Draw a diagram if it is helpful.

$\frac{12}{5} = 12 \times$

$\frac{12}{5} = 6 \times$

$\frac{12}{5} = 4 \times$

$\frac{12}{5} = 3 \times$

$\frac{12}{5} = 2 \times$

$\frac{12}{5} = 1 \times$

Here are two sets of numbers:

Set A:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11

Set B:

$\frac{1}{7}, \frac{2}{7}, \frac{3}{7}, \frac{4}{7}, \frac{5}{7}, \frac{6}{7}, \frac{7}{7}$

Choose a number from set A and a number from set B to complete this equation and make it true:
$\frac{6}{7} =$ $\times$
Choose a different number from set A and a number from set B to complete the equation to make it true.
$\frac{6}{7} =$ $\times$

Explain or show how you know that the two equations you wrote are both true.

Here is a set of expressions.

$6 \times \frac{1}{10}$

B.
$2 \times 4 \times \frac{1}{9}$

$4 \times \frac{1}{5}$

D.
$3 \times 2 \times \frac{1}{10}$

E.
$5 \times 2 \times \frac{1}{12}$

F.
$2 \times 2 \times \frac{1}{5}$

G.
$4 \times 4 \times \frac{1}{9}$

H.
$10 \times \frac{1}{12}$

I.
$4 \times \frac{1}{12}$

Match each expression to one of the following fractions, if possible. Record your matches. Be prepared to explain how you know there is or isn’t a match. Some expressions might not have a match. Record your matches. Be prepared to explain how you know there is or isn’t a match.
$\frac{4}{5}$
$\frac{10}{12}$
$\frac{6}{10}$
$\frac{8}{9}$
Complete each equation to make it true. Try to do so without using unit fractions.
$\frac{4}{5} =$ $\times$
$\frac{10}{12} =$ $\times$
$\frac{6}{10} =$ $\times$
$\frac{8}{9} =$ $\times$
$\frac{4}{5} =$ $\times$
$\frac{10}{12} =$ $\times$
$\frac{6}{10} =$ $\times$
$\frac{8}{9} =$ $\times$

Find the number that makes each equation true. Draw a diagram if it is helpful.