Question

1. multiply and model. rewrite each expression as a number sentence with decimal factors. the first one is done for you.

a. $\frac{1}{10} \times \frac{1}{10}$
$= \frac{1 \times 1}{10 \times 10}$
$= \frac{1}{100}$
$0.1 \times 0.1 = 0.01$

b. $\frac{6}{10} \times \frac{2}{10}$

c. $\frac{1}{10} \times 1.6$

d. $\frac{6}{10} \times 1.9$

Explanation:

Step1: Convert fractions to decimals

For part b: $\frac{6}{10}=0.6$, $\frac{2}{10}=0.2$

Step2: Multiply the decimals

$0.6 \times 0.2 = 0.12$
(Model: Shade 6 columns (0.6) and 2 rows (0.2) of the 10x10 grid; the overlapping 12 squares represent 0.12)

Step3: Convert fraction to decimal (part c)

$\frac{1}{10}=0.1$

Step4: Multiply the decimals

$0.1 \times 1.6 = 0.16$
(Model: 1 full 10x10 grid + 6 columns of a second grid (for 1.6); shade $\frac{1}{10}$ (1 column) of this area, resulting in 16 shaded squares = 0.16)

Step5: Convert fraction to decimal (part d)

$\frac{6}{10}=0.6$

Step6: Multiply the decimals

$0.6 \times 1.9 = 1.14$
(Model: 1 full 10x10 grid + 9 columns of a second grid (for 1.9); shade 6 columns of this area: 60 squares from the first grid + 54 squares from the second = 114 squares = 1.14)

Answer:

b. $0.6 \times 0.2 = 0.12$
c. $0.1 \times 1.6 = 0.16$
d. $0.6 \times 1.9 = 1.14$