Question

1. multiply using fraction form and unit form. check your answer by counting the decimal places.

the first one is done for you.
a. $3.3 \times 1.6 = \frac{33}{10} \times \frac{16}{10}$
$= \frac{33 \times 16}{100}$
$= \frac{528}{100}$
$= 5.28$
3 3 tenths
$\underline{\times \quad 1 6\text{ tenths}}$
$\

$$\begin{matrix}1\\ 9\\ 8\\\\+\\ 3\\ 3\\ 0\\end{matrix}$$

$
5 2 8 hundredths
b. $3.3 \times 0.8 =$
3 3 tenths
$\underline{\times \quad 8\text{ tenths}}$
c. $4.4 \times 3.2 =$
d. $2.2 \times 1.6 =$

1. multiply using fraction form and unit form. the first one is partially done for you.

a. $3.36 \times 1.4 = \frac{336}{100} \times \frac{14}{10}$
$= \frac{336 \times 14}{1,000}$
$= \frac{4,704}{1,000}$
$= 4.704$
3 3 6 hundredths
$\underline{\times \quad 1 4\text{ tenths}}$
b. $3.35 \times 0.7 =$
3 3 5 hundredths
$\underline{\times \quad 7\text{ tenths}}$
c. $4.04 \times 3.2 =$
d. $4.4 \times 0.16 =$

Explanation:

Problem Set 1

Step1: Convert decimals to fractions

Step2: Multiply numerators and denominators

Step3: Simplify to get decimal

Step4: Verify with unit form multiplication

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1b. $3.3 \times 0.8$

Step1: Convert to fraction form

$3.3 \times 0.8 = \frac{33}{10} \times \frac{8}{10}$

Step2: Multiply numerators/denominators

$=\frac{33 \times 8}{100} = \frac{264}{100}$

Step3: Simplify to decimal

$=2.64$

Step4: Unit form check

$33$ tenths $\times 8$ tenths

$$\begin{align*} 33\\ \times\ 8\\ \hline 264 \end{align*}$$

264 hundredths = $2.64$

Step1: Convert decimals to fractions

Step2: Multiply numerators and denominators

Step3: Simplify to get decimal

Step4: Verify with unit form multiplication

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2b. $3.35 \times 0.7$

Step1: Convert to fraction form

$3.35 \times 0.7 = \frac{335}{100} \times \frac{7}{10}$

Step2: Multiply numerators/denominators

$=\frac{335 \times 7}{1000} = \frac{2345}{1000}$

Step3: Simplify to decimal

$=2.345$

Step4: Unit form check

$335$ hundredths $\times 7$ tenths

$$\begin{align*} 335\\ \times\ 7\\ \hline 2345 \end{align*}$$

2345 thousandths = $2.345$

Answer:

$2.64$

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1c. $4.4 \times 3.2$

Step1: Convert to fraction form

$4.4 \times 3.2 = \frac{44}{10} \times \frac{32}{10}$

Step2: Multiply numerators/denominators

$=\frac{44 \times 32}{100} = \frac{1408}{100}$

Step3: Simplify to decimal

$=14.08$

Step4: Unit form check

$44$ tenths $\times 32$ tenths

$$\begin{align*} 44\\ \times\ 32\\ \hline 88\\ +1320\\ \hline 1408 \end{align*}$$

1408 hundredths = $14.08$