Multiplying Fractions

Examples and Exercises

	$(3.9)(4.075)$
Determine the sign of the product. The signs are the same.	The product will be positive.
Write the numbers in vertical format, lining up the numbers on the right.	$\begin{array}{r}4.075 \\\times 3.9 \\\hline\end{array}$
Multiply the numbers as if they were whole numbers, temporarily ignoring the decimal points.	$\begin{array}{r}4.075 \\\times \, \, 3.9 \\\hline 36675 \\\text{12225} \, \, \, \\\hline 158925\end{array}$
Place the decimal point. Add the number of decimal places in the factors $(1+3)$ . Place the decimal point 4 places from the right.	$\begin{array}{rl}4.075 & \text{3 places} \\ \underline{\times \, \, 3.9} &\text{1 place} \\ 36675 \\ \underline{\text{12225} \, \, \, }\\\color{cyan}{\underbrace{\color{black}{158925}}} & \text{4 places} \end{array}$
The product is positive.	$(3.9)(4.075)=15.8925$

	$(-8.2)(5.19)$
The signs are different.	The product will be negative.
Write in vertical format, lining up the numbers on the right.	$\begin{array}{r}5.19 \\\times 8.2 \\\hline\end{array}$
Multiply.	$\begin{array}{r}5.19 \\\times 8.2 \\\hline 1038 \\\text{4152 } \, \, \\\hline 42558\end{array}$
Place the decimal point 3 places from the right.	$\begin{array}{r}5.19 \\\times 8.2 \\\hline 1038 \\\text{4152 } \, \, \\\hline 42.558\end{array}$
The product is negative.	$(-8.2)(5.19)=-42.558$

	$(0.03)(0.045)$
The product is positive.
Write in vertical format, lining up the numbers on the right.	$\begin{array}{r}0.045 \\\times 0.03 \\\hline\end{array}$
Multiply.	$\begin{array}{r}0.045 \\\times 0.03 \\\hline 135\end{array}$
The decimal point must be 5 places from the right. Add zeros as needed to get the 5 places.
The product is positive.	$(0.03)(0.045) = 0.00135$