Multiplying Fractions

Examples and Exercises

Answers

EXAMPLE 5.15

	\((3.9)(4.075)\)
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.	\((3.9)(4.075)=15.8925\)

EXAMPLE 5.16

	\((-8.2)(5.19)\)
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.	\((-8.2)(5.19)=-42.558\)

EXAMPLE 5.17

	\((0.03)(0.045)\)
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.	\((0.03)(0.045) = 0.00135\)

TRY IT 5.29

\(27.4815\)

TRY IT 5.30

\(87.6148\)

TRY IT 5.31

\(-13.427\)

TRY IT 5.32

\(38.122\)

TRY IT 5.33

\(0.00348\)

TRY IT 5.34

\(0.00603\)