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Decimal Operations

Exercises

Answers

EXAMPLE 5.11

  \(3.7+12.4\)
Write the numbers vertically so the decimal points line up. \(
\begin{array}{r}
3.7 \\
+12.4 \\
\hline
\end{array}
\)
Place holders are not needed since both numbers have the same number of decimal places.  
Add the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers. \(
\begin{array}{r}
1 \, \, \, \, \\
3.7 \\
+12.4 \\
\hline 16.1
\end{array}
\)


EXAMPLE 5.12

  \(23.5+41.38\)
Write the numbers vertically so the decimal points line up. \(\begin{aligned} & 23.5 \\+& 41.38 \\ \hline \end{aligned}\)
Place \(0\) as a place holder after the \(5\) in \(23.5\), so that both numbers have two decimal places. \(
\begin{array}{r}
23.5 \color{red}{0} \\
+41.38 \\
\hline
\end{array}
\)
Add the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers. \(
\begin{array}{r}
23.50 \\
+41.38 \\
\hline 64.88
\end{array}
\)


EXAMPLE 5.13

  \(20-14.65\)
Write the numbers vertically so the decimal points line up. Remember \(20\) is a whole number, so place the decimal point after the \(0\). \(
\begin{array}{r}
20. \quad \\
- 14.65 \\
\hline
\end{array}
\)
Place two zeros after the decimal point in \(20\), as place holders so that both numbers have two decimal places. \(
\begin{array}{r}
20.\color{red}{00} \\
-14.65 \\
\hline
\end{array}
\)
Subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the given numbers. Subtract the numbers as if they were whole numbers. Then place the decimal in the answer under the decimal points in the give


EXAMPLE 5.14

If we subtract \(7.4\) from \(2.51\), the answer will be negative since \(7.4 > 2.51\). To subtract easily, we can subtract \(2.51\) from \(7.4\). Then we will place the negative sign in the result.

  \(2.51-7.4\)
Write the numbers vertically so the decimal points line up. \(
\begin{array}{r}
7.4 \, \, \\
-2.51 \\
\hline
\end{array}
\)
Place zero after the \(4\) in \(7.4\) as a place holder, so that both numbers have two decimal places. \(
\begin{array}{r}
7.4 \color{red}{0}\\
-2.51 \\
\hline
\end{array}
\)
Subtract and place the decimal in the answer. \(
\begin{array}{r}
7.40 \\
-2.51 \\
\hline 4.89
\end{array}
\)
Remember that we are really subtracting \(2.51-7.4\) so the answer is negative. \(2.51-7.4=-4.89\)