Question

subtract.
79.42 - 7.8

Explanation:

Step1: Align the decimal points

To subtract decimals, we first align the decimal points. So we can rewrite \(7.8\) as \(7.80\) to have the same number of decimal places as \(79.42\). Now the problem becomes \(79.42 - 7.80\).

Step2: Subtract the numbers

We subtract the numbers column by column starting from the rightmost digit.

• The hundredths place: \(2 - 0 = 2\)
• The tenths place: \(4 - 8\). Since \(4<8\), we borrow \(1\) from the ones place of \(79.42\). The \(9\) in the ones place becomes \(8\), and the \(4\) in the tenths place becomes \(14\). Then \(14 - 8 = 6\)
• The ones place: We had borrowed \(1\) earlier, so the \(9\) (now \(8\)) in the ones place of \(79.42\) and we subtract \(7\) from it. Wait, actually, the ones place of \(79.42\) is \(9\) (before borrowing for tenths place), but after borrowing for tenths, it's \(8\)? Wait no, let's do it properly. The number \(79.42\) can be thought of as \(7\times10 + 9\times1+ 4\times\frac{1}{10}+2\times\frac{1}{100}\) and \(7.80\) is \(7\times1 + 8\times\frac{1}{10}+0\times\frac{1}{100}\). When subtracting the ones place: \(9 - 7 = 2\) (wait, no, the \(79.42\) has \(9\) in the ones place and \(7.80\) has \(7\) in the ones place. Wait, I made a mistake earlier. Let's correct that. The number \(79.42\) is \(79 + 0.42\) and \(7.80\) is \(7+0.80\). So subtracting the whole number parts and the decimal parts separately: \(79 - 7=72\) and \(0.42 - 0.80\). Wait, no, that's not the right way. Let's do column - by - column subtraction:

\[

$$\begin{align*} &\ \ 79.42\\ &-\ \ 7.80\\ &\overline{\ \ 71.62} \end{align*}$$

\]

Wait, let's do it digit by digit:

• Hundredths: \(2-0 = 2\)
• Tenths: \(4 - 8\). We need to borrow from the ones place. The \(9\) in the ones place of \(79.42\) becomes \(8\), and we add \(10\) to the tenths place, so \(4 + 10=14\). Then \(14-8 = 6\)
• Ones place: The \(9\) (now \(8\)) in the ones place of \(79.42\) and we subtract \(7\) from it: \(8 - 7=1\)? Wait, no, the number is \(79.42\), the ones place is \(9\), tens place is \(7\). When we borrow \(1\) from the ones place (for the tenths place), the ones place becomes \(9 - 1=8\), and the tenths place becomes \(4 + 10 = 14\). Then:

• Tenths place: \(14-8 = 6\)
• Ones place: \(8-7 = 1\)
• Tens place: \(7-0 = 7\)

So putting it all together, we get \(71.62\)

Answer:

\(71.62\)