Subtração de numeros decimais

(Video) Decimal Arithmetic

by Math Antics

This video by mathantics covers adding decimals, subtracting decimals, multiplying decimals, and dividing decimals.

$\large{\text{Summary}}$

Subtracting decimal numbers follows the exact same process as subtracting two integers. You need to to correctly line up the numbers, then you can subtract vertically in each place value. The key is to line up your numbers at the decimal point.

Let's look at an example: $7.122-3.41$

Start by lining up the numbers vertically at the decimal point. $$\begin{align} &7.122\\ -\quad&3.41\\ \hline \end{align}$$ Add zeros after the decimal point to any empty spaces. $$\begin{align} &7.122\\ -\quad&3.41\color{#29A603}{0}\\ \hline \end{align}$$ Finally, we add as we would integers. $$\begin{align} &7.122\\ -\quad&3.410\\ \hline &3.712 \end{align}$$

We're going to line up the decimal points and subtract. $$\begin{align}10&.53\

• \phantom{00} 7&.3 \color{gray}{0}\ \hline 3&.23 \end{align}$$

Subtracting Decimals

Here is an example of how to subtract one decimal from another: $$13.75-5.5=8.25$$

In the step where you "tack on zero(s)," all you have to do is add the necessary amount of zeros so that both decimals have the same amount of digits after the decimal point. Lining up your numbers like this may make it easier to subtract later!

Let's do another example to practice.

Step One: Line Up the Decimal Points

$$\begin{align} 174&.3\\ - \quad \phantom{ } 16&.57\\ \hline \end{align}$$

Step Two: Tack On Zero(s)

$$\begin{align} 174&.30\\ - \quad \phantom{ } 16&.57\\ \hline \end{align}$$

(Now, each of our decimals has $2$ digits after the decimal point!)

Step Three: Drop Down Decimal Point

$$\begin{align} 174&.30\\ - \quad \phantom{ } 16&.57\\ \hline &. \end{align}$$

Step Four: Subtract Normally

$$\begin{align} 174&.30\\ - \quad \phantom{ } 16&.57\\ \hline 157&.73 \end{align}$$

Subtracting decimals works the same way as subtracting whole numbers. For decimals with multiple digits (or decimals that are attached to whole numbers), line up the numbers by place value and then subtract column by column.

The Steps

Subtracting multi-digit numbers can be tricky, so here are some steps:

1. Line up the numbers by their decimal point
2. Write the decimal point in the same place on your answer line and add $0$'s to the end of the shorter number so that they're the same length.
3. Subtract the numbers column by column, starting with the rightmost digit and moving left.

Let's try it on $32.1 - 5.986$.

Step 1: Line up the numbers.

That's petty simple. Just find the decimal point, then stack the numbers on top of each other so that the decimal points line up.

$$\begin{align*} 32&.1\\ - 5&.986\end{align*}$$

Step 2: Set up the numbers.

Now, just add $0$'s to the end of the shorter number (in this case, $32.1$) so that both numbers are the same length, and find the spot for the decimal point on the line where you're going to write the answer.

$$\begin{align*} 32&.100\\ - 5&.986\\\hline &.\end{align*}$$

Step 3: Subtract column by column.

Now, the actual subtraction begins! To subtract multi-digit numbers, we just subtract each place individually, moving from right to left in the numbers.

In this situation, we'll have to borrow from places with higher value in the number. To do this, we essentially "steal" from the place in the number that's one above the one you're subtracting. For the problem we're doing, that would be the hundredth place...but that's $0$ too! So, we have to move up to the tenths place, steal the $1$, and sort of cascade down so that we end up with "$9$" in the hundredths place and "$10$" in the thousandths place. $10 - 6 = 4$, so we get $4$ in the thousandths place.

We can keep using this strategy to move leftward through the number until we get:

$$\begin{align*} 32&.100\\ - 5&.986\\\hline 26&.114\end{align*}$$

Done!