ধ্বনাত্মক পূর্ণসংখ্যার যোগ

Just add!

Natural numbers ($1, 2, 3, 4,$ etc.) are the numbers you see most often. They don't have any fractions or decimals attached to them, and they exist above or to the right of $0$ on the number line.

When you add natural numbers, you just move up (or to the right) on the number line. For example, when you add $4 + 5$ you can start at $4$:

Then, count up $5$ points. You can think of "$+$" as sending a number to the right.

Done! Adding $5$ means we stepped $5$ places up the number line, so $4 + 5 = 9$.

$\\$

Count backwards

Subtracting a positive number from a positive number works the same way as adding a negative number to a positive number. It might help to conceptualize it a little differently, though. Let's work with the expression $6 - 2$.

First, let's find all our numbers on the number line.

Since we're subtracting $2$ from $6$, we're going want to use $6$ as our new anchor point and figure out $2$'s position from it. So, let's find $2$'s position relative to $0$.

Now, we're subtracting $2$. Subtracting a number is pretty much the same as adding the negative version of the same number, so we could rewrite our expression as $6 + (-2)$. To find this, we can just flip $2$'s position relative to $0$:

Now, let's just transpose $-2$ to the same relative position to $6$ as it is to $0$ now.

Now we can see that $6 - 2 = 4$. When you subtract a number, you basically change it's sign (so positive numbers become negative, and negative numbers become positive) and then add it like you would otherwise.

Subtracting Positives or Zero

Subtracting a positive integer is essentially the same as adding a negative integer.

When you subtract positive integers, you are moving down (or to the left) on the number line.

For example, let’s take a look at the expression $9-2$.

First, let’s draw a number line and start at $9$.

We now have to subtract $2$ from $9$.

Count down $2$ points starting from $9$.

Now, try this problem.

Draw a number line starting at $10$ and subtract $5$ from $10$ by counting down $5$ points starting from $10$.

The process of subtracting large and multiple internets is the same.

Let’s look at the expression $47{,}989-2{,}823$.

First, we want to stack the numbers vertically. $$\begin{align} &47989 \\ -&\,\,\,2823 \\ \hline \end{align}$$ We want to subtract the one digits: $9-3=6$. $$\begin{align} &47989 \\ -&\,\,\,2823 \\ \hline &\,\,\,\,\,\,\,\,\,\,\,\,6 \end{align}$$ We now want to subtract the tens digits: $8-2=6$. We can drop the tens digit ($6$) below. $$\begin{align} &47989 \\ -&\,\,\,2823 \\ \hline &\,\,\,\,\,\,\,\,\,66 \end{align}$$ Next, subtract the hundreds digits: $9-8=1$. We can drop the hundreds digit ($1$) below. $$\begin{align} &47989 \\ -&\,\,\,2823 \\ \hline &\,\,\,\,\,\,166 \end{align}$$ Next, subtract the thousands digits: $7-2=5$. We can drop the thousands digit ($5$) below. $$\begin{align} &47989 \\ -&\,\,\,2823 \\ \hline &\,\,\,5166 \end{align}$$ Lastly, subtract the ten thousands digits: $4-0=4$. We can drop the ten thousands digit ($4$) below. $$\begin{align} &47989 \\ -&\,\,\,2823 \\ \hline &45166 \end{align}$$

Let's try an example.

First, we want to stack the numbers vertically. $$\begin{align} &56348 \\ -&15384 \\ \hline \end{align}$$ We want to subtract the one digits: $8-4=4$. $$\begin{align} &5634\color{#29A603}{8} \\ -&1538\color{#29A603}{4} \\ \hline &\,\,\,\,\,\,\,\,\,\,\,\,\color{#29A603}4 \end{align}$$ Next, we want to subtract the tens column: $4-8$. This number is negative, so we need to “borrow” $1$ from the hundreds column. This gives us $14-8=6$. Drop the tens digit below ($6$), but make sure to subtract $1$ from the hundreds place. $$\begin{align} &56\color{#29A603}{24}8 \\ -&153\color{#29A603}{8}4 \\ \hline &\,\,\,\,\,\,\,\,\,\color{#29A603}{6}4 \end{align}$$ Now we need to subtract the hundreds column: $2-3$. This number is negative, so we need to "borrow" $1$ from the thousands column. This gives us $12-3=9$. Drop the hundreds digit below ($9$), but make sure to subtract $1$ from the thousands place. $$\begin{align} &5\color{#29A603}{52}48 \\ -&15\color{#29A603}{3}84 \\ \hline &\,\,\,\,\,\,\color{#29A603}{9}64 \end{align}$$ Next, subtract the thousands column: $5-5=0$. $$\begin{align} &5\color{#29A603}{5}248 \\ -&1\color{#29A603}{5}384 \\ \hline &\,\,\,\color{#29A603}{0}964 \end{align}$$ Lastly, subtract the ten thousands column: $5-1=4$. $$\begin{align} &\color{#29A603}{5}5248 \\ -&\color{#29A603}{1}5384 \\ \hline &\color{#29A603}{4}0964 \end{align}$$ Answer: $56{,}348-15{,}384 = 40{,}964$

Adding Positive Integers or Zero $\\$ When you add two positive integers together, you move up (to the right) on the number line. $\\$ Let’s take a look at an example. Solve: $5+2$. $\\$ First, draw a number line and start at $5$.

Next, add $2$ to $5$. Count up $2$ units starting from $5$.

As illustrated in the number line above, $5+2=7$. $\\$ Let's look at one more example. $\\$ Solve: $3+3$ $\\$ First, draw a number line and start at $3$.

Next, add $3$ to $3$. Count up $3$ units starting from $3$.

As illustrated in the number line above, $3+3=6$. $\\$ Now, try a couple of examples without drawing a number line.

$$6+5=11$$

$$\begin{align} 8+19+11 &= 27 + 11 \\ &= 38 \\ \end{align}$$

(Video) Adding and Subtracting Integers

by Math Antics

This video by Math Antics goes over all the different ways to add and subtract integers. It covers adding and subtracting whole numbers, subtracting a positive from a negative, adding negatives or zero, negative plus positive, subtracting negatives or zero, and subtracting a negative from a positive.

$\large{\text{Summary}}$

Adding positive numbers falls under the first case shown in the video. We are taking a positive number and making it more positive. $$7+3$$ We are starting at $7$ and making it more positive by $3$ units. We are going to move $3$ units to the right on the number line up to $10$.