Subtraction on a Number Line

Subtraction on a number line helps us to find the difference between two numbers easily, given the numbers are small. These include integers, fractions, and decimal numbers. It also helps us to locate the result of a subtraction problem.

The three main parts of a subtraction problem are:

1. Minuend: The number from which we subtract
2. Subtrahend: The number that we subtract from the minuend
3. Difference: The result of subtraction

For example, 10 – 3 gives 7

To perform subtraction, we first locate the minuend on the number line. Then we move back the number of steps based on the value of the subtrahend.

There can be three such cases:

Positive Number from a Positive Number

Subtracting a positive number from a positive number is just a normal subtraction. In the above example, 10 – 3 gives 7. Here, 10 is the minuend, 3 is the subtrahend, while 7 is the difference or the result of subtraction.

As the minuend 10 is a positive number, we move 10 steps to the right of 0.

Similarly, the subtrahend 3 is also positive; thus, we move 3 steps to the left of 10.

Thus, the answer is 7.

Subtracting Decimals

Subtracting Fractions

Positive Number from a Negative Number

While subtracting a positive number from a negative number, the operation turns into the addition between those two numbers, and the sign becomes negative. While subtracting two numbers, we can change the sign of the subtrahend and follow the addition rules.

For example, (-12) – 2 = (-14). Here, (-12) is the minuend, 2 is the subtrahend, while (-14) is the difference or the result.

Now (-12) – 2 is written as (-12) + (- 2) 

 (-12) being a negative number, we move 12 steps to the left of 0.

Finally, (- 2) being negative, we move 2 more steps to the left side of (-12) to get the result.

Thus, the answer is (-14).

Negative Number from a Negative Number

Subtraction of a negative number from another negative number turns into addition, an addition operation. Thus subtracting a negative number is the same as adding the absolute value of that number. For example,

(-9) – (-4) = (-5). Here, (-9) is the minuend, (-4) is the subtrahend, while (-5) is the difference or the result.

Now (-9) – (-4) is written as (-9) + 4  

As (-9) is a negative number, we move 9 steps to the left of 0.

Next, 4 being a positive number, we move 4 steps to the right side from (-9) to get the answer.

Thus, we get the answer (-5)

Subtraction on an Open Number Line

For 2-digit and 3-digit subtraction, we use an open number line with no numbers marked on it.

2-Digit subtraction

For example, 55 – 34 gives 21. Here, 55 is the minuend, 34 is the subtrahend, while 21 is the difference or the result.

As minuend 55 is a positive number, we mark it on an open number line to the right side of 0.

Next, we count the number of tens and ones in the subtrahend, i.e., 34.

34 = (3 × 10) + (4 × 1)

Finally, we skip count back 3 times by 10s and then 4 times by 1s and mark the numbers (45, 35, 25,…., 21) simultaneously on the number line after every jump.

Thus the result is 55 – 34 = 21.

3 -Digit Subtraction

Like 2-digit subtraction, we can also perform 3-digit subtractions using an open number line.

For example, 390 – 259 gives 231. Here, 390 is the minuend, 259 is the subtrahend, and 131 is the difference or the result.

As minuend 390 is a positive number, we mark it on an open number line to the right side of 0.

Next, we count the number of hundreds, tens, and ones in the subtrahend, i.e., 259.

259 = (2 × 100) + (5 × 10) + (9 × 1)

Now we take 2 longer jumps to count back 100s, 5 moderate jumps to count back 10s, and 9 shorter jumps to count back 1s. We can also skip count to show all the jumps and mark the numbers (190, 140, 131) simultaneously on the number line after every jump.

Thus we get the result 390 – 259 = 131

Rules for Subtracting Two Numbers

Let us summarize the rules for subtracting two numbers below. We denote minuend by M and subtrahend by S.

Numbers Sign	Operation	Answer Sign	Example
(+) – (+),|M| > |S|	Subtract	+	5 – 2 = 3
(+) – (+), |M| < |S|	Subtract	–	7 – 9 = (-2)
(+) – (-), |M| > |S| or |M| < |S|	Add	+	6 – (-4) =  10, 4 – (-6) = 10
(-) – (-), |M| > |S|	Subtract	–	(-7) – (-4) = (-3)
(-) – (-), |S| > |M|	Subtract	+	(-4) – (-7) = 3
(-) – (+), |M| > |S| or |S| > |M|	Add	–	(-9) – (4) = (-13), (-4) – (9) = (-13)