Subtraction
Removing things, or numbers from a group of things or a number is what subtraction means in math. When we subtract from a group, the number of items in the group decreases. In subtraction, the minuend is the larger number, and the subtrahend, on the other hand, refers to the part that is being taken away. The answer, or what’s left after subtraction, is called the difference.
For example, “I used to have six pencils, but my brother took three away, so now I only have three.” 3 is subtracted from 6 in this case, to get 3. This can be depicted on a number line as shown in the image.
Here we are counting back by ones. When dealing with larger numbers, this can be accomplished by counting backwards (to the left) by tens, hundreds and even thousands, or by taking the appropriate number of steps to the left of the number line to help us arrive at the solution.
Subtracting by “Adding On”
“What do you add to 3 to get to 6?” is another way of thinking about the subtraction of three from six. This can also be depicted using a number line.
So we start from 3 and count on to reach 6. The number of jumps is the difference.
Subtraction of a Single digit Number from a Two-digit Number
Consider 78 – 5. This can be written as 70 + 8 – 5 .
Now, 8 – 5 = 3.
So, 78 – 5 = 70 + 3 = 73
Similarly, 52 − 6 = 52 − 2 – 4 = 50 – 4 = 46
Regrouping using Models
Regrouping is the process of converting one ten into ten ones or 1 hundred into 10 tens, which is 100 ones. When a digit in the minuend is smaller than the corresponding digit in the subtrahend, we apply the regrouping method. Subtraction by regrouping is also known as trading or borrowing.
Let’s understand this using models. Each cube is a one. This stack contains ten ones.
Let’s consider that there are ten stacks in total.
Ten stacks of ten ones each is equal to one hundred.
1 hundred = 10 tens = 100.
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Solved Examples
Example 1: Each cube is a one. 10 cubes can be grouped to form 1 ten and 10 tens can be grouped to form 1 hundred. Write the number that each of these figures represents.
Solution
1. Here we have 11 stacks of tens. 10 stacks can be grouped to form 1 hundred. So we have 1 hundred and 1 ten. So we have 100 + 10 = 110. Therefore the number is 110.
2. Here we have 13 stacks of tens. 10 stacks can be grouped to form 1 hundred. So we have 1 hundred and 3 tens. So we have 100 + 30 = 130. Therefore the number is 130.
Example 2: Show 243 as its ones, tens and hundreds places.
Solution
In 243, we have 3 ones, 4 tens and 2 hundreds
With the use of blocks:
In a tabular form:
Example 3: 422 – 23 = ?
First we place the digits in their respective places. Then we start from the extreme right.
In ones place,
2 < 3, so we need to borrow. We borrow 1 ten from the ten’ s place then the ten’s place digit becomes 1 and the 2 in the ones place becomes, 10 + 2 = 12.
12 – 3 = 9.
In tens place,
1 < 2, so we borrow 1 hundred from the hundreds place. So the ten’s place is 1 ten + 10 tens = 11 tens.
We then calculate the difference, 11 – 2 = 9.
In the hundreds place,
3 – 0 = 3.
Therefore, 422 – 23 = 399.
Example 4: Chris has 75 math problems to complete as part of his homework. He is aware that eight of the problems are simple, and the remaining are difficult. How many math problems are difficult?
Solution: We need to find the number of difficult problems, so we need to calculate the difference between 75 and 8.
First we place the digits in their respective places. Then we start from the extreme right.
In the ones place,
5 < 8, so we need to borrow. We borrow 1 ten from the ten’ s place, with the ten’s place digit becoming 6, and the 5 in the ones place becomes, 10 + 5 = 15.
Then we calculate the difference in the ones place, 15 – 8 = 7.
In the tens place,
6 – 0 = 6
Therefore, the math problems which are difficult for Tom are 67.
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“Borrow” in subtraction indicates that we take out either tens, hundreds, thousands and so on from one number with a specific place value and assign it to the next number to the right of the number in terms of place value.
No regrouping does not change the number, it only changes how the number is expressed. For example 34 is 3 tens and 4 ones, on regrouping we can also write this as 2 tens and 14 ones, which is the same as 34.
The subtrahend is the number that takes away from the minuend. So if the minuend is smaller than the subtrahend, we won’t be able to take away the needed number. Let’s say that we have 15 balls and you need to take away 20 balls (that is 15 – 20), now this is not possible! You will also learn more on how we can do this in higher grades using the concept of negative numbers.