Introduction to Subtraction
Let’s understand the meaning of subtraction through an example. George has $7. He goes to a shop and buys some candies for which he pays $6. How much is George left with? We can find the change through the subtraction operation. The term “subtraction” refers to the process of subtracting or taking away a given number from another. In other words, it is used to figure out the difference between two numbers. Subtraction refers to calculating the difference between two quantities. Subtraction is the opposite of addition and is signified by the minus sign (-).
Subtraction Strategies
Subtraction can be made easier through four strategies:
1. Subtraction using an open number line
2. Compensation
3. Using models to subtract
4. Regrouping
Let us discuss these strategies in detail:
Subtraction using an open number line
A number line is a straight line with numbers placed at equal intervals or segments along its length. A number line can be drawn horizontally and can be extended in any direction indefinitely.
Why do we need an open number line?
We use a number line because it is a convenient/good way to represent numbers using a visually understandable figure. It is also easy to visualize operations like subtraction and addition on a number line. Let us have a look at how we can subtract two numbers using a number line.
Subtracting tens using a number line:
To subtract 10 from 64 using a number line, first we move backwards and start counting from one to ten. So, we will start counting from 64, 63, 62 ,61,……, 54. The tenth position, which is 54 on the number line, will be the result.
Subtracting hundreds using a number line:
To subtract 100 from 233 using a number line, first we move backwards and start counting from one to hundred. So, we will start counting from 233, 232, 231, 230,,……., 133. The hundredth position, which is 133 on the number line, will be the answer.
Compensation Strategy
The compensation strategy of subtraction is the process in which we use an approximate number near the tens and then we subtract. Usually, we take approximations near tens, twenties, hundreds, etc.
Example: It is easy to do simple subtractions like 20 – 10 = 10, but 21 – 7 might seem tricky as we can’t calculate it quickly. So, we can approximate 7 by 10 through the compensation method. The equation following the compensation strategy will be: 21 – 7 = 11.
Now add 3 to 11 as we earlier compensated the 3. The final answer is 14.
By using compensation, we can do mental math to add or subtract greater numbers.
We compensate a number with figures from other numbers to make mental math easier.
We can use the equal addition method when we subtract numbers.
We add the same amount to each number so they are more compatible.
Example: Subtract 7 from 33.
As we can see, 7 is the nearest to 10. We will add 3 in 7. After compensation, the new number will be 10. So, we will subtract 10 from 33 (33 – 10 = 23).
We get 23 as a result. As we incremented from 7 to 10 by adding 3,we will add 3 to the result and get the final answer which is 26.
Example: Subtract 29 from 74 by compensation strategy.
As we can see, 29 is the nearest to 30. We will add 1 to 29. After compensation, the new number will be 30. So, we will subtract 30 from 74 (74 – 30 = 44).
We get 44 as a result. As we incremented 29 to 30 by adding 1, we will add 1 to the result and we will get the final answer which is 45.
Using the model strategy to subtract
The model method involves visualization. Firstly when we see the two numbers then easily we can visualize that this method we have to use like place value, by regrouping etc. Sometimes when we see the pictures we are able to find the difference.
Here’s an example of the model strategy:
William has 7 oranges. He gives 2 oranges to Noah. How many oranges is William left with?
We can take 2 oranges out of a total of 7. Then William will be left with 5 oranges.
Regrouping
What is meant by regrouping in math?
Regrouping can be defined as the process of grouping numbers in tens. It is a method of subtracting numbers below a hundred. It makes math operations such as addition and subtraction easier.
Consider the following question: 11 + 9 = ?.
When we add 1 + 9 in the unit’s place, the result will be 10. In this case, we need to regroup. So, 1 will go to 1’s column and the sum will be 20.
What is subtraction with regrouping?
In the process of regrouping for subtraction, each place value reaches its highest place individually. Regrouping is ideal for subtracting big numbers.
For example, while subtracting 28 from 72, we are met with the challenge that 8 is greater than 2. We will use the regrouping method here.
First, write the equation in column form.
From tens, 1 will go to 2. So the new number is 12. As a result, we will subtract 8 from 12 which equals 4.
Now, At Tens we have 6 Tens as earlier regroup 1 as 10 ones with 2.
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Solved Examples on Subtraction Strategies
Example 1: Use a number line to subtract 20 from 62.
Answer:
First, identify the numbers 20 and 62 on the number line.
.
To subtract 20 from 62 using a number line, move backwards and start counting from one to 20. 20 is the same as the 20. After 20 ones, we get 42. Hence, 42 is the solution .
Example 2: Use the compensation method to subtract.
Answer:
It is easier to subtract 50 as compared to 46 from any number. Here we subtract a further 4 than we need to subtract and therefore, to get the right solution at last we have to add 4.
Example 3: Use a model to solve the following:
37 – 4.
Answer:
37 and 4 can be written in the model form as:
Now, from the unit place, subtract 4 from 7. Count the tens and the ones that are left.
From the above figure, we can conclude that we have 3 tens and 3 ones. Therefore, the result will be 30+3=33.
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The four strategies for subtraction include: using models for subtraction, compensation, using open number lines, and regrouping.
Subtraction is a mathematical operation that represents the removal of objects from a collection.
Regrouping in subtraction is possible if a single digit is being subtracted from a double digit and for double-digit subtraction. Regrouping can be done in subtraction when the answer is greater.