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Subtraction Within 100

What is Subtraction?


Imagine you have 32 cubes. If you give 14 of them to a friend, how can you figure out how many you have left?
\(-\) \(=\; ?\)
This is called subtraction. Let's explore how it works!

When we start with 32 and take 14 away, we can see what is left.
\(-\) \(=\)
We can see that there are 18 cubes left!$$32-14=18$$Counting blocks one by one can take a long time. In this chapter, we will learn some powerful strategies to subtract any two numbers.


Definition Subtraction
Subtraction means taking an amount away from a group to find out what is left. This result is called the difference.
  • The minus sign (\(-\)) tells us to subtract.
  • The equals sign (\(=\)) shows that both sides have the same value.
We can show "thirty-two minus fourteen equals eighteen" in different ways:
  • With numbers: $$32 - 14 = 18$$
  • With cubes:
    \(-\) \(=\)
  • With part whole model:

Subtracting Ones Then Tens

Method Subtracting Ones Then Tens Using Cubes
To calculate:
\(37 - 14\)
\(-\)
  • Step 1: Subtract the ones $$7 \text{ ones} - 4 \text{ ones} = 3 \text{ ones}$$
  • Step 2: Subtract the tens $$3 \text{ tens} - 1 \text{ ten} = 2 \text{ tens}$$
  • Result: There are 2 tens and 3 ones. So, $$37 - 14 = 23$$
    \(-\) \(=\)
Now let's try \(32 - 14\). When we look at the ones place, we need to do:$$2 \text{ ones} - 4 \text{ ones}$$We don't have enough ones to take 4 away! To solve this, we can regroup. We will trade 1 ten for 10 new ones. Now we will have enough. Let's see how it's done!
Method Subtracting Ones Then Tens with Regrouping
To calculate:
\(32 - 14\)
\(-\)
  • Step 1: Subtract the ones with regrouping $$2 \text{ ones} - 4 \text{ ones}$$ We don’t have enough ones, so we borrow 1 ten from the tens place, turning it into 10 ones. Now we have \(12\) ones. $$12 \text{ ones} - 4 \text{ ones} = 8 \text{ ones}$$
    \(-\) \(=\)
  • Step 2: Subtract the tens $$3 \text{ tens of 32} - 1 \text{ ten of 14} - 1 \text{ ten of borrowing} = 1 \text{ ten}$$
  • Result: There is 1 ten and 8 ones. So, $$32 - 14 = 18$$ \(-\) \(=\)

Subtraction in Columns

Method Subtraction in Columns
To calculate:$$37 - 14$$
  • Step 1: Set up the subtraction
    Write the numbers in a vertical column, making sure the digits line up by place value (ones under ones, tens under tens).
  • Step 2: Subtract the ones $$7 \text{ ones} - 4 \text{ ones} = 3 \text{ ones}$$
  • Step 3: Subtract the tens $$3 \text{ tens} - 1 \text{ ten} = 2 \text{ tens}$$
  • Result: There are 2 tens and 3 ones. So,$$37 - 14 = 23$$
Method Column Subtraction with Regrouping
To calculate:
\(32 - 14\)
  • Step 1: Set up the subtraction
    Write the numbers in a vertical column, making sure the digits line up by place value (ones under ones, tens under tens).
  • Step 2: Regroup 1 Ten $$2 \text{ ones} - 4 \text{ ones}$$ We don’t have enough ones, so we borrow 1 ten from the tens place, turning it into 10 ones. Now we have \(12\) ones.
  • Step 3: Subtract the ones $$12 \text{ ones} - 4 \text{ ones} = 8 \text{ ones}$$
  • Step 4: Subtract the tens $$3 \text{ tens (from 32)} - 1 \text{ ten (from 14)} - 1 \text{ ten (borrowed)} = 1 \text{ ten}$$
  • Result: There is 1 ten and 8 ones. So, $$32 - 14 = 18$$