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Adding 2-Digit Numbers

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Basics on the topic Adding 2-Digit Numbers

Adding Two Digit Numbers

Imagine you own 14 toys and your sibling owns 17 toys. Now you want to calculate how many toys you own together! In order to do this, you can use standard algorithm to solve 2 digit addition without regrouping and 2 digit addition with regrouping.

In this text, we will learn how to do 2 digit addition using the standard algorithm.

The standard algorithm is a method to use where the numbers are set up vertically, based on place values. This is an efficient way to find sums when there are several equations you need to solve.

In the explanation, there will be examples that have you adding 2 digit numbers without regrouping as well as adding 2 digit numbers with regrouping.

Adding Two Digit Numbers – Example

Adding two digit numbers using standard algorithm without regrouping

To solve this 2-digit addition problem, we set the equation up vertically, with one addend on top of the other in order of their place values. We will find the sum of the numbers by adding the digits from right to left, beginning with the ones place.

What is six plus two more?
Place the eight below the line directly under the ones place.

Next, we move one place over to the left and now we add the tens place.

How many are three tens and two tens? We can write the digit five below the line under the tens place because the five represents five tens or fifty.

The sum is 58.

Adding two digit numbers using standard algorithm with regrouping

In this problem, we will need to do 2-digit addition with regrouping. We are going to find the sum of fourteen and forty-seven.

Starting with the ones place, four plus seven equals eleven. What do you notice about the sum of the ones place?

Eleven is a two-digit digit number made up of a one and one ten. So, one is written underneath the ones place and one is regrouped on top of the tens place.

Now we add the tens, including this new value added at the top. What is the sum of ten, forty, and ten? Sixty, which means we have six tens.

The sum is 61.

Do you now know how many toys your sibling and you own together? Correct, it is 31 toys in total! For this equation, you needed to regroup a number.

Adding Two Digit Numbers – Additional Practice

How do you add two digit numbers using the standard algorithm?

Remember: The standard algorithm is a method to use where the numbers are set up vertically, based on place values.

With the standard algorithm you can represent an addition of two numbers neatly to solve it with ease. Have another look at our example addition from earlier:

Tens Ones
1 4
+ 4 7
6 1

At the end of the video, you can find exercises for the continued practice of 2 digit addition as well as a 2 digit addition worksheets. Enjoy!

Transcript Adding 2-Digit Numbers

Mr. Squeaks and Imani are taking part in the annual lake clean up contest. They are hoping this is the year they will take their place on the winners' stand! Although the real reward is a clean lake, the winner of this contest will be the participant that collects the greatest total weight of litter. In order to find the winner we need to use an efficient, or quick, way of adding sets of numbers called column addition. “Adding Two Digit Numbers Using Column Addition" Let’s look at the items our contestants have retrieved from the lake. As you can see we have several two digit addition problems to solve, so we will want to use the best way to find the answers without having to do a lot of steps. Let's use the spotted mouse's numbers as an example. Spotted Mouse collected a thirty-six kilogram bike and a twenty-two kilogram chair. You already have been shown how to add two digit numbers using number lines and the base ten blocks. In the column addition, we use those same ideas, but we simplify the problem. We set the equation up vertically, with one number or addend on top of the other in order of their place values. We line up the place values by putting the two underneath the six and the two tens under the three tens. Make sure to include the addition sign. We always want to remember what we are supposed to be doing with the numbers. We will find the sum of the numbers by adding the digits from right to left, beginning with the ones place. What is six plus two more? Place the eight below the line directly under the ones place. Next, we move one place over to the left and now we add the tens place. How many are three tens and two tens? We can write the digit five below the line under the tens place because the five represents five tens or fifty. Spotted Mouse collected fifty-eight kilograms of litter. Let’s try it out with Imani's finds and see how she did. We are going to find the sum of fourteen and forty-seven. Starting with the ones, four plus seven equals eleven. What do you notice about the sum of the ones place? Eleven is a two digit number made of one one and one ten. So one is written underneath the ones place and one is regrouped on top of the tens place. Now we add the tens, including this new value added at the top. What is the sum of ten, forty and ten? Sixty. So,we have six tens. Imani took sixty-one kilograms of litter from the lake. Wow! There is one more contestant that needs their collection rounds added. Our own, Mr. Squeaks! How did Mr. Squeaks do in the contest? We set up the problem by writing the sixty-five over the seventy-four. We add five and four in the ones place and get nine. No regrouping is needed. We add six and seven in the tens place and that made thirteen tens. Hmmm, we have more than one digit in this answer. Based on the last problem, can you think what we need to do next? When we have a two digit sum, we'll regroup it to the next place value. The next place value is the hundreds. Because thirteen has a value greater than ten, we regrouped the final digit, one, to the hundreds place. Mr. Squeaks has one hundred and thirty-nine kilograms! Remember in column addition, we line up numbers vertically, or one top of the other, based on place values. We start adding with the ones place and move to the left to add the tens. Sometimes we need to regroup into the next place value when our answer is greater than ten. Let’s head back to the leader board and see about declaring a winner! Yes! He did it! Mr. Squeaks has taken first place! Congratulations Mr. Squeaks, well done! You've won the trophy and everyone made the lake beautiful again!

Adding 2-Digit Numbers exercise

Would you like to apply the knowledge you’ve learnt? You can review and practice it with the tasks for the video Adding 2-Digit Numbers .
  • Calculate the answer.

    Hints

    Add the digits in the ones column first.

    Add the tens column next.

    Solution

    Add the digits in the ones column first.

    4 + 5 = 9

    Then add the digits in the tens.

    3 tens + 2 tens = 5 tens

    34 + 29 = 59

  • Place the digits onto the grid.

    Hints

    Make sure the tens number is in the T column.

    Make sure the ones are in the O column.

    The H column represents hundreds.

    Solution

    We need to make sure the numbers are in the correct column.

    If it has 3 digits it will have a hundred, tens, and ones digit.

    310 has 3 hundreds, 1 ten and 0 ones

    27 has 2 tens and 7 ones

    Then add each column.

    0 + 7 = 7

    1 ten + 2 tens = 3 tens

    3 hundreds + 0 hundreds = 3 hundreds

    310 + 27 = 337

  • Calculate the answers to the equations.

    Hints

    Add up the ones column first.

    Make sure if your answer is 2* or more digits you carry it across.

    After adding the ones column, move on to the tens column.

    Don't forget to check if there are any numbers that you carried across from the ones column.

    Solution

    See image for the 1st problem

    For the 2nd problem:

    45 + 63 = 108

    For the 3rd problem:

    44 + 12 = 56

    For the 4th problem:

    69 + 72 = 141

  • Match the question to the correct answer.

    Hints

    Layout the numbers in the format above.

    Add the digits in the ones column first, followed by the digits in the tens column.

    Add up all of the digits in the ones column first. If the answer is greater than 9, carry across the extra ten.

    If the number in the tens column is greater than 9, make sure you carry across to the hundreds column.

    Solution

    Using the layout above, workout the answers to the equations.

    1. First add your ones column.
    2. Don't forget if your answer from adding the ones column is 2 digits, carry the tens number from your answer across to the tens column.
    3. Next, add your tens column.
    4. If your answer from the tens column is more than 2 digits, carry across the hundreds digit (the first digit from the number).

    38 + 64 = 102 see image above

    27 + 35 = 62

    39 + 54 = 93

    74 + 57 = 131

  • Identify the place value of the numbers below.

    Hints

    If the number has two digits and ends in a zero, it is a ten.

    If it is a single digit it is a one.

    The blue lines represent ten.

    The yellow cubes represent one.

    In this example, you can see how all the one numbers are in the O column. We have a mixture of words, numerals and yellow ones cubes.

    In the tens column, we have a mixture of words, numerals and base 10 blocks. They all show values of ten

    Solution

    Two digit numbers have tens in them.

    Single digit numbers are classed as ones.

  • Calculate the answers to the equations.

    Hints

    Solution

    First, add the digits in the ones column.

    4 + 7 = 11. 1 ten would go into the tens column with the other tens digits, and the 1 representing the ones would go in the answer box under the ones

    Then add all of the digits in the tens column.

    1 + 8 + 3 = 12

    As the answer to this is greater than 9, we need to carry across to the hundreds column.

    33 + 42 = 75

    18 + 71 = 89

    84 + 37 = 121

    69 + 33 = 102