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Multiplying 2 digit numbers by 2 digit numbers

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Basics on the topic Multiplying 2 digit numbers by 2 digit numbers

2 Digit by 2 Digit Multiplication

Multiplication is an essential mathematical operation. But how do you multiply 2-digit numbers by 2-digit numbers without regrouping? Here you can learn how to multiply by double digits. After learning how to multiply 2-digit numbers, try out our double digit multiplication worksheets and practice exercises!

How do you multiply a 2 digit number by a 2 digit number? Multiplying by two digit numbers can be done in a few easy steps:

Step # What to do
1 Multiply the ones placed in the bottom factor by both
place values in the top factor, regrouping as needed.
2 Add a placeholder, or zero.
3 Multiply the tens placed in the bottom factor by both
place values in the top factor, regrouping as needed.
4 Add the partial products to get the total.

If you are still wondering how to multiply two digit numbers by two digit numbers, look at the example below.

Multiplying a 2 digit number by a 2 digit number

In this example, we will be multiplying two digit numbers in order to find out how many sunflower seeds they have. Since there are forty-eight containers with thirty-two in each, we will find the product of forty-eight and thirty-two.

The first step is to multiply the ones place in both numbers, so we multiply two times eight to get sixteen, regrouping the one to the tens place. Next multiply two times four to get eight, adding the one we regrouped to get nine.

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The second step is to add the placeholder, or zero.

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The third step is to multiply the tens place in the bottom number by both place values in the top number. We multiply three and eight to get twenty-four, and regroup the two to the tens place. Next multiply three times four to get twelve, adding the two we regrouped to get fourteen.

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The last step is to add the partial products ninety-six and one thousand four hundred and forty to get the final product. Forty-eight times thirty-two is one thousand five hundred and thirty-six.

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Multiplying Two Digit by Two Digit Numbers – Summary

Remember, when we are multiplying two 2 digit numbers, you can follow these easy steps:

  • Multiply the ones placed in the bottom number by both place values in the top number, regrouping as needed.
  • **Add a placeholder, or zero.
  • Multiply the tens place in the bottom number by both place values in the top number, regrouping as needed.
  • Add the partial products.

Have you practised how to multiply 2-digit numbers yet? On this website you can find a multiplying two digit numbers by two digit numbers worksheet, multiplying two digit numbers by two digit numbers word problems, activities, and exercises.

Transcript Multiplying 2 digit numbers by 2 digit numbers

When a cool breeze whizzed through Mr. Squeaks' and Imani's home, they started to harvest some food into containers for winter. They've collected corn and sunflower seeds for their hibernation, but they need help calculating how much they have. In order to do that, we need to practice "Multiplying Two-Digit Numbers by Two-Digit Numbers". They have thirteen containers with twenty-one cobs of corn in each. We need to find the product of thirteen times twenty-one. The first step is to multiply the ONES place in the bottom number by BOTH place values in the top number. Start by multiplying the numbers in the ONES place. Which numbers are in the ONES place? The bottom number has a ONE, and the top number has a THREE, so multiply one times three to get the product three. We make sure to put the three in the ONES place, because that is the place value we multiplied. Next multiply the ONES place in the bottom number by the TENS place in the top number. One times one equals one. We make sure to put the one in the TENS place, because that is the place value we multiplied. Now that we've multiplied the ones place by both numbers in the top number, the second step is to add a placeholder, or a zero HERE. A placeholder is used because we are multiplying the TENS place in the bottom number next, so we write the products starting in the TENS place. Now multiply the TENS place in the bottom number by the ONES place in the top number. Two times three equals six. Next multiply the two and one in the TENS place to get the product two. Last, find the sum of the partial products thirteen and two hundred and sixty. Thirteen times twenty-one is two hundred and seventy-three. That's a lot of corn! Next, let's calculate how many sunflower seeds they have. There are forty-eight containers with thirty-two seeds in each. The first step is to multiply the ONES place in the bottom number by BOTH place values in the top number. What do we get when we multiply the ONES place in both numbers? Two times eight is sixteen, and since sixteen is a TWO DIGIT number we need to regroup, so write the six HERE and regroup the one to the tens place HERE. Next, multiply the ONES place in the bottom number by the TENS place in the top number. Two times four is eight, and add the one we regrouped to get nine. Before we move on, cross out the ONE that we regrouped, that way, if we need to regroup later we won't get confused. The second step is to add the placeholder HERE. Next, multiply BOTH place values in the top number by the TENS place in the bottom number. Three times eight is twenty four, so write the four HERE and regroup the two to the tens place HERE. Next, multiply three times four to get twelve and add the two we regrouped to get fourteen. The last step is to find the sum of the partial products ninety-six and one thousand four hundred and forty. Mr. Squeaks and Imani have one thousand five hundred and thirty-six sunflower seeds. Remember, when you multiply a two-digit number by a two-digit number you first "Multiply the ONES place in the bottom number by both place values in the top number", regrouping as needed. The second step is to, "add a placeholder". The third step is to, "Multiply the TENS place in the bottom number by both place values in the top number", regrouping as needed. The last step is to find the sum of the partial products to get the final answer. After all that calculating, Mr. Squeaks realises he has even more food than he thought because Imani doesn't have a mouth to eat all of that food! So, what does Imani eat?

Multiplying 2 digit numbers by 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 Multiplying 2 digit numbers by 2 digit numbers.
  • Can you remember how to multiply a 2-digit number by another 2-digit number?

    Hints

    Do you multiply the top number by the tens or the ones in the bottom number first?

    The picture gives you a clue about where to start when multiplying a 2-digit number by another 2-digit number.

    The partial products are the values you have once you have multiplied both digits in the bottom number, by both digits in the top number.

    How do you find your final answer?

    Solution

    When multiplying a 2-digit number by another 2-digit number you:

    1. Multiply the ones in the bottom number by both of the digits in the top number.
    2. Add the zero (placeholder).
    3. Multiply the tens in the bottom number by both digits in the top number.
    4. Add the partial products to calculate the answer.
  • Can you complete the multiplication equation?

    Hints

    Don't forget the add the 0 as a placeholder.

    Remember to add on any tens you have carried over.

    Solution

    Here is the completed equation.

    Mr. Squeaks has 516 pieces of corn in his new batch.

    ____________________________________________________

    • The first part of the equation had been done for you. 2 x 3 = 6 which was written in the ones place and 1 x 3 = 3 which was written in the tens place. We can see these numbers in red.
    • Next we need to add the zero as a placeholder in the ones column.
    • We then multiply 2 x 4 to get 8 and write that in the tens column.
    • Next we multiply 1 x 4 to get 4 and write that in the hundreds column. We can see these numbers in blue.
    • Finally, we add up the digits in each place value column to find our answer.
    • 6 + 0 = 6 so we write this in the ones column.
    • 3 + 8 = 11 so we write 1 in the tens column and carry 1 over.
    • We therefore add 4 + 1 which equals 5 and write that in the hundreds column.
    • Our answer is 516.
  • Solve the multiplication problem.

    Hints

    Read the information carefully to work out which numbers you are multiplying.

    Use a pencil and paper to write out the equation.

    Don't forget the zero!

    Remember to add on any numbers you have carried over.

    Solution

    Here is 36 x 49 written out using this method.

    • First, we multiplied the 9 in 49 with both digits in 36. 6 x 9 is 54 so we write the 4 below the ones and carry the 5 across. We then multiply 3 x 9 which is 27 and add the 5 we carried which equals 32. We write the 2 below the tens and the 3 in the hundreds column. We can see these numbers in red.
    • Next, we add the 0 as the placeholder in the ones column.
    • We then multiply the 4 in 49 with both digits in 36. 6 x 4 is 24 so we write 4 in the tens column and carry the 2 across. 3 x 4 is 12 plus the 2 we carried is 14, so we write 4 in the hundreds column and 1 in the thousands column. We can see these numbers in blue.
    • Finally, we add the partial products to get 1764.
    • 36 x 49 = 1764
  • Can you match the multiplication problems with the correct answers?

    Hints

    You could use a pen and paper to write each equation out.

    Have a look at this example. Does it give you a clue as to where to start?

    Don't forget about the placeholder!

    After you have multiplied with the ones place of the bottom number, what do you multiply next?

    Remember, when you multiply the ones place of the bottom number with the ones place of the top number, this gives you a clue as to what number will be in the ones place of the final answer.

    Solution

    Here is 14 x 23 written out using this method.

    • First, we multiplied the 3 in 23 with both digits in 14. 4 x 3 is 12 so we write the 2 below the ones and carry the 1 across. We then multiply 1 x 3 which is 3, and add the 1 we carried which equals 4. We write this below the tens. We can see these numbers in red.
    • Next, we add the 0 as the placeholder in the ones column.
    • We then multiply the 2 in 23 with both digits in 14. 4 x 2 is 8 so we write this in the tens column. 1 x 2 is 2 so we write this in the hundreds column. We can see these numbers in blue.
    • Finally, we add the partial products to get 322.
    • 14 x 23 = 322

    ___________________________________________________

    Following the same steps we can also work out that:

    • 24 x 21 = 504
    • 33 x 25 = 825
    • 44 x 27 = 1188
  • Which jar should Mr. Squeaks put the seeds in?

    Hints

    Use the multiplication equation in the header to help you.

    What do we need to do once we have the two partial products?

    Add the ones, then the tens, then the hundreds - not forgetting any you have carried over.

    Solution

    Here is what the completed equation looks like.

    Mr. Squeaks has a new batch of 294 seeds so needs to put it in the jar with the label 294!

    ____________________________________________________

    • We already had the partial products multiplied for us, so we needed to add them together to find the total.
    • 4 + 0 = 4 so we write 4 in the ones place.
    • 1 + 8 = 9 so we write 9 in the tens place.
    • We then just have 2 in the hundreds place with nothing to add to it, so we write 2 in the hundreds place at the bottom.
    • We therefore have a total of 294.
  • Complete the multiplication equations.

    Hints

    Use a pencil and some paper to write out each equation.

    Think about which part of each number is multiplied first and which part is multiplied second.

    Don't forget to add the zero as the placeholder!

    Solution

    Here is 63 x 42 written out using this method.

    • First, we multiplied the 2 in 42 with both digits in 63. 3 x 2 is 6 so we write the 6 below the ones. We then multiply 6 x 2 which is 12. We write 2 below the tens and 1 in the hundreds column.
    • Next, we add the 0 as the placeholder in the ones column.
    • We then multiply the 4 in 42 with both digits in 63. 3 x 4 is 12 so we write the 2 in the tens column and carry the 1. 6 x 4 is 24 plus the 1 we carried is 25 so we write 5 in the hundreds column and 2 in the thousands column.
    • Finally, we add the partial products to get 2646.
    • 63 x 42 = 2646

    ___________________________________________________

    Following the same steps we can also work out that:

    • 57 x 39 = 2223
    • 81 x 23 = 1863
    • 92 x 37 = 3404