Multiplying Two-Digit Numbers by Two-Digit Numbers

Multiplying Two-Digit Numbers by Two-Digit Numbers exercise

• 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 halve 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 to put 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.

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  • 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 figure 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 put 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!

  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.

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

  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

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  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. Don't forget any numbers 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!

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  • 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 put 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 put 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

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  Following the same steps we can also work out that:

  • 57 x 39 = 2223

  • 81 x 23 = 1863

  • 92 x 37 = 3404