Standard Algorithm for Multiplication We will be able to multiply bigger numbers using an algorithm with ease! By Betsy Weigle ~ Classroom Caboodle

You Can Do It! Mathematics is all about accuracy and efficiency. What is efficiency? Being able to accomplish something with the least waste of time and effort. Let’s use what we know about regrouping to be more efficient at multiplying large numbers. You Can Do It!

6 7 x 5 3 21 180 350 3,000 + 3,551 Add the results Calculate 3 X 7 We know how to use Partial Products to multiply larger numbers. It takes a lot of work and paper to decompose numbers, multiply and add them all! 6 7 Always start here x 5 3 21 Calculate 3 X 7 180 Calculate 3 X 60 350 Calculate 50 X 7 3,000 + Calculate 50 X 60 3,551 Add the results

What if I told you there was a short cut?

The Multiplication Algorithm Have you watched adults multiply large numbers on paper before? It might seem confusing at first, but once you have the pattern down, you’ll be able to multiply large numbers quickly. Remember, when you feel frustrated…that’s the feeling of your brain growing. Keep practicing! The Multiplication Algorithm

6 7 x 5 3 1 1 Let’s take a short cut! First step: Multiply the ones. Ones times ones +2 6 7 x 5 3 Circle your starting place 1 1 First step: Multiply the ones. Calculate 3 X 7. It’s 21. Write the 1 in the one’s place. Place the 2 above the ten’s place since it’s really 20. We’ll add it in with the next step.

6 7 x 5 3 20 1 2 Second step: Multiply ones times tens. +2 6 7 x 5 3 Second step: Multiply ones times tens. Calculate 3 X 6. It’s 18. 20 1 2 Now add in the 2 tens from the last step. 18 + 2 = 20 You have 20 tens or 2 hundreds and no tens. Write that down. Cross out the +2 once you’ve added it in.

6 7 x 5 3 20 1 3 5 Third step: Multiply tens times ones. Let’s move to the ten’s place. We know anything times 10 has a zero on the end. Go ahead a put that zero in the one’s place since we know we’ll need it when multiplying tens. Tens times ones +3 +2 6 7 x 5 3 20 1 3 Third step: Multiply tens times ones. Calculate 5 X 7. It’s 35. Put the 5 from 35 in the ten’s place. 5 Place +3 above the ten’s place. We’ll add it in the next step.

6 7 x 5 3 20 1 4 33 5 Fourth step: Multiply tens times tens. +3 +2 6 7 Tens times tens x 5 3 Fourth step: Multiply tens times tens. Calculate 5 x 6. It’s 30. 20 1 4 33 5 Add in the 3 from the last step. 30 + 3 = 33 You can write that down. It was really 50 x 60 = 3,000 plus 3 more hundreds. Cross out that +3 once you’ve added it in.

+3 +2 6 7 x 5 3 201 5 + 3350 3,551 Fifth step: Add the results

8 2 x 4 5 1 Let’s try another one! Calculate 5 x 2. Ones times ones +1 8 2 x 4 5 Circle your starting place 1 Calculate 5 x 2. Zero in the one’s place. +1 above the ten’s place to add in next step.

8 2 x 4 5 41 2 You can do it! Calculate 5 x 8. Add +1 Ones times tens You can do it! +1 8 2 x 4 5 41 2 Calculate 5 x 8. Add +1 Write it down and cross off +1.

8 2 x 4 5 41 3 8 Move to the ten’s place! +1 8 2 x 4 5 Tens times ones 41 3 Put a zero in the one’s place since we are multiplying tens. Calculate 4 x 2. 8

8 2 4 5 x 41 4 32 8 Move to the ten’s place! Calculate 4 x 8 +1 Tens times tens 4 5 x 41 4 32 8 Calculate 4 x 8

Final Step! +1 8 2 x 4 5 41 5 32 + 8 3,690 Add the results

Try this on your own! 2 6 x 1 8

How did you do? +4 2 6 x 1 8 20 8 + 2 6 468

Remember the Pattern Circle the start Multiply bottom numbers times top numbers: Ones times ones Ones times tens Tens times ones Tens times tens Add ‘em up

+4 2 6 2 Ones times tens 1 Ones times ones 1 8 x 2 0 8

+4 2 6 4 Tens times tens 3 Tens times ones 1 8 x 2 0 8 2 6 0

5 Add ‘em up! 6 2 1 8 x 2 0 8 2 6 0 + 4 6 8

Let’s try one more! You can work this one on your own. 8 1 x 5 3