Sketch a new set of base pieces for each product in exercises 5 and 6, and then show regrouping.
Multiply 168 by 3.
Product: 168 x 3
New set of base pieces:
- For the ones place: 3 bundles of 1 (3 x 1 = 3)
- For the tens place: 3 bundles of 10 (3 x 10 = 30)
- For the hundreds place: 3 bundles of 100 (3 x 100 = 300)
Regrouping:
To regroup, we need to exchange 10 ones bundles for 1 tens bundle, and exchange 10 tens bundles for 1 hundreds bundle.
Starting with the ones place:
3 bundles of 1
= 3
Exchange 10 ones bundles for 1 tens bundle:
= 1 bundle of 10 + 3
Moving to the tens place:
3 bundles of 10
= 3 x 10 = 30
Exchange 10 tens bundles for 1 hundreds bundle:
= 1 bundle of 100 + 30
Lastly, in the hundreds place:
3 bundles of 100
= 3 x 100 = 300
Combining all the values:
300 (hundreds place) + 31 (tens place) + 3 (ones place) = 331
Therefore, 168 multiplied by 3 is equal to 331.
To sketch a set of base pieces for multiplying 168 by 3, we can represent this multiplication using base-10 blocks.
Step 1: Start by drawing a rectangle to represent the first number 168. Divide the rectangle into three rows to represent the second number 3.
III
III
III
Step 2: Next, divide each row of the rectangle into individual blocks by drawing vertical lines. This will create a set of 168 base-10 blocks.
111111111111111111111111111111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111111111111111111111111111111
Step 3: Take one row of blocks from the rectangle and regroup them into a new group. This represents the first product of 168 multiplied by 3.
111111111111111111111111111111111111111111111111111111111111111111111111111
Step 4: Repeat step 3 for the remaining two rows of blocks. This represents the second and third products of 168 multiplied by 3.
111111111111111111111111111111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111111111111111111111111111111
Step 5: Count the total number of blocks in the regrouped groups to find the product of 168 multiplied by 3.
111111111111111111111111111111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111111111111111111111111111111
111111111111111111111111111111111111111111111111111111111111111111111111111
There are 504 blocks, so the product of 168 multiplied by 3 is 504.
To multiply 168 by 3, you can use the traditional method of long multiplication. Here's how you can go about it:
Step 1: Write down the multiplication question
```
168
x 3
------
```
Step 2: Multiply the ones place digit of the bottom number (3) by each digit of the top number (168) starting from right to left. Write the results below one another.
```
168
x 3
------
504 <-- 8 times 3
336 <-- 6 times 3
504 <-- 1 times 3 (add a zero since we are in the tens column)
------
```
Step 3: Add up all the partial products.
```
168
x 3
------
504
336
+ 504
------
504
```
Step 4: Your final answer is 504, so 168 multiplied by 3 equals 504.
Now, regarding the explanation about sketching new base pieces and regrouping, it seems like you are referring to a specific math exercise question that involves base pieces and regrouping. Could you please provide additional context or details about exercises 5 and 6? With more information, I can help you better with the sketching and regrouping aspects of those exercises.