Sketch base-ten pieces for the number 1140 and explain how the test for divisibility by 8 can be used to obtain the remainder when dividing 1140 by 8.
To sketch base-ten pieces for the number 1140, we can break it down into its place values:
- Thousands: We have 1 thousand, so we draw a single large rectangle representing 1000.
- Hundreds: We have 1 hundred, so we draw a smaller rectangle representing 100.
- Tens: We have 4 tens, so we draw 4 smaller squares representing 10 each.
- Ones: We have 0 ones, so we don't need to draw anything.
Now, to explain how the test for divisibility by 8 can be used to obtain the remainder when dividing 1140 by 8:
When dividing a number by 8, if the sum of the sum of the digits in the ones place, tens place, and hundreds place is divisible by 8, then the original number is divisible by 8.
In the case of 1140, the sum of the digits in the ones, tens, and hundreds place is 1 + 1 + 4 + 0 = 6. Since 6 is not divisible by 8, we conclude that 1140 is not divisible by 8.
Thus, when dividing 1140 by 8, the remainder would be 6.