Division of Whole Numbers and Decimal Numbers Learning Task 1: Find the quotient and check. 1. 0.8\overline{)208} 2. 0.5\overline{)355} 3. 0.6\overline{)312}
The Correct Answer and Explanation is:
Here are the solutions for Division of Whole Numbers and Decimal Numbers with detailed explanations:
1. 0.8⟌208
Step 1: Eliminate the decimal by multiplying both divisor and dividend by 10
0.8 × 10 = 8
208 × 10 = 2080
So the problem becomes: 8⟌2080
Step 2: Perform the division
2080 ÷ 8 = 260
Final Answer:
260
Checking:
260 × 0.8 = 208 ✔️
2. 0.5⟌355
Step 1: Eliminate the decimal by multiplying both divisor and dividend by 10
0.5 × 10 = 5
355 × 10 = 3550
So the problem becomes: 5⟌3550
Step 2: Perform the division
3550 ÷ 5 = 710
Final Answer:
710
Checking:
710 × 0.5 = 355 ✔️
3. 0.6⟌312
Step 1: Eliminate the decimal by multiplying both divisor and dividend by 10
0.6 × 10 = 6
312 × 10 = 3120
So the problem becomes: 6⟌3120
Step 2: Perform the division
3120 ÷ 6 = 520
Final Answer:
520
Checking:
520 × 0.6 = 312 ✔️
Explanation
When dividing whole numbers by decimal numbers, the easiest way to solve the problem is to remove the decimal from the divisor. This is done by multiplying both the divisor and the dividend by the same power of 10 to make the divisor a whole number. The value of the quotient does not change because both numbers are scaled equally.
In the first problem, 0.8 is the divisor. By multiplying both 0.8 and 208 by 10, we get a new, simpler division problem: 8 divided into 2080. The answer to that is 260. To confirm, we multiply 260 by 0.8 and get back to 208, ensuring the solution is correct.
The same approach applies to the second example. The divisor is 0.5, so we multiply both numbers by 10 to get 5⟌3550. The quotient is 710, and verifying by multiplying shows the answer matches the original dividend.
The third problem uses the same logic. We multiply 0.6 and 312 by 10, simplifying the division to 6⟌3120. Solving gives 520, and multiplying back confirms the accuracy.
This method helps avoid working with decimals during division, making the process faster and less prone to errors. It is important to always check the answer by reversing the operation to confirm its correctness.
