Here are the step-by-step solutions for each problem on the worksheet.
1. The product of two numbers is 450. Their quotient is 2. What are the two numbers?
*
Step 1: Understand the clues. "Product" means multiplication ($A \times B = 450$). "Quotient" means division ($A \div B = 2$).
*
Step 2: If one number divided by the other equals 2, it means the larger number is exactly double the smaller number. Let's call the smaller number $x$. Then the larger number is $2x$.
*
Step 3: Multiply them together: $x \times 2x = 2x^2 = 450$.
*
Step 4: Divide by 2 to isolate $x^2$: $450 \div 2 = 225$. So, $x^2 = 225$.
*
Step 5: Find the square root of 225. We know that $10 \times 10 = 100$ and $20 \times 20 = 400$, so the answer is between 10 and 20. Since the number ends in 5, let's try 15. $15 \times 15 = 225$.
*
Step 6: So the smaller number is 15. The larger number is double that: $15 \times 2 = 30$.
*
Check: $30 \times 15 = 450$ and $30 \div 15 = 2$.
2. $246 - 14 =$
*
Step 1: Subtract the ones place: $6 - 4 = 2$.
*
Step 2: Subtract the tens place: $4 - 1 = 3$.
*
Step 3: Bring down the hundreds place: 2.
*
Result: 232.
3. A candy factory made 1042 of strawberry flavored candies, 2021 of blueberry flavored candies, and 820 of cherry flavored candies. How many candies did the factory make in all?
*
Step 1: Set up the addition problem vertically to keep the places aligned.
```
1042
2021
+ 820
------
```
*
Step 2: Add the ones column: $2 + 1 + 0 = 3$.
*
Step 3: Add the tens column: $4 + 2 + 2 = 8$.
*
Step 4: Add the hundreds column: $0 + 0 + 8 = 8$.
*
Step 5: Add the thousands column: $1 + 2 = 3$.
*
Result: 3883.
4. $4623 - 2586 =$
*
Step 1: Subtract the ones place: You cannot take 6 from 3. Borrow from the tens place (the 2 becomes a 1, and the 3 becomes 13). $13 - 6 = 7$.
*
Step 2: Subtract the tens place: Now you have 1. You cannot take 8 from 1. Borrow from the hundreds place (the 6 becomes a 5, and the 1 becomes 11). $11 - 8 = 3$.
*
Step 3: Subtract the hundreds place: Now you have 5. $5 - 5 = 0$.
*
Step 4: Subtract the thousands place: $4 - 2 = 2$.
*
Result: 2037.
5. $4 \times 6 \times 12 =$
*
Step 1: Multiply the first two numbers: $4 \times 6 = 24$.
*
Step 2: Multiply that result by the last number: $24 \times 12$.
*
Step 3: Break it down:
* $24 \times 10 = 240$
* $24 \times 2 = 48$
* $240 + 48 = 288$
*
Result: 288.
Final Answer:
1. 30 and 15
2. 232
3. 3883
4. 2037
5. 288
Parent Tip: Review the logic above to help your child master the concept of english worksheet 3rd grade.
