To solve 52 ÷ 4 using place-value thinking, what are the correct steps?
ASubtract 4 from 52 repeatedly and count how many subtractions it takes
BDivide 5 tens by 4: get 1 ten with 1 ten (10 ones) leftover; add to 2 ones = 12 ones; divide 12 ones by 4 = 3; answer is 13
CMultiply 52 × 4, then divide the product by 2 to get the answer
DSplit 52 into 50 and 2, divide each by 4 independently and add the results
Place-value decomposition: 52 = 5 tens and 2 ones. Ask: how many times does 4 go into 5 tens? Once (4 tens), with 1 ten leftover. Convert the leftover ten to 10 ones and combine with the existing 2 ones: 12 ones. Now ask: how many times does 4 go into 12 ones? Three times exactly. Result: 1 ten + 3 ones = 13. Option D fails because 50 ÷ 4 = 12.5 (not a whole number), so you cannot divide the tens independently without handling the remainder — the leftover must be passed down to the ones place.
Question 2 Multiple Choice
After dividing the tens digit in 48 ÷ 3, there is 1 ten left over. What do you do with that leftover ten?
AIgnore it — remainders in the tens place are too small to affect the answer
BWrite it as a decimal remainder in the final answer
CConvert it to 10 ones and add it to the existing ones before dividing again
DSubtract it from the original number and start the division over
The leftover ten cannot stay as a ten — you are now working in the ones place. So you convert it: 1 ten = 10 ones. Add those 10 ones to the existing ones digit (8) to get 18 ones total, then divide: 18 ÷ 3 = 6. This 'bring down' move is the core of the place-value decomposition strategy, and it is exactly what the long division algorithm formalizes. Ignoring the remainder would produce a wrong answer (1 ten = 10 is a significant part of 48).
Question 3 True / False
After dividing 48 ÷ 3 = 16, you can verify your answer by computing 3 × 16 = 48.
TTrue
FFalse
Answer: True
Multiplication is the inverse of division, so multiplying the quotient by the divisor should return the dividend. 3 × 16 = 48 confirms that 48 ÷ 3 = 16 is correct. This check is always available and takes only a few seconds. It also reinforces the conceptual relationship: division and multiplication are reverse operations — every division problem has a corresponding multiplication equation.
Question 4 True / False
If the tens digit of a two-digit number can seldom be divided evenly by the divisor, there is no valid answer and the problem cannot be completed.
TTrue
FFalse
Answer: False
An uneven division of the tens digit is normal and expected — it simply produces a remainder that gets converted to ones and added to the existing ones digit before dividing again. For example, in 52 ÷ 4, the tens (5) don't divide evenly by 4: 4 goes into 5 once with 1 leftover. That leftover ten becomes 10 ones, combined with 2 to make 12 ones, which divides evenly by 4 to give 3. The answer is 13. The 'no valid answer' misconception comes from applying whole-number thinking at each step independently, rather than carrying the remainder forward.
Question 5 Short Answer
Explain in your own words how place-value decomposition helps you divide 63 ÷ 3. Show the steps.
Think about your answer, then reveal below.
Model answer: 63 = 6 tens and 3 ones. Divide the tens: 6 tens ÷ 3 = 2 tens exactly, no remainder. Divide the ones: 3 ones ÷ 3 = 1 one exactly. Combine: 2 tens + 1 one = 21. Check: 3 × 21 = 63. Answer: 21.
When the tens divide evenly (as in this example), place-value decomposition is especially clean. The key insight is that dividing each place value separately and combining the results is equivalent to dividing the whole number — because of how our base-10 number system works. When there is a remainder in the tens, you carry it forward; when there is not, you simply move on. This strategy is the conceptual foundation of the long division algorithm.