Questions: Mental Math: Adding and Subtracting Tens

Question 1

What is 63 + 20?

• A. 83 — add 2 to the tens digit, leave the ones digit unchanged
• B. 85 — add 20 to both the tens and ones digits
• C. 65 — add 2 to the ones digit
• D. 280 — add the digits and multiply by 10

Answer: (A)

Adding 20 means adding 2 tens. Only the tens digit changes: 6 tens + 2 tens = 8 tens. The ones digit (3) stays exactly as it is. The answer is 83. Option C shows the most common error — mistakenly adding to the ones digit instead of the tens digit.

Question 2

A student computes 47 + 30 and gets 80. What mistake did she most likely make?

• A. She added 30 to the ones digit (7 + 3 = 10, carried, and lost the original ones digit)
• B. She added the individual digits of 47 and 30 together and multiplied
• C. She used subtraction instead of addition
• D. She forgot to carry a digit into the hundreds place

Answer: (A)

The most common error when adding tens is accidentally modifying the ones digit. If she computed 7 + 3 = 10 and wrote 8 tens with 0 ones, she got 80 instead of 77. The correct reasoning: adding 30 only affects the tens digit. 4 tens + 3 tens = 7 tens, ones digit stays 7, answer = 77. The ones digit is completely untouched by adding a multiple of 10.

Question 3

When you add 40 to a two-digit number, the ones digit of the result is always the same as the ones digit of the original number.

• T. True
• F. False

Answer: True

True. Adding 40 means adding 4 tens. Tens additions only affect the tens column. The ones digit is completely independent and unchanged. This holds for any two-digit number plus any multiple of 10, as long as the tens sum does not exceed 9 and carry into the hundreds.

Question 4

The mental strategy of 'mainly change the tens digit' typically produces a two-digit answer, even when large multiples of 10 are added.

• T. True
• F. False

Answer: False

False. When the tens digits sum to 10 or more, the result crosses into the hundreds. For example, 75 + 40: 7 tens + 4 tens = 11 tens = 1 hundred and 1 ten, plus the 5 ones = 115. The ones digit (5) is still unchanged, but there is now a hundreds digit. The strategy still works conceptually — you only add the tens — but regrouping into the hundreds must be handled.

Question 5

Why does adding 30 to 47 change only the tens digit and not the ones digit? Explain using place value.

Model answer: Because 30 is made entirely of tens — it has 0 ones. When you add 30 to 47, you are adding 3 tens to the 4 tens in 47. The ones column (which has 7 ones) receives nothing from 30, so it stays at 7. Place value columns are independent: a tens addition only interacts with the tens column. The result is 7 tens and 7 ones = 77.

Place value separates numbers into independent columns. A multiple of 10 like 30 has no ones component, so it can only interact with the tens column. This independence is what makes the mental math strategy work — and also reveals why the common mistake of changing the ones digit is wrong: nothing in 30 touches the ones place.