Questions: Comparing Two-Digit Numbers

Question 1

A student says 48 is greater than 51 because 'the ones digit 8 is bigger than the ones digit 1.' What mistake is the student making?

• A. The student is correct — 8 > 1, so 48 > 51
• B. The student is comparing ones digits without first comparing tens digits. 51 has 5 tens and 48 has only 4 tens, so 51 > 48 regardless of the ones
• C. The student needs to add all the digits: 4 + 8 = 12 and 5 + 1 = 6, so 48 wins
• D. Both numbers are equal because they each have exactly two digits

Answer: (B)

This is the core misconception this topic addresses. Tens must always be compared first because one ten (10) is worth more than any possible ones digit (maximum 9). No matter how large the ones digit of 48 is, 48 can never exceed 51 while having fewer tens. Once the tens differ, the comparison is decided — the ones digits are irrelevant.

Question 2

Compare 73 and 76. Which statement is correct, and why?

• A. 73 > 76, because 3 ones is less than 6 ones and smaller parts make the whole larger
• B. 73 < 76, because the tens digits are equal, so the ones digits decide: 3 ones < 6 ones
• C. 73 = 76, because both numbers have the same tens digit (7)
• D. 73 > 76, because 7 + 3 = 10, which is larger than 7 + 6 = 13

Answer: (B)

When the tens digits are equal — both numbers have 7 tens — the tens cannot break the tie. You then move to the ones: 3 < 6, so 73 < 76. This is the second step of the comparison rule: start at the tens, move to ones only if needed. Option 2 is wrong because equal tens do not mean equal numbers — you still need to check ones.

Question 3

When comparing 62 and 57, you should look at the ones digits to determine which number is greater.

• T. True
• F. False

Answer: False

62 has 6 tens and 57 has 5 tens. Since the tens digits differ, the comparison is decided by the tens alone: 6 tens > 5 tens, so 62 > 57. You never need to look at the ones digits when the tens are already different. The rule is: compare tens first; only move to ones if tens are equal.

Question 4

A number with 3 tens and 9 ones is always greater than any number with only 2 tens.

• T. True
• F. False

Answer: True

A number with 3 tens and 9 ones is 39. Any number with only 2 tens is at most 29 (2 tens and 9 ones). Since 3 tens > 2 tens, the first number wins regardless of the ones digit. One ten equals 10, which is larger than the maximum ones digit (9), so a difference of even one full ten can never be overcome by the ones digit alone.

Question 5

Explain why you always compare the tens digits first when comparing two two-digit numbers, and when you need to look at the ones digits.

Model answer: You compare tens first because tens are worth more than ones. A single ten (10) is already greater than the largest possible ones digit (9), so any difference in the tens place determines which number is larger — the ones digits cannot change that outcome. You only need to compare ones digits when the tens digits are exactly equal, because only then does the tens place leave the comparison unresolved.

This same 'start with the highest place value' logic extends to three-digit, four-digit, and larger numbers. The principle is always: compare the most significant digit first, move right only when digits tie. Understanding why it works — not just that it works — lets students apply the rule confidently to larger numbers.