Ten in a place carries forward

2.NBT.A.13.NBT.A.2 · take · grade 3

Archetype: Place-Value Regrouping · step in a 7-type progression

There is a three-digit number made up of $6$ hundreds, $13$ tens, and $24$ ones. The number that is $264$ less than this number is made up of how many tens?

Show solution

Understand

A number is described loosely as 6 hundreds, 13 tens, and 24 ones -- but the tens and ones go past a single digit, so I first regroup to find the real number. Then I subtract 264 from it and ask how many tens make up that result.

Givens

The number is 6 hundreds, 13 tens, and 24 ones.
A second number is 264 less than this one.

Unknowns

How many tens make up the number that is 264 less.

Constraints

10 ones regroup into 1 ten; 10 tens regroup into 1 hundred.
'How many tens' means the total value divided into groups of ten.

Plan

#15 Organize Information in More Ways · also uses: #7 Identify Subproblems

The counts (13 tens, 24 ones) are written in an unusual way, so the key move is to re-organize them into standard place value by carrying. Then the task splits into clear subproblems: find the number, subtract 264, and re-read the answer as a count of tens.

Execute

#15 Organize Information in More Ways 2.NBT.A.1

Add up the values: 6 hundreds is 600, 13 tens is 130, and 24 ones is 24. Combine them by carrying the extra tens and ones into the next place.

600 + 130 + 24 = 754

Place value lets me trade 10 ones for a ten and 10 tens for a hundred, which is core Grade 2 understanding of three-digit numbers.

#7 Identify Subproblems 3.NBT.A.2

Now take 264 away from 754 to get the number that is 264 less.

754 - 264 = 490

Subtracting two three-digit numbers with regrouping is a Grade 3 fluency skill.

#15 Organize Information in More Ways 2.NBT.A.1

Read 490 as a count of tens: 490 is 49 groups of ten (with 0 ones left over).

490 = 49 \times 10

Seeing 490 as 49 tens is just place-value reading, the same skill as knowing 490 has a 9 in the tens place plus 4 hundreds = 49 tens.

Answer: 49

Review

490 is a whole number of tens (ends in 0), so 'how many tens' has a clean answer of 49. Check: 49 tens = 490, and 490 + 264 = 754, which matches the original number, so the subtraction was right.

Guess and check (Tool 6): a number that is 49 tens is 490; verify 490 + 264 = 754 and 754 = 600 + 130 + 24, confirming the description, so 49 tens is correct.

Standards · min grade 3

2.NBT.A.1 Understand that the three digits of a three-digit number represent hundreds, tens, and ones — Regrouping 6 hundreds, 13 tens, 24 ones into 754 and re-reading 490 as 49 tens.
3.NBT.A.2 Fluently add and subtract within 1000 — Computing 754 - 264 = 490 with regrouping.

💡 Trade your tens and ones into neat place value, and reading 490 as 49 tens is easy Grade 3 sense!