Ten of a unit carries to the next place

4.NBT.A.14.NBT.A.2 · adapt · grade 4

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

Liam's piggy bank holds $12$ one-hundred-dollar bills, $33$ ten-dollar bills, $45$ one-dollar coins, and $39$ dimes. How much money is in the piggy bank in all?

Show solution

Understand

Add up the money in a piggy bank that holds 12 hundred-dollar bills, 33 ten-dollar bills, 45 one-dollar coins, and 39 dimes, then give the grand total.

Givens

12 one-hundred-dollar bills
33 ten-dollar bills
45 one-dollar coins
39 dimes (each dime is 10 cents, i.e. $0.10)

Unknowns

The total amount of money in the piggy bank

Constraints

Each bundle is worth its count times the unit's value; ten of one unit makes one of the next-bigger unit.

Plan

#7 Identify Subproblems · also uses: #8 Analyze the Units#1 Draw a Diagram

Find the value of each bundle separately (count times unit value), watching the units carefully because dimes are tenths of a dollar, then add the four amounts.

Execute

#8 Analyze the Units 4.NBT.A.1

12 bills of

100 each are worth 12 × 100 =

1,200.

12 \times 100 = 1{,}200

Each bill is one hundred, so twelve of them is twelve hundreds.

#8 Analyze the Units 4.NBT.A.1

33 bills of

10 each are worth 33 × 10 =

330.

33 \times 10 = 330

Ten dollars repeated 33 times shifts 33 up one place to 330.

#8 Analyze the Units 4.NBT.A.1

45 coins of

1 each are worth 45 × 1 =

45.

45 \times 1 = 45

Forty-five ones is just $45.

#8 Analyze the Units 4.NBT.A.1

39 dimes of

0.10 each are worth 39 × 0.10 =

3.90. (Ten dimes make a dollar, so 39 dimes is 3 dollars and 9 dimes.)

39 \times 0.10 = 3.90

Ten dimes bundle into one dollar, so 39 dimes regroup into $3.90.

#7 Identify Subproblems 4.NBT.A.2

Total = 1,200 + 330 + 45 + 3.90 = 1,578.90 dollars.

1{,}200 + 330 + 45 + 3.90 = 1{,}578.90

Summing the separate bundle values gives the whole piggy bank.

Answer: $1,578.90

Review

The big bundles dominate: $1,200 plus$ 330 is already $1,530, plus$ 45 and a few dollars of dimes lands near $1,579, which matches$ 1,578.90. Units stay in dollars throughout.

Regroup first (tool 15): bundle ten dimes into dollars and ten tens into a hundred, then read the place-value total directly.

Standards · min grade 4

4.NBT.A.1 Recognize that a digit represents ten times what it represents in place to its right — Valuing each bundle by its unit and regrouping ten of a unit into the next place.
4.NBT.A.2 Read and write multi-digit whole numbers and compare using symbols — Adding the bundle values into one multi-digit total.

💡 This only needs Grade 4 place-value sense: each bundle is its count times its value, and ten of one unit climbs to the next!