← Ten of a unit carries to the next place · Place-Value Regrouping

Ten of a unit carries to the next place · 10 practice problems

4.NBT.A.14.NBT.A.2

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Generated variants — 10

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Variant 1 easy

Liam's piggy bank holds $5$ one-hundred-dollar bills, $12$ ten-dollar bills, $8$ one-dollar coins, and $14$ dimes. How much money is in the piggy bank in all?

Your answer

Show solution

1 · Understandwhat's really being asked

Add up the money in a piggy bank that holds 5 hundred-dollar bills, 12 ten-dollar bills, 8 one-dollar coins, and 14 dimes, then give the grand total.

Givens

5 one-hundred-dollar bills
12 ten-dollar bills
8 one-dollar coins
14 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.

2 · Planchoose the strategy

#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.

3 · Execute5 carry out the plan

1Value of the hundred-dollar bills

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

5 bills of $100 each are worth 5 x 100 = $500.

5 \times 100 = 500

Each bill is one hundred, so this many of them is that many hundreds.

2Value of the ten-dollar bills

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

12 bills of $10 each are worth 12 x 10 = $120.

12 \times 10 = 120

Ten dollars repeated 12 times shifts 12 up one place to 120.

3Value of the one-dollar coins

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

8 coins of $1 each are worth 8 x 1 = $8.

8 \times 1 = 8

That many ones is just $8.

4Value of the dimes

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

14 dimes of $0.10 each are worth 14 x 0.10 = $1.40. (Ten dimes make a dollar, so 14 dimes is 1 dollars and 4 dimes.)

14 \times 0.10 = 1.40

Ten dimes bundle into one dollar, so 14 dimes regroup into $1.40.

5Add the four amounts

#7 Identify Subproblems 4.NBT.A.2

Total = 500 + 120 + 8 + 1.40 = 629.40 dollars.

500 + 120 + 8 + 1.40 = 629.40

Summing the separate bundle values gives the whole piggy bank.

Answer: $629.40

4 · Reviewdoes it hold up?

The big bundles dominate: $500 plus$ 120 is already $620, plus$ 8 and a few dollars of dimes lands near 629, which matches $629.40. Units stay in dollars throughout.

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

Standardsmin 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.

💡Takeaway. 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!

Variant 2 easy

Liam's piggy bank holds $8$ one-hundred-dollar bills, $21$ ten-dollar bills, $17$ one-dollar coins, and $25$ dimes. How much money is in the piggy bank in all?

Your answer

Show solution

1 · Understandwhat's really being asked

Add up the money in a piggy bank that holds 8 hundred-dollar bills, 21 ten-dollar bills, 17 one-dollar coins, and 25 dimes, then give the grand total.

Givens

8 one-hundred-dollar bills
21 ten-dollar bills
17 one-dollar coins
25 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.

2 · Planchoose the strategy

#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.

3 · Execute5 carry out the plan

1Value of the hundred-dollar bills

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

8 bills of $100 each are worth 8 x 100 = $800.

8 \times 100 = 800

Each bill is one hundred, so this many of them is that many hundreds.

2Value of the ten-dollar bills

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

21 bills of $10 each are worth 21 x 10 = $210.

21 \times 10 = 210

Ten dollars repeated 21 times shifts 21 up one place to 210.

3Value of the one-dollar coins

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

17 coins of $1 each are worth 17 x 1 = $17.

17 \times 1 = 17

That many ones is just $17.

4Value of the dimes

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

25 dimes of $0.10 each are worth 25 x 0.10 = $2.50. (Ten dimes make a dollar, so 25 dimes is 2 dollars and 5 dimes.)

25 \times 0.10 = 2.50

Ten dimes bundle into one dollar, so 25 dimes regroup into $2.50.

5Add the four amounts

#7 Identify Subproblems 4.NBT.A.2

Total = 800 + 210 + 17 + 2.50 = 1,029.50 dollars.

800 + 210 + 17 + 2.50 = 1{,}029.50

Summing the separate bundle values gives the whole piggy bank.

Answer: $1,029.50

4 · Reviewdoes it hold up?

The big bundles dominate: $800 plus$ 210 is already $1,010, plus$ 17 and a few dollars of dimes lands near 1,030, which matches $1,029.50. Units stay in dollars throughout.

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

Standardsmin 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.

💡Takeaway. 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!

Variant 3 easy

Liam's piggy bank holds $9$ one-hundred-dollar bills, $18$ ten-dollar bills, $22$ one-dollar coins, and $31$ dimes. How much money is in the piggy bank in all?

Your answer

Show solution

1 · Understandwhat's really being asked

Add up the money in a piggy bank that holds 9 hundred-dollar bills, 18 ten-dollar bills, 22 one-dollar coins, and 31 dimes, then give the grand total.

Givens

9 one-hundred-dollar bills
18 ten-dollar bills
22 one-dollar coins
31 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.

2 · Planchoose the strategy

#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.

3 · Execute5 carry out the plan

1Value of the hundred-dollar bills

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

9 bills of $100 each are worth 9 x 100 = $900.

9 \times 100 = 900

Each bill is one hundred, so this many of them is that many hundreds.

2Value of the ten-dollar bills

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

18 bills of $10 each are worth 18 x 10 = $180.

18 \times 10 = 180

Ten dollars repeated 18 times shifts 18 up one place to 180.

3Value of the one-dollar coins

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

22 coins of $1 each are worth 22 x 1 = $22.

22 \times 1 = 22

That many ones is just $22.

4Value of the dimes

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

31 dimes of $0.10 each are worth 31 x 0.10 = $3.10. (Ten dimes make a dollar, so 31 dimes is 3 dollars and 1 dimes.)

31 \times 0.10 = 3.10

Ten dimes bundle into one dollar, so 31 dimes regroup into $3.10.

5Add the four amounts

#7 Identify Subproblems 4.NBT.A.2

Total = 900 + 180 + 22 + 3.10 = 1,105.10 dollars.

900 + 180 + 22 + 3.10 = 1{,}105.10

Summing the separate bundle values gives the whole piggy bank.

Answer: $1,105.10

4 · Reviewdoes it hold up?

The big bundles dominate: $900 plus$ 180 is already $1,080, plus$ 22 and a few dollars of dimes lands near 1,105, which matches $1,105.10. Units stay in dollars throughout.

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

Standardsmin 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.

💡Takeaway. 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!

Variant 4 medium

Liam's piggy bank holds $14$ one-hundred-dollar bills, $36$ ten-dollar bills, $19$ one-dollar coins, and $28$ dimes. How much money is in the piggy bank in all?

Your answer

Show solution

1 · Understandwhat's really being asked

Add up the money in a piggy bank that holds 14 hundred-dollar bills, 36 ten-dollar bills, 19 one-dollar coins, and 28 dimes, then give the grand total.

Givens

14 one-hundred-dollar bills
36 ten-dollar bills
19 one-dollar coins
28 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.

2 · Planchoose the strategy

#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.

3 · Execute5 carry out the plan

1Value of the hundred-dollar bills

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

14 bills of $100 each are worth 14 x 100 = $1,400.

14 \times 100 = 1{,}400

Each bill is one hundred, so this many of them is that many hundreds.

2Value of the ten-dollar bills

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

36 bills of $10 each are worth 36 x 10 = $360.

36 \times 10 = 360

Ten dollars repeated 36 times shifts 36 up one place to 360.

3Value of the one-dollar coins

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

19 coins of $1 each are worth 19 x 1 = $19.

19 \times 1 = 19

That many ones is just $19.

4Value of the dimes

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

28 dimes of $0.10 each are worth 28 x 0.10 = $2.80. (Ten dimes make a dollar, so 28 dimes is 2 dollars and 8 dimes.)

28 \times 0.10 = 2.80

Ten dimes bundle into one dollar, so 28 dimes regroup into $2.80.

5Add the four amounts

#7 Identify Subproblems 4.NBT.A.2

Total = 1,400 + 360 + 19 + 2.80 = 1,781.80 dollars.

1{,}400 + 360 + 19 + 2.80 = 1{,}781.80

Summing the separate bundle values gives the whole piggy bank.

Answer: $1,781.80

4 · Reviewdoes it hold up?

The big bundles dominate: $1,400 plus$ 360 is already $1,760, plus$ 19 and a few dollars of dimes lands near 1,782, which matches $1,781.80. Units stay in dollars throughout.

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

Standardsmin 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.

💡Takeaway. 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!

Variant 5 medium

Liam's piggy bank holds $11$ one-hundred-dollar bills, $27$ ten-dollar bills, $44$ one-dollar coins, and $13$ dimes. How much money is in the piggy bank in all?

Your answer

Show solution

1 · Understandwhat's really being asked

Add up the money in a piggy bank that holds 11 hundred-dollar bills, 27 ten-dollar bills, 44 one-dollar coins, and 13 dimes, then give the grand total.

Givens

11 one-hundred-dollar bills
27 ten-dollar bills
44 one-dollar coins
13 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.

2 · Planchoose the strategy

#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.

3 · Execute5 carry out the plan

1Value of the hundred-dollar bills

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

11 bills of $100 each are worth 11 x 100 = $1,100.

11 \times 100 = 1{,}100

Each bill is one hundred, so this many of them is that many hundreds.

2Value of the ten-dollar bills

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

27 bills of $10 each are worth 27 x 10 = $270.

27 \times 10 = 270

Ten dollars repeated 27 times shifts 27 up one place to 270.

3Value of the one-dollar coins

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

44 coins of $1 each are worth 44 x 1 = $44.

44 \times 1 = 44

That many ones is just $44.

4Value of the dimes

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

13 dimes of $0.10 each are worth 13 x 0.10 = $1.30. (Ten dimes make a dollar, so 13 dimes is 1 dollars and 3 dimes.)

13 \times 0.10 = 1.30

Ten dimes bundle into one dollar, so 13 dimes regroup into $1.30.

5Add the four amounts

#7 Identify Subproblems 4.NBT.A.2

Total = 1,100 + 270 + 44 + 1.30 = 1,415.30 dollars.

1{,}100 + 270 + 44 + 1.30 = 1{,}415.30

Summing the separate bundle values gives the whole piggy bank.

Answer: $1,415.30

4 · Reviewdoes it hold up?

The big bundles dominate: $1,100 plus$ 270 is already $1,370, plus$ 44 and a few dollars of dimes lands near 1,415, which matches $1,415.30. Units stay in dollars throughout.

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

Standardsmin 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.

💡Takeaway. 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!

Variant 6 medium

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?

Your answer

Show solution

1 · Understandwhat's really being asked

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.

2 · Planchoose the strategy

#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.

3 · Execute5 carry out the plan

1Value of the hundred-dollar bills

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

12 bills of $100 each are worth 12 x 100 = $1,200.

12 \times 100 = 1{,}200

Each bill is one hundred, so this many of them is that many hundreds.

2Value of the ten-dollar bills

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

33 bills of $10 each are worth 33 x 10 = $330.

33 \times 10 = 330

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

3Value of the one-dollar coins

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

45 coins of $1 each are worth 45 x 1 = $45.

45 \times 1 = 45

That many ones is just $45.

4Value of the dimes

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

39 dimes of $0.10 each are worth 39 x 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.

5Add the four amounts

#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

4 · Reviewdoes it hold up?

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.

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

Standardsmin 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.

💡Takeaway. 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!

Variant 7 medium

Liam's piggy bank holds $18$ one-hundred-dollar bills, $22$ ten-dollar bills, $33$ one-dollar coins, and $45$ dimes. How much money is in the piggy bank in all?

Your answer

Show solution

1 · Understandwhat's really being asked

Add up the money in a piggy bank that holds 18 hundred-dollar bills, 22 ten-dollar bills, 33 one-dollar coins, and 45 dimes, then give the grand total.

Givens

18 one-hundred-dollar bills
22 ten-dollar bills
33 one-dollar coins
45 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.

2 · Planchoose the strategy

#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.

3 · Execute5 carry out the plan

1Value of the hundred-dollar bills

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

18 bills of $100 each are worth 18 x 100 = $1,800.

18 \times 100 = 1{,}800

Each bill is one hundred, so this many of them is that many hundreds.

2Value of the ten-dollar bills

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

22 bills of $10 each are worth 22 x 10 = $220.

22 \times 10 = 220

Ten dollars repeated 22 times shifts 22 up one place to 220.

3Value of the one-dollar coins

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

33 coins of $1 each are worth 33 x 1 = $33.

33 \times 1 = 33

That many ones is just $33.

4Value of the dimes

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

45 dimes of $0.10 each are worth 45 x 0.10 = $4.50. (Ten dimes make a dollar, so 45 dimes is 4 dollars and 5 dimes.)

45 \times 0.10 = 4.50

Ten dimes bundle into one dollar, so 45 dimes regroup into $4.50.

5Add the four amounts

#7 Identify Subproblems 4.NBT.A.2

Total = 1,800 + 220 + 33 + 4.50 = 2,057.50 dollars.

1{,}800 + 220 + 33 + 4.50 = 2{,}057.50

Summing the separate bundle values gives the whole piggy bank.

Answer: $2,057.50

4 · Reviewdoes it hold up?

The big bundles dominate: $1,800 plus$ 220 is already $2,020, plus$ 33 and a few dollars of dimes lands near 2,058, which matches $2,057.50. Units stay in dollars throughout.

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

Standardsmin 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.

💡Takeaway. 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!

Variant 8 hard

Liam's piggy bank holds $20$ one-hundred-dollar bills, $25$ ten-dollar bills, $36$ one-dollar coins, and $47$ dimes. How much money is in the piggy bank in all?

Your answer

Show solution

1 · Understandwhat's really being asked

Add up the money in a piggy bank that holds 20 hundred-dollar bills, 25 ten-dollar bills, 36 one-dollar coins, and 47 dimes, then give the grand total.

Givens

20 one-hundred-dollar bills
25 ten-dollar bills
36 one-dollar coins
47 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.

2 · Planchoose the strategy

#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.

3 · Execute5 carry out the plan

1Value of the hundred-dollar bills

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

20 bills of $100 each are worth 20 x 100 = $2,000.

20 \times 100 = 2{,}000

Each bill is one hundred, so this many of them is that many hundreds.

2Value of the ten-dollar bills

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

25 bills of $10 each are worth 25 x 10 = $250.

25 \times 10 = 250

Ten dollars repeated 25 times shifts 25 up one place to 250.

3Value of the one-dollar coins

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

36 coins of $1 each are worth 36 x 1 = $36.

36 \times 1 = 36

That many ones is just $36.

4Value of the dimes

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

47 dimes of $0.10 each are worth 47 x 0.10 = $4.70. (Ten dimes make a dollar, so 47 dimes is 4 dollars and 7 dimes.)

47 \times 0.10 = 4.70

Ten dimes bundle into one dollar, so 47 dimes regroup into $4.70.

5Add the four amounts

#7 Identify Subproblems 4.NBT.A.2

Total = 2,000 + 250 + 36 + 4.70 = 2,290.70 dollars.

2{,}000 + 250 + 36 + 4.70 = 2{,}290.70

Summing the separate bundle values gives the whole piggy bank.

Answer: $2,290.70

4 · Reviewdoes it hold up?

The big bundles dominate: $2,000 plus$ 250 is already $2,250, plus$ 36 and a few dollars of dimes lands near 2,291, which matches $2,290.70. Units stay in dollars throughout.

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

Standardsmin 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.

💡Takeaway. 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!

Variant 9 hard

Liam's piggy bank holds $15$ one-hundred-dollar bills, $40$ ten-dollar bills, $30$ one-dollar coins, and $50$ dimes. How much money is in the piggy bank in all?

Your answer

Show solution

1 · Understandwhat's really being asked

Add up the money in a piggy bank that holds 15 hundred-dollar bills, 40 ten-dollar bills, 30 one-dollar coins, and 50 dimes, then give the grand total.

Givens

15 one-hundred-dollar bills
40 ten-dollar bills
30 one-dollar coins
50 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.

2 · Planchoose the strategy

#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.

3 · Execute5 carry out the plan

1Value of the hundred-dollar bills

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

15 bills of $100 each are worth 15 x 100 = $1,500.

15 \times 100 = 1{,}500

Each bill is one hundred, so this many of them is that many hundreds.

2Value of the ten-dollar bills

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

40 bills of $10 each are worth 40 x 10 = $400.

40 \times 10 = 400

Ten dollars repeated 40 times shifts 40 up one place to 400.

3Value of the one-dollar coins

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

30 coins of $1 each are worth 30 x 1 = $30.

30 \times 1 = 30

That many ones is just $30.

4Value of the dimes

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

50 dimes of $0.10 each are worth 50 x 0.10 = $5.00. (Ten dimes make a dollar, so 50 dimes is 5 dollars and 0 dimes.)

50 \times 0.10 = 5.00

Ten dimes bundle into one dollar, so 50 dimes regroup into $5.00.

5Add the four amounts

#7 Identify Subproblems 4.NBT.A.2

Total = 1,500 + 400 + 30 + 5.00 = 1,935.00 dollars.

1{,}500 + 400 + 30 + 5.00 = 1{,}935.00

Summing the separate bundle values gives the whole piggy bank.

Answer: $1,935.00

4 · Reviewdoes it hold up?

The big bundles dominate: $1,500 plus$ 400 is already $1,900, plus$ 30 and a few dollars of dimes lands near 1,935, which matches $1,935.00. Units stay in dollars throughout.

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

Standardsmin 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.

💡Takeaway. 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!

Variant 10 hard

Liam's piggy bank holds $7$ one-hundred-dollar bills, $30$ ten-dollar bills, $15$ one-dollar coins, and $60$ dimes. How much money is in the piggy bank in all?

Your answer

Show solution

1 · Understandwhat's really being asked

Add up the money in a piggy bank that holds 7 hundred-dollar bills, 30 ten-dollar bills, 15 one-dollar coins, and 60 dimes, then give the grand total.

Givens

7 one-hundred-dollar bills
30 ten-dollar bills
15 one-dollar coins
60 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.

2 · Planchoose the strategy

#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.

3 · Execute5 carry out the plan

1Value of the hundred-dollar bills

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

7 bills of $100 each are worth 7 x 100 = $700.

7 \times 100 = 700

Each bill is one hundred, so this many of them is that many hundreds.

2Value of the ten-dollar bills

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

30 bills of $10 each are worth 30 x 10 = $300.

30 \times 10 = 300

Ten dollars repeated 30 times shifts 30 up one place to 300.

3Value of the one-dollar coins

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

15 coins of $1 each are worth 15 x 1 = $15.

15 \times 1 = 15

That many ones is just $15.

4Value of the dimes

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

60 dimes of $0.10 each are worth 60 x 0.10 = $6.00. (Ten dimes make a dollar, so 60 dimes is 6 dollars and 0 dimes.)

60 \times 0.10 = 6.00

Ten dimes bundle into one dollar, so 60 dimes regroup into $6.00.

5Add the four amounts

#7 Identify Subproblems 4.NBT.A.2

Total = 700 + 300 + 15 + 6.00 = 1,021.00 dollars.

700 + 300 + 15 + 6.00 = 1{,}021.00

Summing the separate bundle values gives the whole piggy bank.

Answer: $1,021.00

4 · Reviewdoes it hold up?

The big bundles dominate: $700 plus$ 300 is already $1,000, plus$ 15 and a few dollars of dimes lands near 1,021, which matches $1,021.00. Units stay in dollars throughout.

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

Standardsmin 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.

💡Takeaway. 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!

Where next?

← Back to the problem: Ten of a unit carries to the next place