← Times ten adds one place · Place-Value Regrouping

Times ten adds one place · 10 practice problems

4.NBT.A.1

Generated variants — 10

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 easy answer: 10,000

Multiplying $7{,}000$ by $10$ gives a number that equals $7$ multiplied by how many?

Show solution

1 · Understandwhat's really being asked

The number 7,000 x 10 equals 7 multiplied by some factor; find that factor.

Givens

7,000 x 10 is one value.
That value also equals 7 x (unknown factor).

Unknowns

The factor that the small number is multiplied by

Constraints

Multiplying by 10 or 100 shifts digits to higher places (adds zeros).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem#11 Work Backwards

Use the place-value pattern that multiplying by 10 appends zeros to compute 7,000 x 10, then work backwards to see how many times 7 fits into it.

3 · Execute3 carry out the plan

1Compute 7,000 x 10

#5 Look for a Pattern 4.NBT.A.1

Multiplying by 10 adds 1 zero(s), so 7,000 x 10 = 70,000.

7{,}000 \times 10 = 70{,}000

Multiplying by a power of ten shifts every digit left, tacking on zeros.

2See how 7 grows to 70,000

#11 Work Backwards 4.NBT.A.1

Start from 7. To reach 70,000 the digits must move 4 place(s) left, which is multiplying by 10,000 (4 zero(s)). So 7 x 10,000 = 70,000.

7 \times 10{,}000 = 70{,}000

Going from 7 to 70,000 means appending 4 zero(s), i.e. multiplying by 10,000.

3State the factor

#9 Solve an Easier Related Problem 4.NBT.A.1

Since 7,000 x 10 = 70,000 = 7 x 10,000, the missing factor is 10,000.

7{,}000 \times 10 = 7 \times 10{,}000

Both sides equal 70,000, so 7 is multiplied by 10,000.

Answer: 10,000

4 · Reviewdoes it hold up?

Check: 7 x 10,000 = 70,000 and 7,000 x 10 = 70,000, so both products match. The factor 10,000 is correct.

Another way: Guess and check with place value (tool 6): 7,000 is 7 x 1,000, so 7,000 x 10 = 7 x 1,000 x 10 = 7 x 10,000.

Standardsmin grade 4

4.NBT.A.1 Recognize that a digit represents ten times what it represents in place to its right — Using the times-ten place-value shift to relate 7,000 x 10 and 7 x 10,000.

💡Takeaway. This only needs Grade 4 place-value sense: every times-ten just slides the digits one place and adds a zero!

Variant 2 easy answer: 100

Multiplying $90$ by $10$ gives a number that equals $9$ multiplied by how many?

Show solution

1 · Understandwhat's really being asked

The number 90 x 10 equals 9 multiplied by some factor; find that factor.

Givens

90 x 10 is one value.
That value also equals 9 x (unknown factor).

Unknowns

The factor that the small number is multiplied by

Constraints

Multiplying by 10 or 100 shifts digits to higher places (adds zeros).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem#11 Work Backwards

Use the place-value pattern that multiplying by 10 appends zeros to compute 90 x 10, then work backwards to see how many times 9 fits into it.

3 · Execute3 carry out the plan

1Compute 90 x 10

#5 Look for a Pattern 4.NBT.A.1

Multiplying by 10 adds 1 zero(s), so 90 x 10 = 900.

90 \times 10 = 900

Multiplying by a power of ten shifts every digit left, tacking on zeros.

2See how 9 grows to 900

#11 Work Backwards 4.NBT.A.1

Start from 9. To reach 900 the digits must move 2 place(s) left, which is multiplying by 100 (2 zero(s)). So 9 x 100 = 900.

9 \times 100 = 900

Going from 9 to 900 means appending 2 zero(s), i.e. multiplying by 100.

3State the factor

#9 Solve an Easier Related Problem 4.NBT.A.1

Since 90 x 10 = 900 = 9 x 100, the missing factor is 100.

90 \times 10 = 9 \times 100

Both sides equal 900, so 9 is multiplied by 100.

Answer: 100

4 · Reviewdoes it hold up?

Check: 9 x 100 = 900 and 90 x 10 = 900, so both products match. The factor 100 is correct.

Another way: Guess and check with place value (tool 6): 90 is 9 x 10, so 90 x 10 = 9 x 10 x 10 = 9 x 100.

Standardsmin grade 4

4.NBT.A.1 Recognize that a digit represents ten times what it represents in place to its right — Using the times-ten place-value shift to relate 90 x 10 and 9 x 100.

💡Takeaway. This only needs Grade 4 place-value sense: every times-ten just slides the digits one place and adds a zero!

Variant 3 easy answer: 1,000

Multiplying $120$ by $100$ gives a number that equals $12$ multiplied by how many?

Show solution

1 · Understandwhat's really being asked

The number 120 x 100 equals 12 multiplied by some factor; find that factor.

Givens

120 x 100 is one value.
That value also equals 12 x (unknown factor).

Unknowns

The factor that the small number is multiplied by

Constraints

Multiplying by 10 or 100 shifts digits to higher places (adds zeros).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem#11 Work Backwards

Use the place-value pattern that multiplying by 100 appends zeros to compute 120 x 100, then work backwards to see how many times 12 fits into it.

3 · Execute3 carry out the plan

1Compute 120 x 100

#5 Look for a Pattern 4.NBT.A.1

Multiplying by 100 adds 2 zero(s), so 120 x 100 = 12,000.

120 \times 100 = 12{,}000

Multiplying by a power of ten shifts every digit left, tacking on zeros.

2See how 12 grows to 12,000

#11 Work Backwards 4.NBT.A.1

Start from 12. To reach 12,000 the digits must move 3 place(s) left, which is multiplying by 1,000 (3 zero(s)). So 12 x 1,000 = 12,000.

12 \times 1{,}000 = 12{,}000

Going from 12 to 12,000 means appending 3 zero(s), i.e. multiplying by 1,000.

3State the factor

#9 Solve an Easier Related Problem 4.NBT.A.1

Since 120 x 100 = 12,000 = 12 x 1,000, the missing factor is 1,000.

120 \times 100 = 12 \times 1{,}000

Both sides equal 12,000, so 12 is multiplied by 1,000.

Answer: 1,000

4 · Reviewdoes it hold up?

Check: 12 x 1,000 = 12,000 and 120 x 100 = 12,000, so both products match. The factor 1,000 is correct.

Another way: Guess and check with place value (tool 6): 120 is 12 x 10, so 120 x 100 = 12 x 10 x 100 = 12 x 1,000.

Standardsmin grade 4

4.NBT.A.1 Recognize that a digit represents ten times what it represents in place to its right — Using the times-ten place-value shift to relate 120 x 100 and 12 x 1,000.

💡Takeaway. This only needs Grade 4 place-value sense: every times-ten just slides the digits one place and adds a zero!

Variant 4 medium answer: 10,000

Multiplying $5{,}000$ by $100$ gives a number that equals $50$ multiplied by how many?

Show solution

1 · Understandwhat's really being asked

The number 5,000 x 100 equals 50 multiplied by some factor; find that factor.

Givens

5,000 x 100 is one value.
That value also equals 50 x (unknown factor).

Unknowns

The factor that the small number is multiplied by

Constraints

Multiplying by 10 or 100 shifts digits to higher places (adds zeros).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem#11 Work Backwards

Use the place-value pattern that multiplying by 100 appends zeros to compute 5,000 x 100, then work backwards to see how many times 50 fits into it.

3 · Execute3 carry out the plan

1Compute 5,000 x 100

#5 Look for a Pattern 4.NBT.A.1

Multiplying by 100 adds 2 zero(s), so 5,000 x 100 = 500,000.

5{,}000 \times 100 = 500{,}000

Multiplying by a power of ten shifts every digit left, tacking on zeros.

2See how 50 grows to 500,000

#11 Work Backwards 4.NBT.A.1

Start from 50. To reach 500,000 the digits must move 4 place(s) left, which is multiplying by 10,000 (4 zero(s)). So 50 x 10,000 = 500,000.

50 \times 10{,}000 = 500{,}000

Going from 50 to 500,000 means appending 4 zero(s), i.e. multiplying by 10,000.

3State the factor

#9 Solve an Easier Related Problem 4.NBT.A.1

Since 5,000 x 100 = 500,000 = 50 x 10,000, the missing factor is 10,000.

5{,}000 \times 100 = 50 \times 10{,}000

Both sides equal 500,000, so 50 is multiplied by 10,000.

Answer: 10,000

4 · Reviewdoes it hold up?

Check: 50 x 10,000 = 500,000 and 5,000 x 100 = 500,000, so both products match. The factor 10,000 is correct.

Another way: Guess and check with place value (tool 6): 5,000 is 50 x 100, so 5,000 x 100 = 50 x 100 x 100 = 50 x 10,000.

Standardsmin grade 4

4.NBT.A.1 Recognize that a digit represents ten times what it represents in place to its right — Using the times-ten place-value shift to relate 5,000 x 100 and 50 x 10,000.

💡Takeaway. This only needs Grade 4 place-value sense: every times-ten just slides the digits one place and adds a zero!

Variant 5 medium answer: 100,000

Multiplying $63{,}000$ by $100$ gives a number that equals $63$ multiplied by how many?

Show solution

1 · Understandwhat's really being asked

The number 63,000 x 100 equals 63 multiplied by some factor; find that factor.

Givens

63,000 x 100 is one value.
That value also equals 63 x (unknown factor).

Unknowns

The factor that the small number is multiplied by

Constraints

Multiplying by 10 or 100 shifts digits to higher places (adds zeros).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem#11 Work Backwards

Use the place-value pattern that multiplying by 100 appends zeros to compute 63,000 x 100, then work backwards to see how many times 63 fits into it.

3 · Execute3 carry out the plan

1Compute 63,000 x 100

#5 Look for a Pattern 4.NBT.A.1

Multiplying by 100 adds 2 zero(s), so 63,000 x 100 = 6,300,000.

63{,}000 \times 100 = 6{,}300{,}000

Multiplying by a power of ten shifts every digit left, tacking on zeros.

2See how 63 grows to 6,300,000

#11 Work Backwards 4.NBT.A.1

Start from 63. To reach 6,300,000 the digits must move 5 place(s) left, which is multiplying by 100,000 (5 zero(s)). So 63 x 100,000 = 6,300,000.

63 \times 100{,}000 = 6{,}300{,}000

Going from 63 to 6,300,000 means appending 5 zero(s), i.e. multiplying by 100,000.

3State the factor

#9 Solve an Easier Related Problem 4.NBT.A.1

Since 63,000 x 100 = 6,300,000 = 63 x 100,000, the missing factor is 100,000.

63{,}000 \times 100 = 63 \times 100{,}000

Both sides equal 6,300,000, so 63 is multiplied by 100,000.

Answer: 100,000

4 · Reviewdoes it hold up?

Check: 63 x 100,000 = 6,300,000 and 63,000 x 100 = 6,300,000, so both products match. The factor 100,000 is correct.

Another way: Guess and check with place value (tool 6): 63,000 is 63 x 1,000, so 63,000 x 100 = 63 x 1,000 x 100 = 63 x 100,000.

Standardsmin grade 4

4.NBT.A.1 Recognize that a digit represents ten times what it represents in place to its right — Using the times-ten place-value shift to relate 63,000 x 100 and 63 x 100,000.

💡Takeaway. This only needs Grade 4 place-value sense: every times-ten just slides the digits one place and adds a zero!

Variant 6 medium answer: 10,000

Multiplying $250$ by $1{,}000$ gives a number that equals $25$ multiplied by how many?

Show solution

1 · Understandwhat's really being asked

The number 250 x 1,000 equals 25 multiplied by some factor; find that factor.

Givens

250 x 1,000 is one value.
That value also equals 25 x (unknown factor).

Unknowns

The factor that the small number is multiplied by

Constraints

Multiplying by 10 or 100 shifts digits to higher places (adds zeros).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem#11 Work Backwards

Use the place-value pattern that multiplying by 1,000 appends zeros to compute 250 x 1,000, then work backwards to see how many times 25 fits into it.

3 · Execute3 carry out the plan

1Compute 250 x 1,000

#5 Look for a Pattern 4.NBT.A.1

Multiplying by 1,000 adds 3 zero(s), so 250 x 1,000 = 250,000.

250 \times 1{,}000 = 250{,}000

Multiplying by a power of ten shifts every digit left, tacking on zeros.

2See how 25 grows to 250,000

#11 Work Backwards 4.NBT.A.1

Start from 25. To reach 250,000 the digits must move 4 place(s) left, which is multiplying by 10,000 (4 zero(s)). So 25 x 10,000 = 250,000.

25 \times 10{,}000 = 250{,}000

Going from 25 to 250,000 means appending 4 zero(s), i.e. multiplying by 10,000.

3State the factor

#9 Solve an Easier Related Problem 4.NBT.A.1

Since 250 x 1,000 = 250,000 = 25 x 10,000, the missing factor is 10,000.

250 \times 1{,}000 = 25 \times 10{,}000

Both sides equal 250,000, so 25 is multiplied by 10,000.

Answer: 10,000

4 · Reviewdoes it hold up?

Check: 25 x 10,000 = 250,000 and 250 x 1,000 = 250,000, so both products match. The factor 10,000 is correct.

Another way: Guess and check with place value (tool 6): 250 is 25 x 10, so 250 x 1,000 = 25 x 10 x 1,000 = 25 x 10,000.

Standardsmin grade 4

4.NBT.A.1 Recognize that a digit represents ten times what it represents in place to its right — Using the times-ten place-value shift to relate 250 x 1,000 and 25 x 10,000.

💡Takeaway. This only needs Grade 4 place-value sense: every times-ten just slides the digits one place and adds a zero!

Variant 7 medium answer: 10,000

Multiplying $800$ by $100$ gives a number that equals $8$ multiplied by how many?

Show solution

1 · Understandwhat's really being asked

The number 800 x 100 equals 8 multiplied by some factor; find that factor.

Givens

800 x 100 is one value.
That value also equals 8 x (unknown factor).

Unknowns

The factor that the small number is multiplied by

Constraints

Multiplying by 10 or 100 shifts digits to higher places (adds zeros).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem#11 Work Backwards

Use the place-value pattern that multiplying by 100 appends zeros to compute 800 x 100, then work backwards to see how many times 8 fits into it.

3 · Execute3 carry out the plan

1Compute 800 x 100

#5 Look for a Pattern 4.NBT.A.1

Multiplying by 100 adds 2 zero(s), so 800 x 100 = 80,000.

800 \times 100 = 80{,}000

Multiplying by a power of ten shifts every digit left, tacking on zeros.

2See how 8 grows to 80,000

#11 Work Backwards 4.NBT.A.1

Start from 8. To reach 80,000 the digits must move 4 place(s) left, which is multiplying by 10,000 (4 zero(s)). So 8 x 10,000 = 80,000.

8 \times 10{,}000 = 80{,}000

Going from 8 to 80,000 means appending 4 zero(s), i.e. multiplying by 10,000.

3State the factor

#9 Solve an Easier Related Problem 4.NBT.A.1

Since 800 x 100 = 80,000 = 8 x 10,000, the missing factor is 10,000.

800 \times 100 = 8 \times 10{,}000

Both sides equal 80,000, so 8 is multiplied by 10,000.

Answer: 10,000

4 · Reviewdoes it hold up?

Check: 8 x 10,000 = 80,000 and 800 x 100 = 80,000, so both products match. The factor 10,000 is correct.

Another way: Guess and check with place value (tool 6): 800 is 8 x 100, so 800 x 100 = 8 x 100 x 100 = 8 x 10,000.

Standardsmin grade 4

4.NBT.A.1 Recognize that a digit represents ten times what it represents in place to its right — Using the times-ten place-value shift to relate 800 x 100 and 8 x 10,000.

💡Takeaway. This only needs Grade 4 place-value sense: every times-ten just slides the digits one place and adds a zero!

Variant 8 hard answer: 10,000

Multiplying $4{,}500$ by $100$ gives a number that equals $45$ multiplied by how many?

Show solution

1 · Understandwhat's really being asked

The number 4,500 x 100 equals 45 multiplied by some factor; find that factor.

Givens

4,500 x 100 is one value.
That value also equals 45 x (unknown factor).

Unknowns

The factor that the small number is multiplied by

Constraints

Multiplying by 10 or 100 shifts digits to higher places (adds zeros).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem#11 Work Backwards

Use the place-value pattern that multiplying by 100 appends zeros to compute 4,500 x 100, then work backwards to see how many times 45 fits into it.

3 · Execute3 carry out the plan

1Compute 4,500 x 100

#5 Look for a Pattern 4.NBT.A.1

Multiplying by 100 adds 2 zero(s), so 4,500 x 100 = 450,000.

4{,}500 \times 100 = 450{,}000

Multiplying by a power of ten shifts every digit left, tacking on zeros.

2See how 45 grows to 450,000

#11 Work Backwards 4.NBT.A.1

Start from 45. To reach 450,000 the digits must move 4 place(s) left, which is multiplying by 10,000 (4 zero(s)). So 45 x 10,000 = 450,000.

45 \times 10{,}000 = 450{,}000

Going from 45 to 450,000 means appending 4 zero(s), i.e. multiplying by 10,000.

3State the factor

#9 Solve an Easier Related Problem 4.NBT.A.1

Since 4,500 x 100 = 450,000 = 45 x 10,000, the missing factor is 10,000.

4{,}500 \times 100 = 45 \times 10{,}000

Both sides equal 450,000, so 45 is multiplied by 10,000.

Answer: 10,000

4 · Reviewdoes it hold up?

Check: 45 x 10,000 = 450,000 and 4,500 x 100 = 450,000, so both products match. The factor 10,000 is correct.

Another way: Guess and check with place value (tool 6): 4,500 is 45 x 100, so 4,500 x 100 = 45 x 100 x 100 = 45 x 10,000.

Standardsmin grade 4

4.NBT.A.1 Recognize that a digit represents ten times what it represents in place to its right — Using the times-ten place-value shift to relate 4,500 x 100 and 45 x 10,000.

💡Takeaway. This only needs Grade 4 place-value sense: every times-ten just slides the digits one place and adds a zero!

Variant 9 hard answer: 100,000

Multiplying $3{,}600$ by $1{,}000$ gives a number that equals $36$ multiplied by how many?

Show solution

1 · Understandwhat's really being asked

The number 3,600 x 1,000 equals 36 multiplied by some factor; find that factor.

Givens

3,600 x 1,000 is one value.
That value also equals 36 x (unknown factor).

Unknowns

The factor that the small number is multiplied by

Constraints

Multiplying by 10 or 100 shifts digits to higher places (adds zeros).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem#11 Work Backwards

Use the place-value pattern that multiplying by 1,000 appends zeros to compute 3,600 x 1,000, then work backwards to see how many times 36 fits into it.

3 · Execute3 carry out the plan

1Compute 3,600 x 1,000

#5 Look for a Pattern 4.NBT.A.1

Multiplying by 1,000 adds 3 zero(s), so 3,600 x 1,000 = 3,600,000.

3{,}600 \times 1{,}000 = 3{,}600{,}000

Multiplying by a power of ten shifts every digit left, tacking on zeros.

2See how 36 grows to 3,600,000

#11 Work Backwards 4.NBT.A.1

Start from 36. To reach 3,600,000 the digits must move 5 place(s) left, which is multiplying by 100,000 (5 zero(s)). So 36 x 100,000 = 3,600,000.

36 \times 100{,}000 = 3{,}600{,}000

Going from 36 to 3,600,000 means appending 5 zero(s), i.e. multiplying by 100,000.

3State the factor

#9 Solve an Easier Related Problem 4.NBT.A.1

Since 3,600 x 1,000 = 3,600,000 = 36 x 100,000, the missing factor is 100,000.

3{,}600 \times 1{,}000 = 36 \times 100{,}000

Both sides equal 3,600,000, so 36 is multiplied by 100,000.

Answer: 100,000

4 · Reviewdoes it hold up?

Check: 36 x 100,000 = 3,600,000 and 3,600 x 1,000 = 3,600,000, so both products match. The factor 100,000 is correct.

Another way: Guess and check with place value (tool 6): 3,600 is 36 x 100, so 3,600 x 1,000 = 36 x 100 x 1,000 = 36 x 100,000.

Standardsmin grade 4

4.NBT.A.1 Recognize that a digit represents ten times what it represents in place to its right — Using the times-ten place-value shift to relate 3,600 x 1,000 and 36 x 100,000.

💡Takeaway. This only needs Grade 4 place-value sense: every times-ten just slides the digits one place and adds a zero!

Variant 10 hard answer: 100,000

Multiplying $1{,}700$ by $1{,}000$ gives a number that equals $17$ multiplied by how many?

Show solution

1 · Understandwhat's really being asked

The number 1,700 x 1,000 equals 17 multiplied by some factor; find that factor.

Givens

1,700 x 1,000 is one value.
That value also equals 17 x (unknown factor).

Unknowns

The factor that the small number is multiplied by

Constraints

Multiplying by 10 or 100 shifts digits to higher places (adds zeros).

2 · Planchoose the strategy

#5 Look for a Pattern · also uses: #9 Solve an Easier Related Problem#11 Work Backwards

Use the place-value pattern that multiplying by 1,000 appends zeros to compute 1,700 x 1,000, then work backwards to see how many times 17 fits into it.

3 · Execute3 carry out the plan

1Compute 1,700 x 1,000

#5 Look for a Pattern 4.NBT.A.1

Multiplying by 1,000 adds 3 zero(s), so 1,700 x 1,000 = 1,700,000.

1{,}700 \times 1{,}000 = 1{,}700{,}000

Multiplying by a power of ten shifts every digit left, tacking on zeros.

2See how 17 grows to 1,700,000

#11 Work Backwards 4.NBT.A.1

Start from 17. To reach 1,700,000 the digits must move 5 place(s) left, which is multiplying by 100,000 (5 zero(s)). So 17 x 100,000 = 1,700,000.

17 \times 100{,}000 = 1{,}700{,}000

Going from 17 to 1,700,000 means appending 5 zero(s), i.e. multiplying by 100,000.

3State the factor

#9 Solve an Easier Related Problem 4.NBT.A.1

Since 1,700 x 1,000 = 1,700,000 = 17 x 100,000, the missing factor is 100,000.

1{,}700 \times 1{,}000 = 17 \times 100{,}000

Both sides equal 1,700,000, so 17 is multiplied by 100,000.

Answer: 100,000

4 · Reviewdoes it hold up?

Check: 17 x 100,000 = 1,700,000 and 1,700 x 1,000 = 1,700,000, so both products match. The factor 100,000 is correct.

Another way: Guess and check with place value (tool 6): 1,700 is 17 x 100, so 1,700 x 1,000 = 17 x 100 x 1,000 = 17 x 100,000.

Standardsmin grade 4

4.NBT.A.1 Recognize that a digit represents ten times what it represents in place to its right — Using the times-ten place-value shift to relate 1,700 x 1,000 and 17 x 100,000.

💡Takeaway. This only needs Grade 4 place-value sense: every times-ten just slides the digits one place and adds a zero!