← Reverse decimal operations to recover the start · Work Backwards to Recover a Start Value

Reverse decimal operations to recover the start · 10 practice problems

5.NBT.B.75.NBT.A.2

Generated variants — 10

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

Variant 1 medium answer: 8090

A certain number's $\frac{1}{100}$ is $0.13$ less than $81.03$ . Find the number.

Show solution

1 · Understandwhat's really being asked

Some number divided by 100 (its one-hundredth) equals a value that is 0.13 less than 81.03. Find the original number.

Givens

(the number) x 1/100 = 81.03 - 0.13.
1/100 of a number means the number divided by 100.

Unknowns

The original number.

Constraints

0.13 is a small decimal, so the right side is computed by exact decimal subtraction.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First compute the value that equals one-hundredth of the number, then undo the 'divide by 100' by multiplying by 100 to recover the original number.

3 · Execute2 carry out the plan

1Find one-hundredth of the number

#11 Work Backwards 5.NBT.B.7

The number's hundredth is 0.13 less than 81.03, so subtract: 81.03 - 0.13 = 80.9.

81.03 - 0.13 = 80.9

'0.13 less than' means subtract 0.13.

2Undo the divide-by-100

#11 Work Backwards 5.NBT.B.7

If 1/100 of the number is 80.9, then the number itself is 100 times that. Multiplying by 100 shifts the decimal point two places right: 80.9 x 100 = 8090.

80.9 \times 100 = 8090

Taking 1/100 shrank the number, so multiplying by 100 grows it back.

Answer: 8090

4 · Reviewdoes it hold up?

Check forward: 8090 / 100 = 80.9, and 80.9 is 0.13 less than 81.03 (81.03 - 80.9 = 0.13). Everything matches.

Another way: Guess and Check the place-value shift: since 1/100 of the answer must be about 81.03, the answer is about 8090; refining makes the hundredth exactly 80.9.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 81.03 - 0.13 and multiplying 80.9 x 100.
5.NBT.A.2 Explain patterns in number of zeros and placement of decimal point — Shifting the decimal point two places when multiplying by 100.

💡Takeaway. '1/100 of it is...' just means divide by 100 - so multiply by 100 to get the number back!

Variant 2 medium answer: 7320

A certain number's $\frac{1}{100}$ is $0.25$ less than $73.45$ . Find the number.

Show solution

1 · Understandwhat's really being asked

Some number divided by 100 (its one-hundredth) equals a value that is 0.25 less than 73.45. Find the original number.

Givens

(the number) x 1/100 = 73.45 - 0.25.
1/100 of a number means the number divided by 100.

Unknowns

The original number.

Constraints

0.25 is a small decimal, so the right side is computed by exact decimal subtraction.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First compute the value that equals one-hundredth of the number, then undo the 'divide by 100' by multiplying by 100 to recover the original number.

3 · Execute2 carry out the plan

1Find one-hundredth of the number

#11 Work Backwards 5.NBT.B.7

The number's hundredth is 0.25 less than 73.45, so subtract: 73.45 - 0.25 = 73.2.

73.45 - 0.25 = 73.2

'0.25 less than' means subtract 0.25.

2Undo the divide-by-100

#11 Work Backwards 5.NBT.B.7

If 1/100 of the number is 73.2, then the number itself is 100 times that. Multiplying by 100 shifts the decimal point two places right: 73.2 x 100 = 7320.

73.2 \times 100 = 7320

Taking 1/100 shrank the number, so multiplying by 100 grows it back.

Answer: 7320

4 · Reviewdoes it hold up?

Check forward: 7320 / 100 = 73.2, and 73.2 is 0.25 less than 73.45 (73.45 - 73.2 = 0.25). Everything matches.

Another way: Guess and Check the place-value shift: since 1/100 of the answer must be about 73.45, the answer is about 7320; refining makes the hundredth exactly 73.2.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 73.45 - 0.25 and multiplying 73.2 x 100.
5.NBT.A.2 Explain patterns in number of zeros and placement of decimal point — Shifting the decimal point two places when multiplying by 100.

💡Takeaway. '1/100 of it is...' just means divide by 100 - so multiply by 100 to get the number back!

Variant 3 medium answer: 3758.6

A certain number's $\frac{1}{100}$ is $0.024$ less than $37.61$ . Find the number.

Show solution

1 · Understandwhat's really being asked

Some number divided by 100 (its one-hundredth) equals a value that is 0.024 less than 37.61. Find the original number.

Givens

(the number) x 1/100 = 37.61 - 0.024.
1/100 of a number means the number divided by 100.

Unknowns

The original number.

Constraints

0.024 is a small decimal, so the right side is computed by exact decimal subtraction.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First compute the value that equals one-hundredth of the number, then undo the 'divide by 100' by multiplying by 100 to recover the original number.

3 · Execute2 carry out the plan

1Find one-hundredth of the number

#11 Work Backwards 5.NBT.B.7

The number's hundredth is 0.024 less than 37.61, so subtract: 37.61 - 0.024 = 37.586.

37.61 - 0.024 = 37.586

'0.024 less than' means subtract 0.024.

2Undo the divide-by-100

#11 Work Backwards 5.NBT.B.7

If 1/100 of the number is 37.586, then the number itself is 100 times that. Multiplying by 100 shifts the decimal point two places right: 37.586 x 100 = 3758.6.

37.586 \times 100 = 3758.6

Taking 1/100 shrank the number, so multiplying by 100 grows it back.

Answer: 3758.6

4 · Reviewdoes it hold up?

Check forward: 3758.6 / 100 = 37.586, and 37.586 is 0.024 less than 37.61 (37.61 - 37.586 = 0.024). Everything matches.

Another way: Guess and Check the place-value shift: since 1/100 of the answer must be about 37.61, the answer is about 3758.6; refining makes the hundredth exactly 37.586.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 37.61 - 0.024 and multiplying 37.586 x 100.
5.NBT.A.2 Explain patterns in number of zeros and placement of decimal point — Shifting the decimal point two places when multiplying by 100.

💡Takeaway. '1/100 of it is...' just means divide by 100 - so multiply by 100 to get the number back!

Variant 4 medium answer: 2985.2

A certain number's $\frac{1}{100}$ is $0.018$ less than $29.87$ . Find the number.

Show solution

1 · Understandwhat's really being asked

Some number divided by 100 (its one-hundredth) equals a value that is 0.018 less than 29.87. Find the original number.

Givens

(the number) x 1/100 = 29.87 - 0.018.
1/100 of a number means the number divided by 100.

Unknowns

The original number.

Constraints

0.018 is a small decimal, so the right side is computed by exact decimal subtraction.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First compute the value that equals one-hundredth of the number, then undo the 'divide by 100' by multiplying by 100 to recover the original number.

3 · Execute2 carry out the plan

1Find one-hundredth of the number

#11 Work Backwards 5.NBT.B.7

The number's hundredth is 0.018 less than 29.87, so subtract: 29.87 - 0.018 = 29.852.

29.87 - 0.018 = 29.852

'0.018 less than' means subtract 0.018.

2Undo the divide-by-100

#11 Work Backwards 5.NBT.B.7

If 1/100 of the number is 29.852, then the number itself is 100 times that. Multiplying by 100 shifts the decimal point two places right: 29.852 x 100 = 2985.2.

29.852 \times 100 = 2985.2

Taking 1/100 shrank the number, so multiplying by 100 grows it back.

Answer: 2985.2

4 · Reviewdoes it hold up?

Check forward: 2985.2 / 100 = 29.852, and 29.852 is 0.018 less than 29.87 (29.87 - 29.852 = 0.018). Everything matches.

Another way: Guess and Check the place-value shift: since 1/100 of the answer must be about 29.87, the answer is about 2985.2; refining makes the hundredth exactly 29.852.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 29.87 - 0.018 and multiplying 29.852 x 100.
5.NBT.A.2 Explain patterns in number of zeros and placement of decimal point — Shifting the decimal point two places when multiplying by 100.

💡Takeaway. '1/100 of it is...' just means divide by 100 - so multiply by 100 to get the number back!

Variant 5 medium answer: 4511.7

A certain number's $\frac{1}{100}$ is $0.003$ less than $45.12$ . Find the number.

Show solution

1 · Understandwhat's really being asked

Some number divided by 100 (its one-hundredth) equals a value that is 0.003 less than 45.12. Find the original number.

Givens

(the number) x 1/100 = 45.12 - 0.003.
1/100 of a number means the number divided by 100.

Unknowns

The original number.

Constraints

0.003 is a small decimal, so the right side is computed by exact decimal subtraction.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First compute the value that equals one-hundredth of the number, then undo the 'divide by 100' by multiplying by 100 to recover the original number.

3 · Execute2 carry out the plan

1Find one-hundredth of the number

#11 Work Backwards 5.NBT.B.7

The number's hundredth is 0.003 less than 45.12, so subtract: 45.12 - 0.003 = 45.117.

45.12 - 0.003 = 45.117

'0.003 less than' means subtract 0.003.

2Undo the divide-by-100

#11 Work Backwards 5.NBT.B.7

If 1/100 of the number is 45.117, then the number itself is 100 times that. Multiplying by 100 shifts the decimal point two places right: 45.117 x 100 = 4511.7.

45.117 \times 100 = 4511.7

Taking 1/100 shrank the number, so multiplying by 100 grows it back.

Answer: 4511.7

4 · Reviewdoes it hold up?

Check forward: 4511.7 / 100 = 45.117, and 45.117 is 0.003 less than 45.12 (45.12 - 45.117 = 0.003). Everything matches.

Another way: Guess and Check the place-value shift: since 1/100 of the answer must be about 45.12, the answer is about 4511.7; refining makes the hundredth exactly 45.117.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 45.12 - 0.003 and multiplying 45.117 x 100.
5.NBT.A.2 Explain patterns in number of zeros and placement of decimal point — Shifting the decimal point two places when multiplying by 100.

💡Takeaway. '1/100 of it is...' just means divide by 100 - so multiply by 100 to get the number back!

Variant 6 medium answer: 5239.1

A certain number's $\frac{1}{100}$ is $0.009$ less than $52.4$ . Find the number.

Show solution

1 · Understandwhat's really being asked

Some number divided by 100 (its one-hundredth) equals a value that is 0.009 less than 52.4. Find the original number.

Givens

(the number) x 1/100 = 52.4 - 0.009.
1/100 of a number means the number divided by 100.

Unknowns

The original number.

Constraints

0.009 is a small decimal, so the right side is computed by exact decimal subtraction.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First compute the value that equals one-hundredth of the number, then undo the 'divide by 100' by multiplying by 100 to recover the original number.

3 · Execute2 carry out the plan

1Find one-hundredth of the number

#11 Work Backwards 5.NBT.B.7

The number's hundredth is 0.009 less than 52.4, so subtract: 52.4 - 0.009 = 52.391.

52.4 - 0.009 = 52.391

'0.009 less than' means subtract 0.009.

2Undo the divide-by-100

#11 Work Backwards 5.NBT.B.7

If 1/100 of the number is 52.391, then the number itself is 100 times that. Multiplying by 100 shifts the decimal point two places right: 52.391 x 100 = 5239.1.

52.391 \times 100 = 5239.1

Taking 1/100 shrank the number, so multiplying by 100 grows it back.

Answer: 5239.1

4 · Reviewdoes it hold up?

Check forward: 5239.1 / 100 = 52.391, and 52.391 is 0.009 less than 52.4 (52.4 - 52.391 = 0.009). Everything matches.

Another way: Guess and Check the place-value shift: since 1/100 of the answer must be about 52.4, the answer is about 5239.1; refining makes the hundredth exactly 52.391.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 52.4 - 0.009 and multiplying 52.391 x 100.
5.NBT.A.2 Explain patterns in number of zeros and placement of decimal point — Shifting the decimal point two places when multiplying by 100.

💡Takeaway. '1/100 of it is...' just means divide by 100 - so multiply by 100 to get the number back!

Variant 7 medium answer: 9024.5

A certain number's $\frac{1}{100}$ is $0.005$ less than $90.25$ . Find the number.

Show solution

1 · Understandwhat's really being asked

Some number divided by 100 (its one-hundredth) equals a value that is 0.005 less than 90.25. Find the original number.

Givens

(the number) x 1/100 = 90.25 - 0.005.
1/100 of a number means the number divided by 100.

Unknowns

The original number.

Constraints

0.005 is a small decimal, so the right side is computed by exact decimal subtraction.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First compute the value that equals one-hundredth of the number, then undo the 'divide by 100' by multiplying by 100 to recover the original number.

3 · Execute2 carry out the plan

1Find one-hundredth of the number

#11 Work Backwards 5.NBT.B.7

The number's hundredth is 0.005 less than 90.25, so subtract: 90.25 - 0.005 = 90.245.

90.25 - 0.005 = 90.245

'0.005 less than' means subtract 0.005.

2Undo the divide-by-100

#11 Work Backwards 5.NBT.B.7

If 1/100 of the number is 90.245, then the number itself is 100 times that. Multiplying by 100 shifts the decimal point two places right: 90.245 x 100 = 9024.5.

90.245 \times 100 = 9024.5

Taking 1/100 shrank the number, so multiplying by 100 grows it back.

Answer: 9024.5

4 · Reviewdoes it hold up?

Check forward: 9024.5 / 100 = 90.245, and 90.245 is 0.005 less than 90.25 (90.25 - 90.245 = 0.005). Everything matches.

Another way: Guess and Check the place-value shift: since 1/100 of the answer must be about 90.25, the answer is about 9024.5; refining makes the hundredth exactly 90.245.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 90.25 - 0.005 and multiplying 90.245 x 100.
5.NBT.A.2 Explain patterns in number of zeros and placement of decimal point — Shifting the decimal point two places when multiplying by 100.

💡Takeaway. '1/100 of it is...' just means divide by 100 - so multiply by 100 to get the number back!

Variant 8 medium answer: 6541.3

A certain number's $\frac{1}{100}$ is $0.007$ less than $65.42$ . Find the number.

Show solution

1 · Understandwhat's really being asked

Some number divided by 100 (its one-hundredth) equals a value that is 0.007 less than 65.42. Find the original number.

Givens

(the number) x 1/100 = 65.42 - 0.007.
1/100 of a number means the number divided by 100.

Unknowns

The original number.

Constraints

0.007 is a small decimal, so the right side is computed by exact decimal subtraction.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First compute the value that equals one-hundredth of the number, then undo the 'divide by 100' by multiplying by 100 to recover the original number.

3 · Execute2 carry out the plan

1Find one-hundredth of the number

#11 Work Backwards 5.NBT.B.7

The number's hundredth is 0.007 less than 65.42, so subtract: 65.42 - 0.007 = 65.413.

65.42 - 0.007 = 65.413

'0.007 less than' means subtract 0.007.

2Undo the divide-by-100

#11 Work Backwards 5.NBT.B.7

If 1/100 of the number is 65.413, then the number itself is 100 times that. Multiplying by 100 shifts the decimal point two places right: 65.413 x 100 = 6541.3.

65.413 \times 100 = 6541.3

Taking 1/100 shrank the number, so multiplying by 100 grows it back.

Answer: 6541.3

4 · Reviewdoes it hold up?

Check forward: 6541.3 / 100 = 65.413, and 65.413 is 0.007 less than 65.42 (65.42 - 65.413 = 0.007). Everything matches.

Another way: Guess and Check the place-value shift: since 1/100 of the answer must be about 65.42, the answer is about 6541.3; refining makes the hundredth exactly 65.413.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 65.42 - 0.007 and multiplying 65.413 x 100.
5.NBT.A.2 Explain patterns in number of zeros and placement of decimal point — Shifting the decimal point two places when multiplying by 100.

💡Takeaway. '1/100 of it is...' just means divide by 100 - so multiply by 100 to get the number back!

Variant 9 medium answer: 6600

A certain number's $\frac{1}{100}$ is $0.6$ less than $66.6$ . Find the number.

Show solution

1 · Understandwhat's really being asked

Some number divided by 100 (its one-hundredth) equals a value that is 0.6 less than 66.6. Find the original number.

Givens

(the number) x 1/100 = 66.6 - 0.6.
1/100 of a number means the number divided by 100.

Unknowns

The original number.

Constraints

0.6 is a small decimal, so the right side is computed by exact decimal subtraction.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First compute the value that equals one-hundredth of the number, then undo the 'divide by 100' by multiplying by 100 to recover the original number.

3 · Execute2 carry out the plan

1Find one-hundredth of the number

#11 Work Backwards 5.NBT.B.7

The number's hundredth is 0.6 less than 66.6, so subtract: 66.6 - 0.6 = 66.

66.6 - 0.6 = 66

'0.6 less than' means subtract 0.6.

2Undo the divide-by-100

#11 Work Backwards 5.NBT.B.7

If 1/100 of the number is 66, then the number itself is 100 times that. Multiplying by 100 shifts the decimal point two places right: 66 x 100 = 6600.

66 \times 100 = 6600

Taking 1/100 shrank the number, so multiplying by 100 grows it back.

Answer: 6600

4 · Reviewdoes it hold up?

Check forward: 6600 / 100 = 66, and 66 is 0.6 less than 66.6 (66.6 - 66 = 0.6). Everything matches.

Another way: Guess and Check the place-value shift: since 1/100 of the answer must be about 66.6, the answer is about 6600; refining makes the hundredth exactly 66.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 66.6 - 0.6 and multiplying 66 x 100.
5.NBT.A.2 Explain patterns in number of zeros and placement of decimal point — Shifting the decimal point two places when multiplying by 100.

💡Takeaway. '1/100 of it is...' just means divide by 100 - so multiply by 100 to get the number back!

Variant 10 medium answer: 4828.8

A certain number's $\frac{1}{100}$ is $0.012$ less than $48.3$ . Find the number.

Show solution

1 · Understandwhat's really being asked

Some number divided by 100 (its one-hundredth) equals a value that is 0.012 less than 48.3. Find the original number.

Givens

(the number) x 1/100 = 48.3 - 0.012.
1/100 of a number means the number divided by 100.

Unknowns

The original number.

Constraints

0.012 is a small decimal, so the right side is computed by exact decimal subtraction.

2 · Planchoose the strategy

#11 Work Backwards · also uses: #6 Guess and Check

First compute the value that equals one-hundredth of the number, then undo the 'divide by 100' by multiplying by 100 to recover the original number.

3 · Execute2 carry out the plan

1Find one-hundredth of the number

#11 Work Backwards 5.NBT.B.7

The number's hundredth is 0.012 less than 48.3, so subtract: 48.3 - 0.012 = 48.288.

48.3 - 0.012 = 48.288

'0.012 less than' means subtract 0.012.

2Undo the divide-by-100

#11 Work Backwards 5.NBT.B.7

If 1/100 of the number is 48.288, then the number itself is 100 times that. Multiplying by 100 shifts the decimal point two places right: 48.288 x 100 = 4828.8.

48.288 \times 100 = 4828.8

Taking 1/100 shrank the number, so multiplying by 100 grows it back.

Answer: 4828.8

4 · Reviewdoes it hold up?

Check forward: 4828.8 / 100 = 48.288, and 48.288 is 0.012 less than 48.3 (48.3 - 48.288 = 0.012). Everything matches.

Another way: Guess and Check the place-value shift: since 1/100 of the answer must be about 48.3, the answer is about 4828.8; refining makes the hundredth exactly 48.288.

Standardsmin grade 5

5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Subtracting 48.3 - 0.012 and multiplying 48.288 x 100.
5.NBT.A.2 Explain patterns in number of zeros and placement of decimal point — Shifting the decimal point two places when multiplying by 100.

💡Takeaway. '1/100 of it is...' just means divide by 100 - so multiply by 100 to get the number back!