← Recover the original number from a wrong product · Work Backwards to Recover a Start Value

Recover the original number from a wrong product · 12 practice problems

3.OA.A.43.OA.C.7

Generated variants — 12

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

Variant 1 easy answer: 750

A certain number was supposed to be multiplied by $5$ , but by mistake $5$ was subtracted instead, giving $145$ . What is the result of the correct calculation?

Show solution

1 · Understandwhat's really being asked

A number should have been multiplied by 5, but instead 5 was subtracted, giving 145. Find what the correct answer (number times 5) should be.

Givens

The correct operation was: the number times 5.
By mistake, 5 was subtracted from the number, giving 145.

Unknowns

The original number, and then the correct result (number x 5).

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

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

We know the result of the wrong operation (subtract 5 gives 145). Undo the subtraction by adding 5 to recover the original number, then do the correct operation (multiply by 5).

3 · Execute2 carry out the plan

1Undo the wrong operation

#11 Work Backwards 3.OA.A.4

The mistake subtracted 5 to get 145. To find the original number, add 5 back.

145 + 5 = 150

Adding undoes subtracting, so we work backward to the start.

2Do the correct operation

#6 Guess and Check 3.OA.C.7

The number should have been multiplied by 5. Break 150 into 100 + 50 and multiply each part by 5, then add.

150 \times 5 = 500 + 250 = 750

Splitting by place value keeps each multiplication small and friendly.

Answer: 750

4 · Reviewdoes it hold up?

Checking the mistake: 150 - 5 = 145 matches the wrong result, and 150 x 5 = 750 is the correct answer, so everything fits.

Another way: Set up the relationship as 'number - 5 = 145' to solve number = 150, then compute 150 x 5 = 750.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Working backward to find the original number from the wrong result.
3.OA.C.7 Fluently multiply and divide within 100 — Multiplying the recovered number by 5.

💡Takeaway. Undo the mistake first, then do it right -- working backwards is a Grade 3 superpower!

Variant 2 easy answer: 800

A certain number was supposed to be multiplied by $4$ , but by mistake $4$ was subtracted instead, giving $196$ . What is the result of the correct calculation?

Show solution

1 · Understandwhat's really being asked

A number should have been multiplied by 4, but instead 4 was subtracted, giving 196. Find what the correct answer (number times 4) should be.

Givens

The correct operation was: the number times 4.
By mistake, 4 was subtracted from the number, giving 196.

Unknowns

The original number, and then the correct result (number x 4).

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

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

We know the result of the wrong operation (subtract 4 gives 196). Undo the subtraction by adding 4 to recover the original number, then do the correct operation (multiply by 4).

3 · Execute2 carry out the plan

1Undo the wrong operation

#11 Work Backwards 3.OA.A.4

The mistake subtracted 4 to get 196. To find the original number, add 4 back.

196 + 4 = 200

Adding undoes subtracting, so we work backward to the start.

2Do the correct operation

#6 Guess and Check 3.OA.C.7

The number should have been multiplied by 4. Break 200 into 200 and multiply each part by 4, then add.

200 \times 4 = 800 = 800

Splitting by place value keeps each multiplication small and friendly.

Answer: 800

4 · Reviewdoes it hold up?

Checking the mistake: 200 - 4 = 196 matches the wrong result, and 200 x 4 = 800 is the correct answer, so everything fits.

Another way: Set up the relationship as 'number - 4 = 196' to solve number = 200, then compute 200 x 4 = 800.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Working backward to find the original number from the wrong result.
3.OA.C.7 Fluently multiply and divide within 100 — Multiplying the recovered number by 4.

💡Takeaway. Undo the mistake first, then do it right -- working backwards is a Grade 3 superpower!

Variant 3 easy answer: 1944

A certain number was supposed to be multiplied by $9$ , but by mistake $9$ was subtracted instead, giving $207$ . What is the result of the correct calculation?

Show solution

1 · Understandwhat's really being asked

A number should have been multiplied by 9, but instead 9 was subtracted, giving 207. Find what the correct answer (number times 9) should be.

Givens

The correct operation was: the number times 9.
By mistake, 9 was subtracted from the number, giving 207.

Unknowns

The original number, and then the correct result (number x 9).

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

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

We know the result of the wrong operation (subtract 9 gives 207). Undo the subtraction by adding 9 to recover the original number, then do the correct operation (multiply by 9).

3 · Execute2 carry out the plan

1Undo the wrong operation

#11 Work Backwards 3.OA.A.4

The mistake subtracted 9 to get 207. To find the original number, add 9 back.

207 + 9 = 216

Adding undoes subtracting, so we work backward to the start.

2Do the correct operation

#6 Guess and Check 3.OA.C.7

The number should have been multiplied by 9. Break 216 into 200 + 10 + 6 and multiply each part by 9, then add.

216 \times 9 = 1800 + 90 + 54 = 1944

Splitting by place value keeps each multiplication small and friendly.

Answer: 1944

4 · Reviewdoes it hold up?

Checking the mistake: 216 - 9 = 207 matches the wrong result, and 216 x 9 = 1944 is the correct answer, so everything fits.

Another way: Set up the relationship as 'number - 9 = 207' to solve number = 216, then compute 216 x 9 = 1944.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Working backward to find the original number from the wrong result.
3.OA.C.7 Fluently multiply and divide within 100 — Multiplying the recovered number by 9.

💡Takeaway. Undo the mistake first, then do it right -- working backwards is a Grade 3 superpower!

Variant 4 easy answer: 1554

A certain number was supposed to be multiplied by $7$ , but by mistake $7$ was subtracted instead, giving $215$ . What is the result of the correct calculation?

Show solution

1 · Understandwhat's really being asked

A number should have been multiplied by 7, but instead 7 was subtracted, giving 215. Find what the correct answer (number times 7) should be.

Givens

The correct operation was: the number times 7.
By mistake, 7 was subtracted from the number, giving 215.

Unknowns

The original number, and then the correct result (number x 7).

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

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

We know the result of the wrong operation (subtract 7 gives 215). Undo the subtraction by adding 7 to recover the original number, then do the correct operation (multiply by 7).

3 · Execute2 carry out the plan

1Undo the wrong operation

#11 Work Backwards 3.OA.A.4

The mistake subtracted 7 to get 215. To find the original number, add 7 back.

215 + 7 = 222

Adding undoes subtracting, so we work backward to the start.

2Do the correct operation

#6 Guess and Check 3.OA.C.7

The number should have been multiplied by 7. Break 222 into 200 + 20 + 2 and multiply each part by 7, then add.

222 \times 7 = 1400 + 140 + 14 = 1554

Splitting by place value keeps each multiplication small and friendly.

Answer: 1554

4 · Reviewdoes it hold up?

Checking the mistake: 222 - 7 = 215 matches the wrong result, and 222 x 7 = 1554 is the correct answer, so everything fits.

Another way: Set up the relationship as 'number - 7 = 215' to solve number = 222, then compute 222 x 7 = 1554.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Working backward to find the original number from the wrong result.
3.OA.C.7 Fluently multiply and divide within 100 — Multiplying the recovered number by 7.

💡Takeaway. Undo the mistake first, then do it right -- working backwards is a Grade 3 superpower!

Variant 5 medium answer: 2176

A certain number was supposed to be multiplied by $8$ , but by mistake $8$ was subtracted instead, giving $264$ . What is the result of the correct calculation?

Show solution

1 · Understandwhat's really being asked

A number should have been multiplied by 8, but instead 8 was subtracted, giving 264. Find what the correct answer (number times 8) should be.

Givens

The correct operation was: the number times 8.
By mistake, 8 was subtracted from the number, giving 264.

Unknowns

The original number, and then the correct result (number x 8).

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

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

We know the result of the wrong operation (subtract 8 gives 264). Undo the subtraction by adding 8 to recover the original number, then do the correct operation (multiply by 8).

3 · Execute2 carry out the plan

1Undo the wrong operation

#11 Work Backwards 3.OA.A.4

The mistake subtracted 8 to get 264. To find the original number, add 8 back.

264 + 8 = 272

Adding undoes subtracting, so we work backward to the start.

2Do the correct operation

#6 Guess and Check 3.OA.C.7

The number should have been multiplied by 8. Break 272 into 200 + 70 + 2 and multiply each part by 8, then add.

272 \times 8 = 1600 + 560 + 16 = 2176

Splitting by place value keeps each multiplication small and friendly.

Answer: 2176

4 · Reviewdoes it hold up?

Checking the mistake: 272 - 8 = 264 matches the wrong result, and 272 x 8 = 2176 is the correct answer, so everything fits.

Another way: Set up the relationship as 'number - 8 = 264' to solve number = 272, then compute 272 x 8 = 2176.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Working backward to find the original number from the wrong result.
3.OA.C.7 Fluently multiply and divide within 100 — Multiplying the recovered number by 8.

💡Takeaway. Undo the mistake first, then do it right -- working backwards is a Grade 3 superpower!

Variant 6 medium answer: 1425

A certain number was supposed to be multiplied by $5$ , but by mistake $5$ was subtracted instead, giving $280$ . What is the result of the correct calculation?

Show solution

1 · Understandwhat's really being asked

A number should have been multiplied by 5, but instead 5 was subtracted, giving 280. Find what the correct answer (number times 5) should be.

Givens

The correct operation was: the number times 5.
By mistake, 5 was subtracted from the number, giving 280.

Unknowns

The original number, and then the correct result (number x 5).

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

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

We know the result of the wrong operation (subtract 5 gives 280). Undo the subtraction by adding 5 to recover the original number, then do the correct operation (multiply by 5).

3 · Execute2 carry out the plan

1Undo the wrong operation

#11 Work Backwards 3.OA.A.4

The mistake subtracted 5 to get 280. To find the original number, add 5 back.

280 + 5 = 285

Adding undoes subtracting, so we work backward to the start.

2Do the correct operation

#6 Guess and Check 3.OA.C.7

The number should have been multiplied by 5. Break 285 into 200 + 80 + 5 and multiply each part by 5, then add.

285 \times 5 = 1000 + 400 + 25 = 1425

Splitting by place value keeps each multiplication small and friendly.

Answer: 1425

4 · Reviewdoes it hold up?

Checking the mistake: 285 - 5 = 280 matches the wrong result, and 285 x 5 = 1425 is the correct answer, so everything fits.

Another way: Set up the relationship as 'number - 5 = 280' to solve number = 285, then compute 285 x 5 = 1425.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Working backward to find the original number from the wrong result.
3.OA.C.7 Fluently multiply and divide within 100 — Multiplying the recovered number by 5.

💡Takeaway. Undo the mistake first, then do it right -- working backwards is a Grade 3 superpower!

Variant 7 medium answer: 1884

A certain number was supposed to be multiplied by $6$ , but by mistake $6$ was subtracted instead, giving $308$ . What is the result of the correct calculation?

Show solution

1 · Understandwhat's really being asked

A number should have been multiplied by 6, but instead 6 was subtracted, giving 308. Find what the correct answer (number times 6) should be.

Givens

The correct operation was: the number times 6.
By mistake, 6 was subtracted from the number, giving 308.

Unknowns

The original number, and then the correct result (number x 6).

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

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

We know the result of the wrong operation (subtract 6 gives 308). Undo the subtraction by adding 6 to recover the original number, then do the correct operation (multiply by 6).

3 · Execute2 carry out the plan

1Undo the wrong operation

#11 Work Backwards 3.OA.A.4

The mistake subtracted 6 to get 308. To find the original number, add 6 back.

308 + 6 = 314

Adding undoes subtracting, so we work backward to the start.

2Do the correct operation

#6 Guess and Check 3.OA.C.7

The number should have been multiplied by 6. Break 314 into 300 + 10 + 4 and multiply each part by 6, then add.

314 \times 6 = 1800 + 60 + 24 = 1884

Splitting by place value keeps each multiplication small and friendly.

Answer: 1884

4 · Reviewdoes it hold up?

Checking the mistake: 314 - 6 = 308 matches the wrong result, and 314 x 6 = 1884 is the correct answer, so everything fits.

Another way: Set up the relationship as 'number - 6 = 308' to solve number = 314, then compute 314 x 6 = 1884.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Working backward to find the original number from the wrong result.
3.OA.C.7 Fluently multiply and divide within 100 — Multiplying the recovered number by 6.

💡Takeaway. Undo the mistake first, then do it right -- working backwards is a Grade 3 superpower!

Variant 8 medium answer: 3078

A certain number was supposed to be multiplied by $9$ , but by mistake $9$ was subtracted instead, giving $333$ . What is the result of the correct calculation?

Show solution

1 · Understandwhat's really being asked

A number should have been multiplied by 9, but instead 9 was subtracted, giving 333. Find what the correct answer (number times 9) should be.

Givens

The correct operation was: the number times 9.
By mistake, 9 was subtracted from the number, giving 333.

Unknowns

The original number, and then the correct result (number x 9).

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

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

We know the result of the wrong operation (subtract 9 gives 333). Undo the subtraction by adding 9 to recover the original number, then do the correct operation (multiply by 9).

3 · Execute2 carry out the plan

1Undo the wrong operation

#11 Work Backwards 3.OA.A.4

The mistake subtracted 9 to get 333. To find the original number, add 9 back.

333 + 9 = 342

Adding undoes subtracting, so we work backward to the start.

2Do the correct operation

#6 Guess and Check 3.OA.C.7

The number should have been multiplied by 9. Break 342 into 300 + 40 + 2 and multiply each part by 9, then add.

342 \times 9 = 2700 + 360 + 18 = 3078

Splitting by place value keeps each multiplication small and friendly.

Answer: 3078

4 · Reviewdoes it hold up?

Checking the mistake: 342 - 9 = 333 matches the wrong result, and 342 x 9 = 3078 is the correct answer, so everything fits.

Another way: Set up the relationship as 'number - 9 = 333' to solve number = 342, then compute 342 x 9 = 3078.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Working backward to find the original number from the wrong result.
3.OA.C.7 Fluently multiply and divide within 100 — Multiplying the recovered number by 9.

💡Takeaway. Undo the mistake first, then do it right -- working backwards is a Grade 3 superpower!

Variant 9 hard answer: 2912

A certain number was supposed to be multiplied by $7$ , but by mistake $7$ was subtracted instead, giving $409$ . What is the result of the correct calculation?

Show solution

1 · Understandwhat's really being asked

A number should have been multiplied by 7, but instead 7 was subtracted, giving 409. Find what the correct answer (number times 7) should be.

Givens

The correct operation was: the number times 7.
By mistake, 7 was subtracted from the number, giving 409.

Unknowns

The original number, and then the correct result (number x 7).

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

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

We know the result of the wrong operation (subtract 7 gives 409). Undo the subtraction by adding 7 to recover the original number, then do the correct operation (multiply by 7).

3 · Execute2 carry out the plan

1Undo the wrong operation

#11 Work Backwards 3.OA.A.4

The mistake subtracted 7 to get 409. To find the original number, add 7 back.

409 + 7 = 416

Adding undoes subtracting, so we work backward to the start.

2Do the correct operation

#6 Guess and Check 3.OA.C.7

The number should have been multiplied by 7. Break 416 into 400 + 10 + 6 and multiply each part by 7, then add.

416 \times 7 = 2800 + 70 + 42 = 2912

Splitting by place value keeps each multiplication small and friendly.

Answer: 2912

4 · Reviewdoes it hold up?

Checking the mistake: 416 - 7 = 409 matches the wrong result, and 416 x 7 = 2912 is the correct answer, so everything fits.

Another way: Set up the relationship as 'number - 7 = 409' to solve number = 416, then compute 416 x 7 = 2912.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Working backward to find the original number from the wrong result.
3.OA.C.7 Fluently multiply and divide within 100 — Multiplying the recovered number by 7.

💡Takeaway. Undo the mistake first, then do it right -- working backwards is a Grade 3 superpower!

Variant 10 hard answer: 2736

A certain number was supposed to be multiplied by $6$ , but by mistake $6$ was subtracted instead, giving $450$ . What is the result of the correct calculation?

Show solution

1 · Understandwhat's really being asked

A number should have been multiplied by 6, but instead 6 was subtracted, giving 450. Find what the correct answer (number times 6) should be.

Givens

The correct operation was: the number times 6.
By mistake, 6 was subtracted from the number, giving 450.

Unknowns

The original number, and then the correct result (number x 6).

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

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

We know the result of the wrong operation (subtract 6 gives 450). Undo the subtraction by adding 6 to recover the original number, then do the correct operation (multiply by 6).

3 · Execute2 carry out the plan

1Undo the wrong operation

#11 Work Backwards 3.OA.A.4

The mistake subtracted 6 to get 450. To find the original number, add 6 back.

450 + 6 = 456

Adding undoes subtracting, so we work backward to the start.

2Do the correct operation

#6 Guess and Check 3.OA.C.7

The number should have been multiplied by 6. Break 456 into 400 + 50 + 6 and multiply each part by 6, then add.

456 \times 6 = 2400 + 300 + 36 = 2736

Splitting by place value keeps each multiplication small and friendly.

Answer: 2736

4 · Reviewdoes it hold up?

Checking the mistake: 456 - 6 = 450 matches the wrong result, and 456 x 6 = 2736 is the correct answer, so everything fits.

Another way: Set up the relationship as 'number - 6 = 450' to solve number = 456, then compute 456 x 6 = 2736.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Working backward to find the original number from the wrong result.
3.OA.C.7 Fluently multiply and divide within 100 — Multiplying the recovered number by 6.

💡Takeaway. Undo the mistake first, then do it right -- working backwards is a Grade 3 superpower!

Variant 11 hard answer: 4160

A certain number was supposed to be multiplied by $8$ , but by mistake $8$ was subtracted instead, giving $512$ . What is the result of the correct calculation?

Show solution

1 · Understandwhat's really being asked

A number should have been multiplied by 8, but instead 8 was subtracted, giving 512. Find what the correct answer (number times 8) should be.

Givens

The correct operation was: the number times 8.
By mistake, 8 was subtracted from the number, giving 512.

Unknowns

The original number, and then the correct result (number x 8).

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

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

We know the result of the wrong operation (subtract 8 gives 512). Undo the subtraction by adding 8 to recover the original number, then do the correct operation (multiply by 8).

3 · Execute2 carry out the plan

1Undo the wrong operation

#11 Work Backwards 3.OA.A.4

The mistake subtracted 8 to get 512. To find the original number, add 8 back.

512 + 8 = 520

Adding undoes subtracting, so we work backward to the start.

2Do the correct operation

#6 Guess and Check 3.OA.C.7

The number should have been multiplied by 8. Break 520 into 500 + 20 and multiply each part by 8, then add.

520 \times 8 = 4000 + 160 = 4160

Splitting by place value keeps each multiplication small and friendly.

Answer: 4160

4 · Reviewdoes it hold up?

Checking the mistake: 520 - 8 = 512 matches the wrong result, and 520 x 8 = 4160 is the correct answer, so everything fits.

Another way: Set up the relationship as 'number - 8 = 512' to solve number = 520, then compute 520 x 8 = 4160.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Working backward to find the original number from the wrong result.
3.OA.C.7 Fluently multiply and divide within 100 — Multiplying the recovered number by 8.

💡Takeaway. Undo the mistake first, then do it right -- working backwards is a Grade 3 superpower!

Variant 12 hard answer: 4249

A certain number was supposed to be multiplied by $7$ , but by mistake $7$ was subtracted instead, giving $600$ . What is the result of the correct calculation?

Show solution

1 · Understandwhat's really being asked

A number should have been multiplied by 7, but instead 7 was subtracted, giving 600. Find what the correct answer (number times 7) should be.

Givens

The correct operation was: the number times 7.
By mistake, 7 was subtracted from the number, giving 600.

Unknowns

The original number, and then the correct result (number x 7).

Constraints

The same starting number is used in both the wrong and the correct calculation.

2 · Planchoose the strategy

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

We know the result of the wrong operation (subtract 7 gives 600). Undo the subtraction by adding 7 to recover the original number, then do the correct operation (multiply by 7).

3 · Execute2 carry out the plan

1Undo the wrong operation

#11 Work Backwards 3.OA.A.4

The mistake subtracted 7 to get 600. To find the original number, add 7 back.

600 + 7 = 607

Adding undoes subtracting, so we work backward to the start.

2Do the correct operation

#6 Guess and Check 3.OA.C.7

The number should have been multiplied by 7. Break 607 into 600 + 7 and multiply each part by 7, then add.

607 \times 7 = 4200 + 49 = 4249

Splitting by place value keeps each multiplication small and friendly.

Answer: 4249

4 · Reviewdoes it hold up?

Checking the mistake: 607 - 7 = 600 matches the wrong result, and 607 x 7 = 4249 is the correct answer, so everything fits.

Another way: Set up the relationship as 'number - 7 = 600' to solve number = 607, then compute 607 x 7 = 4249.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Working backward to find the original number from the wrong result.
3.OA.C.7 Fluently multiply and divide within 100 — Multiplying the recovered number by 7.

💡Takeaway. Undo the mistake first, then do it right -- working backwards is a Grade 3 superpower!