← Find a number satisfying product bounds · Pin Down a Number from Digit and Range Conditions

Find a number satisfying product bounds · 10 practice problems

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

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Variant 1 easy

Find a number, chosen from $1$ through $9$ , that satisfies all of the following conditions.

The number times $7$ is greater than $12$ .
$9$ times the number is less than $20$ .
$6$ times the number is greater than $10$ .

Your answer

Show solution

1 · Understandwhat's really being asked

We need one number from 1 to 9 that meets all three conditions: 7 times it is more than 12, 9 times it is less than 20, and 6 times it is more than 10.

Givens

The number is a whole number from 1 to 9.
Condition 1: the number x 7 > 12.
Condition 2: 9 x the number < 20.
Condition 3: 6 x the number > 10.

Unknowns

The single number satisfying all three conditions.

Constraints

All three conditions must hold at the same time.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #2 Make a Systematic List

Turn each condition into a range of allowed numbers using the times tables, then find the single value common to all three ranges.

3 · Execute3 carry out the plan

1Apply condition 1

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 7 is more than 12: 7 x 1 = 7 (too small), 7 x 2 = 14 (more than 12). So the number is 2 or more.

7 \times 2 = 14 > 12

Checking the 7-times facts shows 2 is the first value pushing the product past 12.

2Apply condition 2

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 9 is less than 20: 9 x 2 = 18 (under 20) but 9 x 3 = 27 (over 20). So the number is 2 or less.

9 \times 2 = 18 < 20,\ 9 \times 3 = 27

The 9-times facts show 2 is the largest value still under 20.

3Apply condition 3 and combine

#2 Make a Systematic List 3.OA.C.7

Condition 3 needs 6 x number > 10: 6 x 1 = 6 (too small) but 6 x 2 = 12 (more than 10), so the number is 2 or more. Combining all three ranges leaves only 2.

6 \times 2 = 12 > 10

Only 2 sits inside every range at once, so it is the common number.

Answer: 2

4 · Reviewdoes it hold up?

Test 2 in all three: 7 x 2 = 14 > 12, 9 x 2 = 18 < 20, and 6 x 2 = 12 > 10, so 2 satisfies every condition.

Another way: You could test each number 1-9 against all three conditions in a table and keep only the row that passes all three, which is 2.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding which numbers satisfy each product condition.
3.OA.C.7 Fluently multiply and divide within 100 — Computing the times facts to combine the ranges.

💡Takeaway. Turn each clue into a range with the times tables, then keep the number that fits them all -- Grade 3 facts do it!

Variant 2 easy

Find a number, chosen from $1$ through $9$ , that satisfies all of the following conditions.

The number times $6$ is greater than $16$ .
$8$ times the number is less than $28$ .
$5$ times the number is greater than $13$ .

Your answer

Show solution

1 · Understandwhat's really being asked

We need one number from 1 to 9 that meets all three conditions: 6 times it is more than 16, 8 times it is less than 28, and 5 times it is more than 13.

Givens

The number is a whole number from 1 to 9.
Condition 1: the number x 6 > 16.
Condition 2: 8 x the number < 28.
Condition 3: 5 x the number > 13.

Unknowns

The single number satisfying all three conditions.

Constraints

All three conditions must hold at the same time.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #2 Make a Systematic List

Turn each condition into a range of allowed numbers using the times tables, then find the single value common to all three ranges.

3 · Execute3 carry out the plan

1Apply condition 1

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 6 is more than 16: 6 x 2 = 12 (too small), 6 x 3 = 18 (more than 16). So the number is 3 or more.

6 \times 3 = 18 > 16

Checking the 6-times facts shows 3 is the first value pushing the product past 16.

2Apply condition 2

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 8 is less than 28: 8 x 3 = 24 (under 28) but 8 x 4 = 32 (over 28). So the number is 3 or less.

8 \times 3 = 24 < 28,\ 8 \times 4 = 32

The 8-times facts show 3 is the largest value still under 28.

3Apply condition 3 and combine

#2 Make a Systematic List 3.OA.C.7

Condition 3 needs 5 x number > 13: 5 x 2 = 10 (too small) but 5 x 3 = 15 (more than 13), so the number is 3 or more. Combining all three ranges leaves only 3.

5 \times 3 = 15 > 13

Only 3 sits inside every range at once, so it is the common number.

Answer: 3

4 · Reviewdoes it hold up?

Test 3 in all three: 6 x 3 = 18 > 16, 8 x 3 = 24 < 28, and 5 x 3 = 15 > 13, so 3 satisfies every condition.

Another way: You could test each number 1-9 against all three conditions in a table and keep only the row that passes all three, which is 3.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding which numbers satisfy each product condition.
3.OA.C.7 Fluently multiply and divide within 100 — Computing the times facts to combine the ranges.

💡Takeaway. Turn each clue into a range with the times tables, then keep the number that fits them all -- Grade 3 facts do it!

Variant 3 easy

Find a number, chosen from $1$ through $9$ , that satisfies all of the following conditions.

The number times $3$ is greater than $14$ .
$5$ times the number is less than $28$ .
$4$ times the number is greater than $18$ .

Your answer

Show solution

1 · Understandwhat's really being asked

We need one number from 1 to 9 that meets all three conditions: 3 times it is more than 14, 5 times it is less than 28, and 4 times it is more than 18.

Givens

The number is a whole number from 1 to 9.
Condition 1: the number x 3 > 14.
Condition 2: 5 x the number < 28.
Condition 3: 4 x the number > 18.

Unknowns

The single number satisfying all three conditions.

Constraints

All three conditions must hold at the same time.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #2 Make a Systematic List

Turn each condition into a range of allowed numbers using the times tables, then find the single value common to all three ranges.

3 · Execute3 carry out the plan

1Apply condition 1

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 3 is more than 14: 3 x 4 = 12 (too small), 3 x 5 = 15 (more than 14). So the number is 5 or more.

3 \times 5 = 15 > 14

Checking the 3-times facts shows 5 is the first value pushing the product past 14.

2Apply condition 2

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 5 is less than 28: 5 x 5 = 25 (under 28) but 5 x 6 = 30 (over 28). So the number is 5 or less.

5 \times 5 = 25 < 28,\ 5 \times 6 = 30

The 5-times facts show 5 is the largest value still under 28.

3Apply condition 3 and combine

#2 Make a Systematic List 3.OA.C.7

Condition 3 needs 4 x number > 18: 4 x 4 = 16 (too small) but 4 x 5 = 20 (more than 18), so the number is 5 or more. Combining all three ranges leaves only 5.

4 \times 5 = 20 > 18

Only 5 sits inside every range at once, so it is the common number.

Answer: 5

4 · Reviewdoes it hold up?

Test 5 in all three: 3 x 5 = 15 > 14, 5 x 5 = 25 < 28, and 4 x 5 = 20 > 18, so 5 satisfies every condition.

Another way: You could test each number 1-9 against all three conditions in a table and keep only the row that passes all three, which is 5.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding which numbers satisfy each product condition.
3.OA.C.7 Fluently multiply and divide within 100 — Computing the times facts to combine the ranges.

💡Takeaway. Turn each clue into a range with the times tables, then keep the number that fits them all -- Grade 3 facts do it!

Variant 4 medium

Find a number, chosen from $1$ through $9$ , that satisfies all of the following conditions.

The number times $8$ is greater than $30$ .
$2$ times the number is less than $9$ .
$5$ times the number is greater than $19$ .

Your answer

Show solution

1 · Understandwhat's really being asked

We need one number from 1 to 9 that meets all three conditions: 8 times it is more than 30, 2 times it is less than 9, and 5 times it is more than 19.

Givens

The number is a whole number from 1 to 9.
Condition 1: the number x 8 > 30.
Condition 2: 2 x the number < 9.
Condition 3: 5 x the number > 19.

Unknowns

The single number satisfying all three conditions.

Constraints

All three conditions must hold at the same time.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #2 Make a Systematic List

Turn each condition into a range of allowed numbers using the times tables, then find the single value common to all three ranges.

3 · Execute3 carry out the plan

1Apply condition 1

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 8 is more than 30: 8 x 3 = 24 (too small), 8 x 4 = 32 (more than 30). So the number is 4 or more.

8 \times 4 = 32 > 30

Checking the 8-times facts shows 4 is the first value pushing the product past 30.

2Apply condition 2

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 2 is less than 9: 2 x 4 = 8 (under 9) but 2 x 5 = 10 (over 9). So the number is 4 or less.

2 \times 4 = 8 < 9,\ 2 \times 5 = 10

The 2-times facts show 4 is the largest value still under 9.

3Apply condition 3 and combine

#2 Make a Systematic List 3.OA.C.7

Condition 3 needs 5 x number > 19: 5 x 3 = 15 (too small) but 5 x 4 = 20 (more than 19), so the number is 4 or more. Combining all three ranges leaves only 4.

5 \times 4 = 20 > 19

Only 4 sits inside every range at once, so it is the common number.

Answer: 4

4 · Reviewdoes it hold up?

Test 4 in all three: 8 x 4 = 32 > 30, 2 x 4 = 8 < 9, and 5 x 4 = 20 > 19, so 4 satisfies every condition.

Another way: You could test each number 1-9 against all three conditions in a table and keep only the row that passes all three, which is 4.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding which numbers satisfy each product condition.
3.OA.C.7 Fluently multiply and divide within 100 — Computing the times facts to combine the ranges.

💡Takeaway. Turn each clue into a range with the times tables, then keep the number that fits them all -- Grade 3 facts do it!

Variant 5 medium

Find a number, chosen from $1$ through $9$ , that satisfies all of the following conditions.

The number times $4$ is greater than $22$ .
$3$ times the number is less than $20$ .
$6$ times the number is greater than $32$ .

Your answer

Show solution

1 · Understandwhat's really being asked

We need one number from 1 to 9 that meets all three conditions: 4 times it is more than 22, 3 times it is less than 20, and 6 times it is more than 32.

Givens

The number is a whole number from 1 to 9.
Condition 1: the number x 4 > 22.
Condition 2: 3 x the number < 20.
Condition 3: 6 x the number > 32.

Unknowns

The single number satisfying all three conditions.

Constraints

All three conditions must hold at the same time.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #2 Make a Systematic List

Turn each condition into a range of allowed numbers using the times tables, then find the single value common to all three ranges.

3 · Execute3 carry out the plan

1Apply condition 1

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 4 is more than 22: 4 x 5 = 20 (too small), 4 x 6 = 24 (more than 22). So the number is 6 or more.

4 \times 6 = 24 > 22

Checking the 4-times facts shows 6 is the first value pushing the product past 22.

2Apply condition 2

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 3 is less than 20: 3 x 6 = 18 (under 20) but 3 x 7 = 21 (over 20). So the number is 6 or less.

3 \times 6 = 18 < 20,\ 3 \times 7 = 21

The 3-times facts show 6 is the largest value still under 20.

3Apply condition 3 and combine

#2 Make a Systematic List 3.OA.C.7

Condition 3 needs 6 x number > 32: 6 x 5 = 30 (too small) but 6 x 6 = 36 (more than 32), so the number is 6 or more. Combining all three ranges leaves only 6.

6 \times 6 = 36 > 32

Only 6 sits inside every range at once, so it is the common number.

Answer: 6

4 · Reviewdoes it hold up?

Test 6 in all three: 4 x 6 = 24 > 22, 3 x 6 = 18 < 20, and 6 x 6 = 36 > 32, so 6 satisfies every condition.

Another way: You could test each number 1-9 against all three conditions in a table and keep only the row that passes all three, which is 6.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding which numbers satisfy each product condition.
3.OA.C.7 Fluently multiply and divide within 100 — Computing the times facts to combine the ranges.

💡Takeaway. Turn each clue into a range with the times tables, then keep the number that fits them all -- Grade 3 facts do it!

Variant 6 medium

Find a number, chosen from $1$ through $9$ , that satisfies all of the following conditions.

The number times $4$ is greater than $18$ .
$6$ times the number is less than $36$ .
$7$ times the number is greater than $33$ .

Your answer

Show solution

1 · Understandwhat's really being asked

We need one number from 1 to 9 that meets all three conditions: 4 times it is more than 18, 6 times it is less than 36, and 7 times it is more than 33.

Givens

The number is a whole number from 1 to 9.
Condition 1: the number x 4 > 18.
Condition 2: 6 x the number < 36.
Condition 3: 7 x the number > 33.

Unknowns

The single number satisfying all three conditions.

Constraints

All three conditions must hold at the same time.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #2 Make a Systematic List

Turn each condition into a range of allowed numbers using the times tables, then find the single value common to all three ranges.

3 · Execute3 carry out the plan

1Apply condition 1

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 4 is more than 18: 4 x 4 = 16 (too small), 4 x 5 = 20 (more than 18). So the number is 5 or more.

4 \times 5 = 20 > 18

Checking the 4-times facts shows 5 is the first value pushing the product past 18.

2Apply condition 2

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 6 is less than 36: 6 x 5 = 30 (under 36) but 6 x 6 = 36 (over 36). So the number is 5 or less.

6 \times 5 = 30 < 36,\ 6 \times 6 = 36

The 6-times facts show 5 is the largest value still under 36.

3Apply condition 3 and combine

#2 Make a Systematic List 3.OA.C.7

Condition 3 needs 7 x number > 33: 7 x 4 = 28 (too small) but 7 x 5 = 35 (more than 33), so the number is 5 or more. Combining all three ranges leaves only 5.

7 \times 5 = 35 > 33

Only 5 sits inside every range at once, so it is the common number.

Answer: 5

4 · Reviewdoes it hold up?

Test 5 in all three: 4 x 5 = 20 > 18, 6 x 5 = 30 < 36, and 7 x 5 = 35 > 33, so 5 satisfies every condition.

Another way: You could test each number 1-9 against all three conditions in a table and keep only the row that passes all three, which is 5.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding which numbers satisfy each product condition.
3.OA.C.7 Fluently multiply and divide within 100 — Computing the times facts to combine the ranges.

💡Takeaway. Turn each clue into a range with the times tables, then keep the number that fits them all -- Grade 3 facts do it!

Variant 7 medium

Find a number, chosen from $1$ through $9$ , that satisfies all of the following conditions.

The number times $6$ is greater than $40$ .
$4$ times the number is less than $35$ .
$3$ times the number is greater than $22$ .

Your answer

Show solution

1 · Understandwhat's really being asked

We need one number from 1 to 9 that meets all three conditions: 6 times it is more than 40, 4 times it is less than 35, and 3 times it is more than 22.

Givens

The number is a whole number from 1 to 9.
Condition 1: the number x 6 > 40.
Condition 2: 4 x the number < 35.
Condition 3: 3 x the number > 22.

Unknowns

The single number satisfying all three conditions.

Constraints

All three conditions must hold at the same time.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #2 Make a Systematic List

Turn each condition into a range of allowed numbers using the times tables, then find the single value common to all three ranges.

3 · Execute3 carry out the plan

1Apply condition 1

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 6 is more than 40: 6 x 6 = 36 (too small), 6 x 7 = 42 (more than 40). So the number is 7 or more.

6 \times 7 = 42 > 40

Checking the 6-times facts shows 7 is the first value pushing the product past 40.

2Apply condition 2

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 4 is less than 35: 4 x 8 = 32 (under 35) but 4 x 9 = 36 (over 35). So the number is 8 or less.

4 \times 8 = 32 < 35,\ 4 \times 9 = 36

The 4-times facts show 8 is the largest value still under 35.

3Apply condition 3 and combine

#2 Make a Systematic List 3.OA.C.7

Condition 3 needs 3 x number > 22: 3 x 7 = 21 (too small) but 3 x 8 = 24 (more than 22), so the number is 8 or more. Combining all three ranges leaves only 8.

3 \times 8 = 24 > 22

Only 8 sits inside every range at once, so it is the common number.

Answer: 8

4 · Reviewdoes it hold up?

Test 8 in all three: 6 x 8 = 48 > 40, 4 x 8 = 32 < 35, and 3 x 8 = 24 > 22, so 8 satisfies every condition.

Another way: You could test each number 1-9 against all three conditions in a table and keep only the row that passes all three, which is 8.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding which numbers satisfy each product condition.
3.OA.C.7 Fluently multiply and divide within 100 — Computing the times facts to combine the ranges.

💡Takeaway. Turn each clue into a range with the times tables, then keep the number that fits them all -- Grade 3 facts do it!

Variant 8 hard

Find a number, chosen from $1$ through $9$ , that satisfies all of the following conditions.

The number times $5$ is greater than $32$ .
$4$ times the number is less than $30$ .
$8$ times the number is greater than $53$ .

Your answer

Show solution

1 · Understandwhat's really being asked

We need one number from 1 to 9 that meets all three conditions: 5 times it is more than 32, 4 times it is less than 30, and 8 times it is more than 53.

Givens

The number is a whole number from 1 to 9.
Condition 1: the number x 5 > 32.
Condition 2: 4 x the number < 30.
Condition 3: 8 x the number > 53.

Unknowns

The single number satisfying all three conditions.

Constraints

All three conditions must hold at the same time.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #2 Make a Systematic List

Turn each condition into a range of allowed numbers using the times tables, then find the single value common to all three ranges.

3 · Execute3 carry out the plan

1Apply condition 1

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 5 is more than 32: 5 x 6 = 30 (too small), 5 x 7 = 35 (more than 32). So the number is 7 or more.

5 \times 7 = 35 > 32

Checking the 5-times facts shows 7 is the first value pushing the product past 32.

2Apply condition 2

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 4 is less than 30: 4 x 7 = 28 (under 30) but 4 x 8 = 32 (over 30). So the number is 7 or less.

4 \times 7 = 28 < 30,\ 4 \times 8 = 32

The 4-times facts show 7 is the largest value still under 30.

3Apply condition 3 and combine

#2 Make a Systematic List 3.OA.C.7

Condition 3 needs 8 x number > 53: 8 x 6 = 48 (too small) but 8 x 7 = 56 (more than 53), so the number is 7 or more. Combining all three ranges leaves only 7.

8 \times 7 = 56 > 53

Only 7 sits inside every range at once, so it is the common number.

Answer: 7

4 · Reviewdoes it hold up?

Test 7 in all three: 5 x 7 = 35 > 32, 4 x 7 = 28 < 30, and 8 x 7 = 56 > 53, so 7 satisfies every condition.

Another way: You could test each number 1-9 against all three conditions in a table and keep only the row that passes all three, which is 7.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding which numbers satisfy each product condition.
3.OA.C.7 Fluently multiply and divide within 100 — Computing the times facts to combine the ranges.

💡Takeaway. Turn each clue into a range with the times tables, then keep the number that fits them all -- Grade 3 facts do it!

Variant 9 hard

Find a number, chosen from $1$ through $9$ , that satisfies all of the following conditions.

The number times $8$ is greater than $55$ .
$5$ times the number is less than $39$ .
$3$ times the number is greater than $19$ .

Your answer

Show solution

1 · Understandwhat's really being asked

We need one number from 1 to 9 that meets all three conditions: 8 times it is more than 55, 5 times it is less than 39, and 3 times it is more than 19.

Givens

The number is a whole number from 1 to 9.
Condition 1: the number x 8 > 55.
Condition 2: 5 x the number < 39.
Condition 3: 3 x the number > 19.

Unknowns

The single number satisfying all three conditions.

Constraints

All three conditions must hold at the same time.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #2 Make a Systematic List

Turn each condition into a range of allowed numbers using the times tables, then find the single value common to all three ranges.

3 · Execute3 carry out the plan

1Apply condition 1

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 8 is more than 55: 8 x 6 = 48 (too small), 8 x 7 = 56 (more than 55). So the number is 7 or more.

8 \times 7 = 56 > 55

Checking the 8-times facts shows 7 is the first value pushing the product past 55.

2Apply condition 2

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 5 is less than 39: 5 x 7 = 35 (under 39) but 5 x 8 = 40 (over 39). So the number is 7 or less.

5 \times 7 = 35 < 39,\ 5 \times 8 = 40

The 5-times facts show 7 is the largest value still under 39.

3Apply condition 3 and combine

#2 Make a Systematic List 3.OA.C.7

Condition 3 needs 3 x number > 19: 3 x 6 = 18 (too small) but 3 x 7 = 21 (more than 19), so the number is 7 or more. Combining all three ranges leaves only 7.

3 \times 7 = 21 > 19

Only 7 sits inside every range at once, so it is the common number.

Answer: 7

4 · Reviewdoes it hold up?

Test 7 in all three: 8 x 7 = 56 > 55, 5 x 7 = 35 < 39, and 3 x 7 = 21 > 19, so 7 satisfies every condition.

Another way: You could test each number 1-9 against all three conditions in a table and keep only the row that passes all three, which is 7.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding which numbers satisfy each product condition.
3.OA.C.7 Fluently multiply and divide within 100 — Computing the times facts to combine the ranges.

💡Takeaway. Turn each clue into a range with the times tables, then keep the number that fits them all -- Grade 3 facts do it!

Variant 10 hard

Find a number, chosen from $1$ through $9$ , that satisfies all of the following conditions.

The number times $9$ is greater than $70$ .
$2$ times the number is less than $19$ .
$3$ times the number is greater than $25$ .

Your answer

Show solution

1 · Understandwhat's really being asked

We need one number from 1 to 9 that meets all three conditions: 9 times it is more than 70, 2 times it is less than 19, and 3 times it is more than 25.

Givens

The number is a whole number from 1 to 9.
Condition 1: the number x 9 > 70.
Condition 2: 2 x the number < 19.
Condition 3: 3 x the number > 25.

Unknowns

The single number satisfying all three conditions.

Constraints

All three conditions must hold at the same time.

2 · Planchoose the strategy

#6 Guess and Check · also uses: #2 Make a Systematic List

Turn each condition into a range of allowed numbers using the times tables, then find the single value common to all three ranges.

3 · Execute3 carry out the plan

1Apply condition 1

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 9 is more than 70: 9 x 7 = 63 (too small), 9 x 8 = 72 (more than 70). So the number is 8 or more.

9 \times 8 = 72 > 70

Checking the 9-times facts shows 8 is the first value pushing the product past 70.

2Apply condition 2

#6 Guess and Check 3.OA.A.4

Find numbers whose product with 2 is less than 19: 2 x 9 = 18 (under 19) but 2 x 10 = 20 (over 19). So the number is 9 or less.

2 \times 9 = 18 < 19,\ 2 \times 10 = 20

The 2-times facts show 9 is the largest value still under 19.

3Apply condition 3 and combine

#2 Make a Systematic List 3.OA.C.7

Condition 3 needs 3 x number > 25: 3 x 8 = 24 (too small) but 3 x 9 = 27 (more than 25), so the number is 9 or more. Combining all three ranges leaves only 9.

3 \times 9 = 27 > 25

Only 9 sits inside every range at once, so it is the common number.

Answer: 9

4 · Reviewdoes it hold up?

Test 9 in all three: 9 x 9 = 81 > 70, 2 x 9 = 18 < 19, and 3 x 9 = 27 > 25, so 9 satisfies every condition.

Another way: You could test each number 1-9 against all three conditions in a table and keep only the row that passes all three, which is 9.

Standardsmin grade 3

3.OA.A.4 Determine unknown whole number in multiplication or division equation — Finding which numbers satisfy each product condition.
3.OA.C.7 Fluently multiply and divide within 100 — Computing the times facts to combine the ranges.

💡Takeaway. Turn each clue into a range with the times tables, then keep the number that fits them all -- Grade 3 facts do it!

Where next?

← Back to the problem: Find a number satisfying product bounds