When you can only add, aim for the multiple above
6.NS.B.3
Generated variants — 12
There are of walnuts to be packed into sacks holding each. To fill every sack completely with none left over, at least how many more kilograms of walnuts are needed?
Show solution
1 · Understandwhat's really being asked
38.15 kg of walnuts go into 1.62 kg sacks. We want the smallest extra amount that leaves no sack part-full and nothing loose.
Givens
- There are 38.15 kg of walnuts.
- Each sack holds 1.62 kg.
- Walnuts may be added, not taken away.
Unknowns
- The least extra weight of walnuts needed.
Constraints
- Every sack must end up completely full.
2 · Planchoose the strategy
#11 Work Backwards
The division will not come out, and the direction we may move decides what to do about it. Since walnuts can only be added, the target is the next multiple of a sack, not the one below.
3 · Execute3 carry out the plan
1See how many sacks fill now
2Aim for one more sack
3Find the gap
4 · Reviewdoes it hold up?
38.15 plus 0.73 is 38.88 kg, which is exactly 24 sacks of 1.62 kg -- nothing over and nothing short.
Standardsmin grade 6
6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing, multiplying and subtracting the decimal weights.
There are of walnuts to be packed into sacks holding each. To fill every sack completely with none left over, at least how many more kilograms of walnuts are needed?
Show solution
1 · Understandwhat's really being asked
41.26 kg of walnuts go into 1.48 kg sacks. We want the smallest extra amount that leaves no sack part-full and nothing loose.
Givens
- There are 41.26 kg of walnuts.
- Each sack holds 1.48 kg.
- Walnuts may be added, not taken away.
Unknowns
- The least extra weight of walnuts needed.
Constraints
- Every sack must end up completely full.
2 · Planchoose the strategy
#11 Work Backwards
The division will not come out, and the direction we may move decides what to do about it. Since walnuts can only be added, the target is the next multiple of a sack, not the one below.
3 · Execute3 carry out the plan
1See how many sacks fill now
2Aim for one more sack
3Find the gap
4 · Reviewdoes it hold up?
41.26 plus 0.18 is 41.44 kg, which is exactly 28 sacks of 1.48 kg -- nothing over and nothing short.
Standardsmin grade 6
6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing, multiplying and subtracting the decimal weights.
There are of walnuts to be packed into sacks holding each. To fill every sack completely with none left over, at least how many more kilograms of walnuts are needed?
Show solution
1 · Understandwhat's really being asked
49.3 kg of walnuts go into 1.26 kg sacks. We want the smallest extra amount that leaves no sack part-full and nothing loose.
Givens
- There are 49.3 kg of walnuts.
- Each sack holds 1.26 kg.
- Walnuts may be added, not taken away.
Unknowns
- The least extra weight of walnuts needed.
Constraints
- Every sack must end up completely full.
2 · Planchoose the strategy
#11 Work Backwards
The division will not come out, and the direction we may move decides what to do about it. Since walnuts can only be added, the target is the next multiple of a sack, not the one below.
3 · Execute3 carry out the plan
1See how many sacks fill now
2Aim for one more sack
3Find the gap
4 · Reviewdoes it hold up?
49.3 plus 1.1 is 50.4 kg, which is exactly 40 sacks of 1.26 kg -- nothing over and nothing short.
Standardsmin grade 6
6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing, multiplying and subtracting the decimal weights.
There are of walnuts to be packed into sacks holding each. To fill every sack completely with none left over, at least how many more kilograms of walnuts are needed?
Show solution
1 · Understandwhat's really being asked
52.4 kg of walnuts go into 1.75 kg sacks. We want the smallest extra amount that leaves no sack part-full and nothing loose.
Givens
- There are 52.4 kg of walnuts.
- Each sack holds 1.75 kg.
- Walnuts may be added, not taken away.
Unknowns
- The least extra weight of walnuts needed.
Constraints
- Every sack must end up completely full.
2 · Planchoose the strategy
#11 Work Backwards
The division will not come out, and the direction we may move decides what to do about it. Since walnuts can only be added, the target is the next multiple of a sack, not the one below.
3 · Execute3 carry out the plan
1See how many sacks fill now
2Aim for one more sack
3Find the gap
4 · Reviewdoes it hold up?
52.4 plus 0.1 is 52.5 kg, which is exactly 30 sacks of 1.75 kg -- nothing over and nothing short.
Standardsmin grade 6
6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing, multiplying and subtracting the decimal weights.
There are of walnuts to be packed into sacks holding each. To fill every sack completely with none left over, at least how many more kilograms of walnuts are needed?
Show solution
1 · Understandwhat's really being asked
56.73 kg of walnuts go into 1.93 kg sacks. We want the smallest extra amount that leaves no sack part-full and nothing loose.
Givens
- There are 56.73 kg of walnuts.
- Each sack holds 1.93 kg.
- Walnuts may be added, not taken away.
Unknowns
- The least extra weight of walnuts needed.
Constraints
- Every sack must end up completely full.
2 · Planchoose the strategy
#11 Work Backwards
The division will not come out, and the direction we may move decides what to do about it. Since walnuts can only be added, the target is the next multiple of a sack, not the one below.
3 · Execute3 carry out the plan
1See how many sacks fill now
2Aim for one more sack
3Find the gap
4 · Reviewdoes it hold up?
56.73 plus 1.17 is 57.9 kg, which is exactly 30 sacks of 1.93 kg -- nothing over and nothing short.
Standardsmin grade 6
6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing, multiplying and subtracting the decimal weights.
There are of walnuts to be packed into sacks holding each. To fill every sack completely with none left over, at least how many more kilograms of walnuts are needed?
Show solution
1 · Understandwhat's really being asked
63.18 kg of walnuts go into 2.14 kg sacks. We want the smallest extra amount that leaves no sack part-full and nothing loose.
Givens
- There are 63.18 kg of walnuts.
- Each sack holds 2.14 kg.
- Walnuts may be added, not taken away.
Unknowns
- The least extra weight of walnuts needed.
Constraints
- Every sack must end up completely full.
2 · Planchoose the strategy
#11 Work Backwards
The division will not come out, and the direction we may move decides what to do about it. Since walnuts can only be added, the target is the next multiple of a sack, not the one below.
3 · Execute3 carry out the plan
1See how many sacks fill now
2Aim for one more sack
3Find the gap
4 · Reviewdoes it hold up?
63.18 plus 1.02 is 64.2 kg, which is exactly 30 sacks of 2.14 kg -- nothing over and nothing short.
Standardsmin grade 6
6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing, multiplying and subtracting the decimal weights.
There are of walnuts to be packed into sacks holding each. To fill every sack completely with none left over, at least how many more kilograms of walnuts are needed?
Show solution
1 · Understandwhat's really being asked
69.05 kg of walnuts go into 3.15 kg sacks. We want the smallest extra amount that leaves no sack part-full and nothing loose.
Givens
- There are 69.05 kg of walnuts.
- Each sack holds 3.15 kg.
- Walnuts may be added, not taken away.
Unknowns
- The least extra weight of walnuts needed.
Constraints
- Every sack must end up completely full.
2 · Planchoose the strategy
#11 Work Backwards
The division will not come out, and the direction we may move decides what to do about it. Since walnuts can only be added, the target is the next multiple of a sack, not the one below.
3 · Execute3 carry out the plan
1See how many sacks fill now
2Aim for one more sack
3Find the gap
4 · Reviewdoes it hold up?
69.05 plus 0.25 is 69.3 kg, which is exactly 22 sacks of 3.15 kg -- nothing over and nothing short.
Standardsmin grade 6
6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing, multiplying and subtracting the decimal weights.
There are of walnuts to be packed into sacks holding each. To fill every sack completely with none left over, at least how many more kilograms of walnuts are needed?
Show solution
1 · Understandwhat's really being asked
71.25 kg of walnuts go into 3.48 kg sacks. We want the smallest extra amount that leaves no sack part-full and nothing loose.
Givens
- There are 71.25 kg of walnuts.
- Each sack holds 3.48 kg.
- Walnuts may be added, not taken away.
Unknowns
- The least extra weight of walnuts needed.
Constraints
- Every sack must end up completely full.
2 · Planchoose the strategy
#11 Work Backwards
The division will not come out, and the direction we may move decides what to do about it. Since walnuts can only be added, the target is the next multiple of a sack, not the one below.
3 · Execute3 carry out the plan
1See how many sacks fill now
2Aim for one more sack
3Find the gap
4 · Reviewdoes it hold up?
71.25 plus 1.83 is 73.08 kg, which is exactly 21 sacks of 3.48 kg -- nothing over and nothing short.
Standardsmin grade 6
6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing, multiplying and subtracting the decimal weights.
There are of walnuts to be packed into sacks holding each. To fill every sack completely with none left over, at least how many more kilograms of walnuts are needed?
Show solution
1 · Understandwhat's really being asked
74.8 kg of walnuts go into 2.36 kg sacks. We want the smallest extra amount that leaves no sack part-full and nothing loose.
Givens
- There are 74.8 kg of walnuts.
- Each sack holds 2.36 kg.
- Walnuts may be added, not taken away.
Unknowns
- The least extra weight of walnuts needed.
Constraints
- Every sack must end up completely full.
2 · Planchoose the strategy
#11 Work Backwards
The division will not come out, and the direction we may move decides what to do about it. Since walnuts can only be added, the target is the next multiple of a sack, not the one below.
3 · Execute3 carry out the plan
1See how many sacks fill now
2Aim for one more sack
3Find the gap
4 · Reviewdoes it hold up?
74.8 plus 0.72 is 75.52 kg, which is exactly 32 sacks of 2.36 kg -- nothing over and nothing short.
Standardsmin grade 6
6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing, multiplying and subtracting the decimal weights.
There are of walnuts to be packed into sacks holding each. To fill every sack completely with none left over, at least how many more kilograms of walnuts are needed?
Show solution
1 · Understandwhat's really being asked
82.5 kg of walnuts go into 4.25 kg sacks. We want the smallest extra amount that leaves no sack part-full and nothing loose.
Givens
- There are 82.5 kg of walnuts.
- Each sack holds 4.25 kg.
- Walnuts may be added, not taken away.
Unknowns
- The least extra weight of walnuts needed.
Constraints
- Every sack must end up completely full.
2 · Planchoose the strategy
#11 Work Backwards
The division will not come out, and the direction we may move decides what to do about it. Since walnuts can only be added, the target is the next multiple of a sack, not the one below.
3 · Execute3 carry out the plan
1See how many sacks fill now
2Aim for one more sack
3Find the gap
4 · Reviewdoes it hold up?
82.5 plus 2.5 is 85 kg, which is exactly 20 sacks of 4.25 kg -- nothing over and nothing short.
Standardsmin grade 6
6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing, multiplying and subtracting the decimal weights.
There are of walnuts to be packed into sacks holding each. To fill every sack completely with none left over, at least how many more kilograms of walnuts are needed?
Show solution
1 · Understandwhat's really being asked
84.06 kg of walnuts go into 2.63 kg sacks. We want the smallest extra amount that leaves no sack part-full and nothing loose.
Givens
- There are 84.06 kg of walnuts.
- Each sack holds 2.63 kg.
- Walnuts may be added, not taken away.
Unknowns
- The least extra weight of walnuts needed.
Constraints
- Every sack must end up completely full.
2 · Planchoose the strategy
#11 Work Backwards
The division will not come out, and the direction we may move decides what to do about it. Since walnuts can only be added, the target is the next multiple of a sack, not the one below.
3 · Execute3 carry out the plan
1See how many sacks fill now
2Aim for one more sack
3Find the gap
4 · Reviewdoes it hold up?
84.06 plus 0.1 is 84.16 kg, which is exactly 32 sacks of 2.63 kg -- nothing over and nothing short.
Standardsmin grade 6
6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing, multiplying and subtracting the decimal weights.
There are of walnuts to be packed into sacks holding each. To fill every sack completely with none left over, at least how many more kilograms of walnuts are needed?
Show solution
1 · Understandwhat's really being asked
96.42 kg of walnuts go into 2.87 kg sacks. We want the smallest extra amount that leaves no sack part-full and nothing loose.
Givens
- There are 96.42 kg of walnuts.
- Each sack holds 2.87 kg.
- Walnuts may be added, not taken away.
Unknowns
- The least extra weight of walnuts needed.
Constraints
- Every sack must end up completely full.
2 · Planchoose the strategy
#11 Work Backwards
The division will not come out, and the direction we may move decides what to do about it. Since walnuts can only be added, the target is the next multiple of a sack, not the one below.
3 · Execute3 carry out the plan
1See how many sacks fill now
2Aim for one more sack
3Find the gap
4 · Reviewdoes it hold up?
96.42 plus 1.16 is 97.58 kg, which is exactly 34 sacks of 2.87 kg -- nothing over and nothing short.
Standardsmin grade 6
6.NS.B.3Fluently add, subtract, multiply, divide multi-digit decimals — Dividing, multiplying and subtracting the decimal weights.