Dividing by a fraction undoes taking that fraction of something
6.NS.A.16.RP.A.36.EE.B.7
Generated variants — 12
Suho saved of his allowance. If he saved won, how much of his allowance is left after saving?
Show solution
1 · Understandwhat's really being asked
Saving 2/7 of an allowance came to 1400 won. We want what is left after that saving.
Givens
- The saving is 2/7 of the allowance.
- The saving is 1400 won.
Unknowns
- How much of the allowance is left.
Constraints
- Only the saved part is given; the allowance itself is not.
2 · Planchoose the strategy
#11 Work Backwards
Taking a fraction of the allowance produced the saving, so dividing by that fraction takes it back. Then read the question again -- it asks for the remainder, not the allowance.
3 · Execute3 carry out the plan
1Find one part
2Build the whole allowance
3Take the saving off
4 · Reviewdoes it hold up?
2/7 of 4900 won is 1400 won, the amount saved -- and what is left, 3500 won, is the other 5/7.
Standardsmin grade 6
6.NS.A.1Divide fractions by fractions — Dividing by the fraction to recover the whole.6.RP.A.3Use ratio and rate reasoning to solve problems — Reading the saving as a share of the allowance.6.EE.B.7Solve one-step equations x+p=q and px=q — Solving for the allowance from one known part.
Suho saved of his allowance. If he saved won, how much of his allowance is left after saving?
Show solution
1 · Understandwhat's really being asked
Saving 3/8 of an allowance came to 1500 won. We want what is left after that saving.
Givens
- The saving is 3/8 of the allowance.
- The saving is 1500 won.
Unknowns
- How much of the allowance is left.
Constraints
- Only the saved part is given; the allowance itself is not.
2 · Planchoose the strategy
#11 Work Backwards
Taking a fraction of the allowance produced the saving, so dividing by that fraction takes it back. Then read the question again -- it asks for the remainder, not the allowance.
3 · Execute3 carry out the plan
1Find one part
2Build the whole allowance
3Take the saving off
4 · Reviewdoes it hold up?
3/8 of 4000 won is 1500 won, the amount saved -- and what is left, 2500 won, is the other 5/8.
Standardsmin grade 6
6.NS.A.1Divide fractions by fractions — Dividing by the fraction to recover the whole.6.RP.A.3Use ratio and rate reasoning to solve problems — Reading the saving as a share of the allowance.6.EE.B.7Solve one-step equations x+p=q and px=q — Solving for the allowance from one known part.
Suho saved of his allowance. If he saved won, how much of his allowance is left after saving?
Show solution
1 · Understandwhat's really being asked
Saving 3/10 of an allowance came to 1800 won. We want what is left after that saving.
Givens
- The saving is 3/10 of the allowance.
- The saving is 1800 won.
Unknowns
- How much of the allowance is left.
Constraints
- Only the saved part is given; the allowance itself is not.
2 · Planchoose the strategy
#11 Work Backwards
Taking a fraction of the allowance produced the saving, so dividing by that fraction takes it back. Then read the question again -- it asks for the remainder, not the allowance.
3 · Execute3 carry out the plan
1Find one part
2Build the whole allowance
3Take the saving off
4 · Reviewdoes it hold up?
3/10 of 6000 won is 1800 won, the amount saved -- and what is left, 4200 won, is the other 7/10.
Standardsmin grade 6
6.NS.A.1Divide fractions by fractions — Dividing by the fraction to recover the whole.6.RP.A.3Use ratio and rate reasoning to solve problems — Reading the saving as a share of the allowance.6.EE.B.7Solve one-step equations x+p=q and px=q — Solving for the allowance from one known part.
Suho saved of his allowance. If he saved won, how much of his allowance is left after saving?
Show solution
1 · Understandwhat's really being asked
Saving 2/5 of an allowance came to 2000 won. We want what is left after that saving.
Givens
- The saving is 2/5 of the allowance.
- The saving is 2000 won.
Unknowns
- How much of the allowance is left.
Constraints
- Only the saved part is given; the allowance itself is not.
2 · Planchoose the strategy
#11 Work Backwards
Taking a fraction of the allowance produced the saving, so dividing by that fraction takes it back. Then read the question again -- it asks for the remainder, not the allowance.
3 · Execute3 carry out the plan
1Find one part
2Build the whole allowance
3Take the saving off
4 · Reviewdoes it hold up?
2/5 of 5000 won is 2000 won, the amount saved -- and what is left, 3000 won, is the other 3/5.
Standardsmin grade 6
6.NS.A.1Divide fractions by fractions — Dividing by the fraction to recover the whole.6.RP.A.3Use ratio and rate reasoning to solve problems — Reading the saving as a share of the allowance.6.EE.B.7Solve one-step equations x+p=q and px=q — Solving for the allowance from one known part.
Suho saved of his allowance. If he saved won, how much of his allowance is left after saving?
Show solution
1 · Understandwhat's really being asked
Saving 3/7 of an allowance came to 2100 won. We want what is left after that saving.
Givens
- The saving is 3/7 of the allowance.
- The saving is 2100 won.
Unknowns
- How much of the allowance is left.
Constraints
- Only the saved part is given; the allowance itself is not.
2 · Planchoose the strategy
#11 Work Backwards
Taking a fraction of the allowance produced the saving, so dividing by that fraction takes it back. Then read the question again -- it asks for the remainder, not the allowance.
3 · Execute3 carry out the plan
1Find one part
2Build the whole allowance
3Take the saving off
4 · Reviewdoes it hold up?
3/7 of 4900 won is 2100 won, the amount saved -- and what is left, 2800 won, is the other 4/7.
Standardsmin grade 6
6.NS.A.1Divide fractions by fractions — Dividing by the fraction to recover the whole.6.RP.A.3Use ratio and rate reasoning to solve problems — Reading the saving as a share of the allowance.6.EE.B.7Solve one-step equations x+p=q and px=q — Solving for the allowance from one known part.
Suho saved of his allowance. If he saved won, how much of his allowance is left after saving?
Show solution
1 · Understandwhat's really being asked
Saving 4/11 of an allowance came to 2400 won. We want what is left after that saving.
Givens
- The saving is 4/11 of the allowance.
- The saving is 2400 won.
Unknowns
- How much of the allowance is left.
Constraints
- Only the saved part is given; the allowance itself is not.
2 · Planchoose the strategy
#11 Work Backwards
Taking a fraction of the allowance produced the saving, so dividing by that fraction takes it back. Then read the question again -- it asks for the remainder, not the allowance.
3 · Execute3 carry out the plan
1Find one part
2Build the whole allowance
3Take the saving off
4 · Reviewdoes it hold up?
4/11 of 6600 won is 2400 won, the amount saved -- and what is left, 4200 won, is the other 7/11.
Standardsmin grade 6
6.NS.A.1Divide fractions by fractions — Dividing by the fraction to recover the whole.6.RP.A.3Use ratio and rate reasoning to solve problems — Reading the saving as a share of the allowance.6.EE.B.7Solve one-step equations x+p=q and px=q — Solving for the allowance from one known part.
Suho saved of his allowance. If he saved won, how much of his allowance is left after saving?
Show solution
1 · Understandwhat's really being asked
Saving 5/12 of an allowance came to 2500 won. We want what is left after that saving.
Givens
- The saving is 5/12 of the allowance.
- The saving is 2500 won.
Unknowns
- How much of the allowance is left.
Constraints
- Only the saved part is given; the allowance itself is not.
2 · Planchoose the strategy
#11 Work Backwards
Taking a fraction of the allowance produced the saving, so dividing by that fraction takes it back. Then read the question again -- it asks for the remainder, not the allowance.
3 · Execute3 carry out the plan
1Find one part
2Build the whole allowance
3Take the saving off
4 · Reviewdoes it hold up?
5/12 of 6000 won is 2500 won, the amount saved -- and what is left, 3500 won, is the other 7/12.
Standardsmin grade 6
6.NS.A.1Divide fractions by fractions — Dividing by the fraction to recover the whole.6.RP.A.3Use ratio and rate reasoning to solve problems — Reading the saving as a share of the allowance.6.EE.B.7Solve one-step equations x+p=q and px=q — Solving for the allowance from one known part.
Suho saved of his allowance. If he saved won, how much of his allowance is left after saving?
Show solution
1 · Understandwhat's really being asked
Saving 7/15 of an allowance came to 2800 won. We want what is left after that saving.
Givens
- The saving is 7/15 of the allowance.
- The saving is 2800 won.
Unknowns
- How much of the allowance is left.
Constraints
- Only the saved part is given; the allowance itself is not.
2 · Planchoose the strategy
#11 Work Backwards
Taking a fraction of the allowance produced the saving, so dividing by that fraction takes it back. Then read the question again -- it asks for the remainder, not the allowance.
3 · Execute3 carry out the plan
1Find one part
2Build the whole allowance
3Take the saving off
4 · Reviewdoes it hold up?
7/15 of 6000 won is 2800 won, the amount saved -- and what is left, 3200 won, is the other 8/15.
Standardsmin grade 6
6.NS.A.1Divide fractions by fractions — Dividing by the fraction to recover the whole.6.RP.A.3Use ratio and rate reasoning to solve problems — Reading the saving as a share of the allowance.6.EE.B.7Solve one-step equations x+p=q and px=q — Solving for the allowance from one known part.
Suho saved of his allowance. If he saved won, how much of his allowance is left after saving?
Show solution
1 · Understandwhat's really being asked
Saving 4/9 of an allowance came to 3200 won. We want what is left after that saving.
Givens
- The saving is 4/9 of the allowance.
- The saving is 3200 won.
Unknowns
- How much of the allowance is left.
Constraints
- Only the saved part is given; the allowance itself is not.
2 · Planchoose the strategy
#11 Work Backwards
Taking a fraction of the allowance produced the saving, so dividing by that fraction takes it back. Then read the question again -- it asks for the remainder, not the allowance.
3 · Execute3 carry out the plan
1Find one part
2Build the whole allowance
3Take the saving off
4 · Reviewdoes it hold up?
4/9 of 7200 won is 3200 won, the amount saved -- and what is left, 4000 won, is the other 5/9.
Standardsmin grade 6
6.NS.A.1Divide fractions by fractions — Dividing by the fraction to recover the whole.6.RP.A.3Use ratio and rate reasoning to solve problems — Reading the saving as a share of the allowance.6.EE.B.7Solve one-step equations x+p=q and px=q — Solving for the allowance from one known part.
Suho saved of his allowance. If he saved won, how much of his allowance is left after saving?
Show solution
1 · Understandwhat's really being asked
Saving 7/12 of an allowance came to 3500 won. We want what is left after that saving.
Givens
- The saving is 7/12 of the allowance.
- The saving is 3500 won.
Unknowns
- How much of the allowance is left.
Constraints
- Only the saved part is given; the allowance itself is not.
2 · Planchoose the strategy
#11 Work Backwards
Taking a fraction of the allowance produced the saving, so dividing by that fraction takes it back. Then read the question again -- it asks for the remainder, not the allowance.
3 · Execute3 carry out the plan
1Find one part
2Build the whole allowance
3Take the saving off
4 · Reviewdoes it hold up?
7/12 of 6000 won is 3500 won, the amount saved -- and what is left, 2500 won, is the other 5/12.
Standardsmin grade 6
6.NS.A.1Divide fractions by fractions — Dividing by the fraction to recover the whole.6.RP.A.3Use ratio and rate reasoning to solve problems — Reading the saving as a share of the allowance.6.EE.B.7Solve one-step equations x+p=q and px=q — Solving for the allowance from one known part.
Suho saved of his allowance. If he saved won, how much of his allowance is left after saving?
Show solution
1 · Understandwhat's really being asked
Saving 5/8 of an allowance came to 4000 won. We want what is left after that saving.
Givens
- The saving is 5/8 of the allowance.
- The saving is 4000 won.
Unknowns
- How much of the allowance is left.
Constraints
- Only the saved part is given; the allowance itself is not.
2 · Planchoose the strategy
#11 Work Backwards
Taking a fraction of the allowance produced the saving, so dividing by that fraction takes it back. Then read the question again -- it asks for the remainder, not the allowance.
3 · Execute3 carry out the plan
1Find one part
2Build the whole allowance
3Take the saving off
4 · Reviewdoes it hold up?
5/8 of 6400 won is 4000 won, the amount saved -- and what is left, 2400 won, is the other 3/8.
Standardsmin grade 6
6.NS.A.1Divide fractions by fractions — Dividing by the fraction to recover the whole.6.RP.A.3Use ratio and rate reasoning to solve problems — Reading the saving as a share of the allowance.6.EE.B.7Solve one-step equations x+p=q and px=q — Solving for the allowance from one known part.
Suho saved of his allowance. If he saved won, how much of his allowance is left after saving?
Show solution
1 · Understandwhat's really being asked
Saving 5/9 of an allowance came to 5000 won. We want what is left after that saving.
Givens
- The saving is 5/9 of the allowance.
- The saving is 5000 won.
Unknowns
- How much of the allowance is left.
Constraints
- Only the saved part is given; the allowance itself is not.
2 · Planchoose the strategy
#11 Work Backwards
Taking a fraction of the allowance produced the saving, so dividing by that fraction takes it back. Then read the question again -- it asks for the remainder, not the allowance.
3 · Execute3 carry out the plan
1Find one part
2Build the whole allowance
3Take the saving off
4 · Reviewdoes it hold up?
5/9 of 9000 won is 5000 won, the amount saved -- and what is left, 4000 won, is the other 4/9.
Standardsmin grade 6
6.NS.A.1Divide fractions by fractions — Dividing by the fraction to recover the whole.6.RP.A.3Use ratio and rate reasoning to solve problems — Reading the saving as a share of the allowance.6.EE.B.7Solve one-step equations x+p=q and px=q — Solving for the allowance from one known part.
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