← Solve multi-step decimal problems in order · Solve a Table or Graph Step by Step from Clues

Solve multi-step decimal problems in order · 12 practice problems

5.NBT.B.7

Generated variants — 12

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

Variant 1 easy answer: Jacob (2.244 km)

Nami walks 1.8 km1.8\ \text{km} in one hour. In one hour, Evan walked 0.3 km0.3\ \text{km} less than 0.90.9 times Nami's distance, and Jacob walked 1.71.7 times Evan's distance. Who walked the farthest in one hour?

Show solution
1 · Understandwhat's really being asked

Nami walks 1.8 km in an hour. Evan's distance is described through Nami's, and Jacob's through Evan's. We must say who covered the most.

Givens
  • Nami: 1.8 km.
  • Evan: 0.3 km less than 0.9 times Nami's.
  • Jacob: 1.7 times Evan's.
Unknowns
  • Who walked the farthest, and how far.
Constraints
  • Each distance is defined through the one before it, so they must be worked out in order.
2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Jacob's distance cannot be found before Evan's, and Evan's not before Nami's is used. Take them one at a time in that order, then compare all three at the end.

3 · Execute3 carry out the plan

1Find Evan's distance

#7 Identify Subproblems 5.NBT.B.7
Take 0.9 times Nami's 1.8 km, then remove 0.3 km.
1.8×0.9=1.62,1.620.3=1.321.8 \times 0.9 = 1.62,\quad 1.62 - 0.3 = 1.32
Evan walked 1.32 km.

2Find Jacob's distance

#7 Identify Subproblems 5.NBT.B.7
Jacob's is 1.7 times Evan's, now that Evan's is known.
1.32×1.7=2.2441.32 \times 1.7 = 2.244
Jacob walked 2.244 km.

3Compare all three distances

#8 Analyze the Units 5.NBT.B.7
Line the three up and read off the largest.
2.244>1.8>1.322.244 > 1.8 > 1.32
Jacob walked the farthest.
Answer: Jacob (2.244 km)
4 · Reviewdoes it hold up?

Evan's 1.32 is a little under 0.9 times Nami's, as the wording says, and Jacob's 2.244 is 1.7 times that -- each step is the right size.

Another way: Chaining it into one expression, (1.8×0.90.3)×1.7(1.8 \times 0.9 - 0.3) \times 1.7, gives Jacob's 2.244 in a single line, but hides the two intermediate distances the question compares.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Every multiplication and subtraction in the chain, and the final comparison.
💡Takeaway. When each amount is described through the one before, the order is not a choice -- work forwards and nothing is guessed.
Variant 2 easy answer: Jacob (2.034 km)

Nami walks 1.9 km1.9\ \text{km} in one hour. In one hour, Evan walked 0.2 km0.2\ \text{km} less than 0.70.7 times Nami's distance, and Jacob walked 1.81.8 times Evan's distance. Who walked the farthest in one hour?

Show solution
1 · Understandwhat's really being asked

Nami walks 1.9 km in an hour. Evan's distance is described through Nami's, and Jacob's through Evan's. We must say who covered the most.

Givens
  • Nami: 1.9 km.
  • Evan: 0.2 km less than 0.7 times Nami's.
  • Jacob: 1.8 times Evan's.
Unknowns
  • Who walked the farthest, and how far.
Constraints
  • Each distance is defined through the one before it, so they must be worked out in order.
2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Jacob's distance cannot be found before Evan's, and Evan's not before Nami's is used. Take them one at a time in that order, then compare all three at the end.

3 · Execute3 carry out the plan

1Find Evan's distance

#7 Identify Subproblems 5.NBT.B.7
Take 0.7 times Nami's 1.9 km, then remove 0.2 km.
1.9×0.7=1.33,1.330.2=1.131.9 \times 0.7 = 1.33,\quad 1.33 - 0.2 = 1.13
Evan walked 1.13 km.

2Find Jacob's distance

#7 Identify Subproblems 5.NBT.B.7
Jacob's is 1.8 times Evan's, now that Evan's is known.
1.13×1.8=2.0341.13 \times 1.8 = 2.034
Jacob walked 2.034 km.

3Compare all three distances

#8 Analyze the Units 5.NBT.B.7
Line the three up and read off the largest.
2.034>1.9>1.132.034 > 1.9 > 1.13
Jacob walked the farthest.
Answer: Jacob (2.034 km)
4 · Reviewdoes it hold up?

Evan's 1.13 is a little under 0.7 times Nami's, as the wording says, and Jacob's 2.034 is 1.8 times that -- each step is the right size.

Another way: Chaining it into one expression, (1.9×0.70.2)×1.8(1.9 \times 0.7 - 0.2) \times 1.8, gives Jacob's 2.034 in a single line, but hides the two intermediate distances the question compares.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Every multiplication and subtraction in the chain, and the final comparison.
💡Takeaway. When each amount is described through the one before, the order is not a choice -- work forwards and nothing is guessed.
Variant 3 easy answer: Jacob (2.5 km)

Nami walks 1.5 km1.5\ \text{km} in one hour. In one hour, Evan walked 0.1 km0.1\ \text{km} less than 0.90.9 times Nami's distance, and Jacob walked 22 times Evan's distance. Who walked the farthest in one hour?

Show solution
1 · Understandwhat's really being asked

Nami walks 1.5 km in an hour. Evan's distance is described through Nami's, and Jacob's through Evan's. We must say who covered the most.

Givens
  • Nami: 1.5 km.
  • Evan: 0.1 km less than 0.9 times Nami's.
  • Jacob: 2 times Evan's.
Unknowns
  • Who walked the farthest, and how far.
Constraints
  • Each distance is defined through the one before it, so they must be worked out in order.
2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Jacob's distance cannot be found before Evan's, and Evan's not before Nami's is used. Take them one at a time in that order, then compare all three at the end.

3 · Execute3 carry out the plan

1Find Evan's distance

#7 Identify Subproblems 5.NBT.B.7
Take 0.9 times Nami's 1.5 km, then remove 0.1 km.
1.5×0.9=1.35,1.350.1=1.251.5 \times 0.9 = 1.35,\quad 1.35 - 0.1 = 1.25
Evan walked 1.25 km.

2Find Jacob's distance

#7 Identify Subproblems 5.NBT.B.7
Jacob's is 2 times Evan's, now that Evan's is known.
1.25×2=2.51.25 \times 2 = 2.5
Jacob walked 2.5 km.

3Compare all three distances

#8 Analyze the Units 5.NBT.B.7
Line the three up and read off the largest.
2.5>1.5>1.252.5 > 1.5 > 1.25
Jacob walked the farthest.
Answer: Jacob (2.5 km)
4 · Reviewdoes it hold up?

Evan's 1.25 is a little under 0.9 times Nami's, as the wording says, and Jacob's 2.5 is 2 times that -- each step is the right size.

Another way: Chaining it into one expression, (1.5×0.90.1)×2(1.5 \times 0.9 - 0.1) \times 2, gives Jacob's 2.5 in a single line, but hides the two intermediate distances the question compares.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Every multiplication and subtraction in the chain, and the final comparison.
💡Takeaway. When each amount is described through the one before, the order is not a choice -- work forwards and nothing is guessed.
Variant 4 easy answer: Nami (2.1 km)

Nami walks 2.1 km2.1\ \text{km} in one hour. In one hour, Evan walked 0.5 km0.5\ \text{km} less than 0.80.8 times Nami's distance, and Jacob walked 1.51.5 times Evan's distance. Who walked the farthest in one hour?

Show solution
1 · Understandwhat's really being asked

Nami walks 2.1 km in an hour. Evan's distance is described through Nami's, and Jacob's through Evan's. We must say who covered the most.

Givens
  • Nami: 2.1 km.
  • Evan: 0.5 km less than 0.8 times Nami's.
  • Jacob: 1.5 times Evan's.
Unknowns
  • Who walked the farthest, and how far.
Constraints
  • Each distance is defined through the one before it, so they must be worked out in order.
2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Jacob's distance cannot be found before Evan's, and Evan's not before Nami's is used. Take them one at a time in that order, then compare all three at the end.

3 · Execute3 carry out the plan

1Find Evan's distance

#7 Identify Subproblems 5.NBT.B.7
Take 0.8 times Nami's 2.1 km, then remove 0.5 km.
2.1×0.8=1.68,1.680.5=1.182.1 \times 0.8 = 1.68,\quad 1.68 - 0.5 = 1.18
Evan walked 1.18 km.

2Find Jacob's distance

#7 Identify Subproblems 5.NBT.B.7
Jacob's is 1.5 times Evan's, now that Evan's is known.
1.18×1.5=1.771.18 \times 1.5 = 1.77
Jacob walked 1.77 km.

3Compare all three distances

#8 Analyze the Units 5.NBT.B.7
Line the three up and read off the largest.
2.1>1.77>1.182.1 > 1.77 > 1.18
Nami walked the farthest.
Answer: Nami (2.1 km)
4 · Reviewdoes it hold up?

Evan's 1.18 is a little under 0.8 times Nami's, as the wording says, and Jacob's 1.77 is 1.5 times that -- each step is the right size.

Another way: Chaining it into one expression, (2.1×0.80.5)×1.5(2.1 \times 0.8 - 0.5) \times 1.5, gives Jacob's 1.77 in a single line, but hides the two intermediate distances the question compares.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Every multiplication and subtraction in the chain, and the final comparison.
💡Takeaway. When each amount is described through the one before, the order is not a choice -- work forwards and nothing is guessed.
Variant 5 medium answer: Jacob (2.592 km)

Nami walks 2.4 km2.4\ \text{km} in one hour. In one hour, Evan walked 0.3 km0.3\ \text{km} less than 0.80.8 times Nami's distance, and Jacob walked 1.61.6 times Evan's distance. Who walked the farthest in one hour?

Show solution
1 · Understandwhat's really being asked

Nami walks 2.4 km in an hour. Evan's distance is described through Nami's, and Jacob's through Evan's. We must say who covered the most.

Givens
  • Nami: 2.4 km.
  • Evan: 0.3 km less than 0.8 times Nami's.
  • Jacob: 1.6 times Evan's.
Unknowns
  • Who walked the farthest, and how far.
Constraints
  • Each distance is defined through the one before it, so they must be worked out in order.
2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Jacob's distance cannot be found before Evan's, and Evan's not before Nami's is used. Take them one at a time in that order, then compare all three at the end.

3 · Execute3 carry out the plan

1Find Evan's distance

#7 Identify Subproblems 5.NBT.B.7
Take 0.8 times Nami's 2.4 km, then remove 0.3 km.
2.4×0.8=1.92,1.920.3=1.622.4 \times 0.8 = 1.92,\quad 1.92 - 0.3 = 1.62
Evan walked 1.62 km.

2Find Jacob's distance

#7 Identify Subproblems 5.NBT.B.7
Jacob's is 1.6 times Evan's, now that Evan's is known.
1.62×1.6=2.5921.62 \times 1.6 = 2.592
Jacob walked 2.592 km.

3Compare all three distances

#8 Analyze the Units 5.NBT.B.7
Line the three up and read off the largest.
2.592>2.4>1.622.592 > 2.4 > 1.62
Jacob walked the farthest.
Answer: Jacob (2.592 km)
4 · Reviewdoes it hold up?

Evan's 1.62 is a little under 0.8 times Nami's, as the wording says, and Jacob's 2.592 is 1.6 times that -- each step is the right size.

Another way: Chaining it into one expression, (2.4×0.80.3)×1.6(2.4 \times 0.8 - 0.3) \times 1.6, gives Jacob's 2.592 in a single line, but hides the two intermediate distances the question compares.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Every multiplication and subtraction in the chain, and the final comparison.
💡Takeaway. When each amount is described through the one before, the order is not a choice -- work forwards and nothing is guessed.
Variant 6 medium answer: Jacob (2.208 km)

Nami walks 1.6 km1.6\ \text{km} in one hour. In one hour, Evan walked 0.2 km0.2\ \text{km} less than 0.70.7 times Nami's distance, and Jacob walked 2.42.4 times Evan's distance. Who walked the farthest in one hour?

Show solution
1 · Understandwhat's really being asked

Nami walks 1.6 km in an hour. Evan's distance is described through Nami's, and Jacob's through Evan's. We must say who covered the most.

Givens
  • Nami: 1.6 km.
  • Evan: 0.2 km less than 0.7 times Nami's.
  • Jacob: 2.4 times Evan's.
Unknowns
  • Who walked the farthest, and how far.
Constraints
  • Each distance is defined through the one before it, so they must be worked out in order.
2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Jacob's distance cannot be found before Evan's, and Evan's not before Nami's is used. Take them one at a time in that order, then compare all three at the end.

3 · Execute3 carry out the plan

1Find Evan's distance

#7 Identify Subproblems 5.NBT.B.7
Take 0.7 times Nami's 1.6 km, then remove 0.2 km.
1.6×0.7=1.12,1.120.2=0.921.6 \times 0.7 = 1.12,\quad 1.12 - 0.2 = 0.92
Evan walked 0.92 km.

2Find Jacob's distance

#7 Identify Subproblems 5.NBT.B.7
Jacob's is 2.4 times Evan's, now that Evan's is known.
0.92×2.4=2.2080.92 \times 2.4 = 2.208
Jacob walked 2.208 km.

3Compare all three distances

#8 Analyze the Units 5.NBT.B.7
Line the three up and read off the largest.
2.208>1.6>0.922.208 > 1.6 > 0.92
Jacob walked the farthest.
Answer: Jacob (2.208 km)
4 · Reviewdoes it hold up?

Evan's 0.92 is a little under 0.7 times Nami's, as the wording says, and Jacob's 2.208 is 2.4 times that -- each step is the right size.

Another way: Chaining it into one expression, (1.6×0.70.2)×2.4(1.6 \times 0.7 - 0.2) \times 2.4, gives Jacob's 2.208 in a single line, but hides the two intermediate distances the question compares.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Every multiplication and subtraction in the chain, and the final comparison.
💡Takeaway. When each amount is described through the one before, the order is not a choice -- work forwards and nothing is guessed.
Variant 7 medium answer: Jacob (2.73 km)

Nami walks 2.7 km2.7\ \text{km} in one hour. In one hour, Evan walked 0.3 km0.3\ \text{km} less than 0.50.5 times Nami's distance, and Jacob walked 2.62.6 times Evan's distance. Who walked the farthest in one hour?

Show solution
1 · Understandwhat's really being asked

Nami walks 2.7 km in an hour. Evan's distance is described through Nami's, and Jacob's through Evan's. We must say who covered the most.

Givens
  • Nami: 2.7 km.
  • Evan: 0.3 km less than 0.5 times Nami's.
  • Jacob: 2.6 times Evan's.
Unknowns
  • Who walked the farthest, and how far.
Constraints
  • Each distance is defined through the one before it, so they must be worked out in order.
2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Jacob's distance cannot be found before Evan's, and Evan's not before Nami's is used. Take them one at a time in that order, then compare all three at the end.

3 · Execute3 carry out the plan

1Find Evan's distance

#7 Identify Subproblems 5.NBT.B.7
Take 0.5 times Nami's 2.7 km, then remove 0.3 km.
2.7×0.5=1.35,1.350.3=1.052.7 \times 0.5 = 1.35,\quad 1.35 - 0.3 = 1.05
Evan walked 1.05 km.

2Find Jacob's distance

#7 Identify Subproblems 5.NBT.B.7
Jacob's is 2.6 times Evan's, now that Evan's is known.
1.05×2.6=2.731.05 \times 2.6 = 2.73
Jacob walked 2.73 km.

3Compare all three distances

#8 Analyze the Units 5.NBT.B.7
Line the three up and read off the largest.
2.73>2.7>1.052.73 > 2.7 > 1.05
Jacob walked the farthest.
Answer: Jacob (2.73 km)
4 · Reviewdoes it hold up?

Evan's 1.05 is a little under 0.5 times Nami's, as the wording says, and Jacob's 2.73 is 2.6 times that -- each step is the right size.

Another way: Chaining it into one expression, (2.7×0.50.3)×2.6(2.7 \times 0.5 - 0.3) \times 2.6, gives Jacob's 2.73 in a single line, but hides the two intermediate distances the question compares.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Every multiplication and subtraction in the chain, and the final comparison.
💡Takeaway. When each amount is described through the one before, the order is not a choice -- work forwards and nothing is guessed.
Variant 8 medium answer: Jacob (3.92 km)

Nami walks 2.5 km2.5\ \text{km} in one hour. In one hour, Evan walked 0.1 km0.1\ \text{km} less than 0.60.6 times Nami's distance, and Jacob walked 2.82.8 times Evan's distance. Who walked the farthest in one hour?

Show solution
1 · Understandwhat's really being asked

Nami walks 2.5 km in an hour. Evan's distance is described through Nami's, and Jacob's through Evan's. We must say who covered the most.

Givens
  • Nami: 2.5 km.
  • Evan: 0.1 km less than 0.6 times Nami's.
  • Jacob: 2.8 times Evan's.
Unknowns
  • Who walked the farthest, and how far.
Constraints
  • Each distance is defined through the one before it, so they must be worked out in order.
2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Jacob's distance cannot be found before Evan's, and Evan's not before Nami's is used. Take them one at a time in that order, then compare all three at the end.

3 · Execute3 carry out the plan

1Find Evan's distance

#7 Identify Subproblems 5.NBT.B.7
Take 0.6 times Nami's 2.5 km, then remove 0.1 km.
2.5×0.6=1.5,1.50.1=1.42.5 \times 0.6 = 1.5,\quad 1.5 - 0.1 = 1.4
Evan walked 1.4 km.

2Find Jacob's distance

#7 Identify Subproblems 5.NBT.B.7
Jacob's is 2.8 times Evan's, now that Evan's is known.
1.4×2.8=3.921.4 \times 2.8 = 3.92
Jacob walked 3.92 km.

3Compare all three distances

#8 Analyze the Units 5.NBT.B.7
Line the three up and read off the largest.
3.92>2.5>1.43.92 > 2.5 > 1.4
Jacob walked the farthest.
Answer: Jacob (3.92 km)
4 · Reviewdoes it hold up?

Evan's 1.4 is a little under 0.6 times Nami's, as the wording says, and Jacob's 3.92 is 2.8 times that -- each step is the right size.

Another way: Chaining it into one expression, (2.5×0.60.1)×2.8(2.5 \times 0.6 - 0.1) \times 2.8, gives Jacob's 3.92 in a single line, but hides the two intermediate distances the question compares.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Every multiplication and subtraction in the chain, and the final comparison.
💡Takeaway. When each amount is described through the one before, the order is not a choice -- work forwards and nothing is guessed.
Variant 9 hard answer: Jacob (3.6 km)

Nami walks 2.8 km2.8\ \text{km} in one hour. In one hour, Evan walked 0.2 km0.2\ \text{km} less than 0.50.5 times Nami's distance, and Jacob walked 33 times Evan's distance. Who walked the farthest in one hour?

Show solution
1 · Understandwhat's really being asked

Nami walks 2.8 km in an hour. Evan's distance is described through Nami's, and Jacob's through Evan's. We must say who covered the most.

Givens
  • Nami: 2.8 km.
  • Evan: 0.2 km less than 0.5 times Nami's.
  • Jacob: 3 times Evan's.
Unknowns
  • Who walked the farthest, and how far.
Constraints
  • Each distance is defined through the one before it, so they must be worked out in order.
2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Jacob's distance cannot be found before Evan's, and Evan's not before Nami's is used. Take them one at a time in that order, then compare all three at the end.

3 · Execute3 carry out the plan

1Find Evan's distance

#7 Identify Subproblems 5.NBT.B.7
Take 0.5 times Nami's 2.8 km, then remove 0.2 km.
2.8×0.5=1.4,1.40.2=1.22.8 \times 0.5 = 1.4,\quad 1.4 - 0.2 = 1.2
Evan walked 1.2 km.

2Find Jacob's distance

#7 Identify Subproblems 5.NBT.B.7
Jacob's is 3 times Evan's, now that Evan's is known.
1.2×3=3.61.2 \times 3 = 3.6
Jacob walked 3.6 km.

3Compare all three distances

#8 Analyze the Units 5.NBT.B.7
Line the three up and read off the largest.
3.6>2.8>1.23.6 > 2.8 > 1.2
Jacob walked the farthest.
Answer: Jacob (3.6 km)
4 · Reviewdoes it hold up?

Evan's 1.2 is a little under 0.5 times Nami's, as the wording says, and Jacob's 3.6 is 3 times that -- each step is the right size.

Another way: Chaining it into one expression, (2.8×0.50.2)×3(2.8 \times 0.5 - 0.2) \times 3, gives Jacob's 3.6 in a single line, but hides the two intermediate distances the question compares.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Every multiplication and subtraction in the chain, and the final comparison.
💡Takeaway. When each amount is described through the one before, the order is not a choice -- work forwards and nothing is guessed.
Variant 10 hard answer: Jacob (3.23 km)

Nami walks 3 km3\ \text{km} in one hour. In one hour, Evan walked 0.7 km0.7\ \text{km} less than 0.80.8 times Nami's distance, and Jacob walked 1.91.9 times Evan's distance. Who walked the farthest in one hour?

Show solution
1 · Understandwhat's really being asked

Nami walks 3 km in an hour. Evan's distance is described through Nami's, and Jacob's through Evan's. We must say who covered the most.

Givens
  • Nami: 3 km.
  • Evan: 0.7 km less than 0.8 times Nami's.
  • Jacob: 1.9 times Evan's.
Unknowns
  • Who walked the farthest, and how far.
Constraints
  • Each distance is defined through the one before it, so they must be worked out in order.
2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Jacob's distance cannot be found before Evan's, and Evan's not before Nami's is used. Take them one at a time in that order, then compare all three at the end.

3 · Execute3 carry out the plan

1Find Evan's distance

#7 Identify Subproblems 5.NBT.B.7
Take 0.8 times Nami's 3 km, then remove 0.7 km.
3×0.8=2.4,2.40.7=1.73 \times 0.8 = 2.4,\quad 2.4 - 0.7 = 1.7
Evan walked 1.7 km.

2Find Jacob's distance

#7 Identify Subproblems 5.NBT.B.7
Jacob's is 1.9 times Evan's, now that Evan's is known.
1.7×1.9=3.231.7 \times 1.9 = 3.23
Jacob walked 3.23 km.

3Compare all three distances

#8 Analyze the Units 5.NBT.B.7
Line the three up and read off the largest.
3.23>3>1.73.23 > 3 > 1.7
Jacob walked the farthest.
Answer: Jacob (3.23 km)
4 · Reviewdoes it hold up?

Evan's 1.7 is a little under 0.8 times Nami's, as the wording says, and Jacob's 3.23 is 1.9 times that -- each step is the right size.

Another way: Chaining it into one expression, (3×0.80.7)×1.9(3 \times 0.8 - 0.7) \times 1.9, gives Jacob's 3.23 in a single line, but hides the two intermediate distances the question compares.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Every multiplication and subtraction in the chain, and the final comparison.
💡Takeaway. When each amount is described through the one before, the order is not a choice -- work forwards and nothing is guessed.
Variant 11 hard answer: Jacob (3.8 km)

Nami walks 3.2 km3.2\ \text{km} in one hour. In one hour, Evan walked 0.4 km0.4\ \text{km} less than 0.60.6 times Nami's distance, and Jacob walked 2.52.5 times Evan's distance. Who walked the farthest in one hour?

Show solution
1 · Understandwhat's really being asked

Nami walks 3.2 km in an hour. Evan's distance is described through Nami's, and Jacob's through Evan's. We must say who covered the most.

Givens
  • Nami: 3.2 km.
  • Evan: 0.4 km less than 0.6 times Nami's.
  • Jacob: 2.5 times Evan's.
Unknowns
  • Who walked the farthest, and how far.
Constraints
  • Each distance is defined through the one before it, so they must be worked out in order.
2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Jacob's distance cannot be found before Evan's, and Evan's not before Nami's is used. Take them one at a time in that order, then compare all three at the end.

3 · Execute3 carry out the plan

1Find Evan's distance

#7 Identify Subproblems 5.NBT.B.7
Take 0.6 times Nami's 3.2 km, then remove 0.4 km.
3.2×0.6=1.92,1.920.4=1.523.2 \times 0.6 = 1.92,\quad 1.92 - 0.4 = 1.52
Evan walked 1.52 km.

2Find Jacob's distance

#7 Identify Subproblems 5.NBT.B.7
Jacob's is 2.5 times Evan's, now that Evan's is known.
1.52×2.5=3.81.52 \times 2.5 = 3.8
Jacob walked 3.8 km.

3Compare all three distances

#8 Analyze the Units 5.NBT.B.7
Line the three up and read off the largest.
3.8>3.2>1.523.8 > 3.2 > 1.52
Jacob walked the farthest.
Answer: Jacob (3.8 km)
4 · Reviewdoes it hold up?

Evan's 1.52 is a little under 0.6 times Nami's, as the wording says, and Jacob's 3.8 is 2.5 times that -- each step is the right size.

Another way: Chaining it into one expression, (3.2×0.60.4)×2.5(3.2 \times 0.6 - 0.4) \times 2.5, gives Jacob's 3.8 in a single line, but hides the two intermediate distances the question compares.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Every multiplication and subtraction in the chain, and the final comparison.
💡Takeaway. When each amount is described through the one before, the order is not a choice -- work forwards and nothing is guessed.
Variant 12 hard answer: Jacob (4.224 km)

Nami walks 3.6 km3.6\ \text{km} in one hour. In one hour, Evan walked 0.6 km0.6\ \text{km} less than 0.70.7 times Nami's distance, and Jacob walked 2.22.2 times Evan's distance. Who walked the farthest in one hour?

Show solution
1 · Understandwhat's really being asked

Nami walks 3.6 km in an hour. Evan's distance is described through Nami's, and Jacob's through Evan's. We must say who covered the most.

Givens
  • Nami: 3.6 km.
  • Evan: 0.6 km less than 0.7 times Nami's.
  • Jacob: 2.2 times Evan's.
Unknowns
  • Who walked the farthest, and how far.
Constraints
  • Each distance is defined through the one before it, so they must be worked out in order.
2 · Planchoose the strategy

#7 Identify Subproblems · also uses: #8 Analyze the Units

Jacob's distance cannot be found before Evan's, and Evan's not before Nami's is used. Take them one at a time in that order, then compare all three at the end.

3 · Execute3 carry out the plan

1Find Evan's distance

#7 Identify Subproblems 5.NBT.B.7
Take 0.7 times Nami's 3.6 km, then remove 0.6 km.
3.6×0.7=2.52,2.520.6=1.923.6 \times 0.7 = 2.52,\quad 2.52 - 0.6 = 1.92
Evan walked 1.92 km.

2Find Jacob's distance

#7 Identify Subproblems 5.NBT.B.7
Jacob's is 2.2 times Evan's, now that Evan's is known.
1.92×2.2=4.2241.92 \times 2.2 = 4.224
Jacob walked 4.224 km.

3Compare all three distances

#8 Analyze the Units 5.NBT.B.7
Line the three up and read off the largest.
4.224>3.6>1.924.224 > 3.6 > 1.92
Jacob walked the farthest.
Answer: Jacob (4.224 km)
4 · Reviewdoes it hold up?

Evan's 1.92 is a little under 0.7 times Nami's, as the wording says, and Jacob's 4.224 is 2.2 times that -- each step is the right size.

Another way: Chaining it into one expression, (3.6×0.70.6)×2.2(3.6 \times 0.7 - 0.6) \times 2.2, gives Jacob's 4.224 in a single line, but hides the two intermediate distances the question compares.

Standardsmin grade 5
  • 5.NBT.B.7 Add, subtract, multiply, and divide decimals to hundredths — Every multiplication and subtraction in the chain, and the final comparison.
💡Takeaway. When each amount is described through the one before, the order is not a choice -- work forwards and nothing is guessed.