Practice · Solve multi-step decimal problems in order · Sensim Math

Variant 1 easy

Nami walks $1.8\ \text{km}$ in one hour. In one hour, Evan walked $0.3\ \text{km}$ less than $0.9$ times Nami's distance, and Jacob walked $1.7$ times Evan's distance. Who walked the farthest in one hour?

Your answer (check it yourself)

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 \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 \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 > 1.32

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, $(1.8 \times 0.9 - 0.3) \times 1.7$ , 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

Nami walks $1.9\ \text{km}$ in one hour. In one hour, Evan walked $0.2\ \text{km}$ less than $0.7$ times Nami's distance, and Jacob walked $1.8$ times Evan's distance. Who walked the farthest in one hour?

Your answer (check it yourself)

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 \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 \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 > 1.13

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, $(1.9 \times 0.7 - 0.2) \times 1.8$ , 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

Nami walks $1.5\ \text{km}$ in one hour. In one hour, Evan walked $0.1\ \text{km}$ less than $0.9$ times Nami's distance, and Jacob walked $2$ times Evan's distance. Who walked the farthest in one hour?

Your answer (check it yourself)

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 \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 \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 > 1.25

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, $(1.5 \times 0.9 - 0.1) \times 2$ , 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

Nami walks $2.1\ \text{km}$ in one hour. In one hour, Evan walked $0.5\ \text{km}$ less than $0.8$ times Nami's distance, and Jacob walked $1.5$ times Evan's distance. Who walked the farthest in one hour?

Your answer (check it yourself)

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 \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 \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 > 1.18

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, $(2.1 \times 0.8 - 0.5) \times 1.5$ , 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

Nami walks $2.4\ \text{km}$ in one hour. In one hour, Evan walked $0.3\ \text{km}$ less than $0.8$ times Nami's distance, and Jacob walked $1.6$ times Evan's distance. Who walked the farthest in one hour?

Your answer (check it yourself)

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 \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 \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 > 1.62

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, $(2.4 \times 0.8 - 0.3) \times 1.6$ , 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

Nami walks $1.6\ \text{km}$ in one hour. In one hour, Evan walked $0.2\ \text{km}$ less than $0.7$ times Nami's distance, and Jacob walked $2.4$ times Evan's distance. Who walked the farthest in one hour?

Your answer (check it yourself)

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 \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 \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 > 0.92

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, $(1.6 \times 0.7 - 0.2) \times 2.4$ , 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

Nami walks $2.7\ \text{km}$ in one hour. In one hour, Evan walked $0.3\ \text{km}$ less than $0.5$ times Nami's distance, and Jacob walked $2.6$ times Evan's distance. Who walked the farthest in one hour?

Your answer (check it yourself)

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 \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 \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 > 1.05

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, $(2.7 \times 0.5 - 0.3) \times 2.6$ , 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

Nami walks $2.5\ \text{km}$ in one hour. In one hour, Evan walked $0.1\ \text{km}$ less than $0.6$ times Nami's distance, and Jacob walked $2.8$ times Evan's distance. Who walked the farthest in one hour?

Your answer (check it yourself)

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 \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 \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 > 1.4

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, $(2.5 \times 0.6 - 0.1) \times 2.8$ , 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

Nami walks $2.8\ \text{km}$ in one hour. In one hour, Evan walked $0.2\ \text{km}$ less than $0.5$ times Nami's distance, and Jacob walked $3$ times Evan's distance. Who walked the farthest in one hour?

Your answer (check it yourself)

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 \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 \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 > 1.2

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, $(2.8 \times 0.5 - 0.2) \times 3$ , 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

Nami walks $3\ \text{km}$ in one hour. In one hour, Evan walked $0.7\ \text{km}$ less than $0.8$ times Nami's distance, and Jacob walked $1.9$ times Evan's distance. Who walked the farthest in one hour?

Your answer (check it yourself)

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 \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 \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 > 1.7

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, $(3 \times 0.8 - 0.7) \times 1.9$ , 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

Nami walks $3.2\ \text{km}$ in one hour. In one hour, Evan walked $0.4\ \text{km}$ less than $0.6$ times Nami's distance, and Jacob walked $2.5$ times Evan's distance. Who walked the farthest in one hour?

Your answer (check it yourself)

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 \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 \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 > 1.52

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, $(3.2 \times 0.6 - 0.4) \times 2.5$ , 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

Nami walks $3.6\ \text{km}$ in one hour. In one hour, Evan walked $0.6\ \text{km}$ less than $0.7$ times Nami's distance, and Jacob walked $2.2$ times Evan's distance. Who walked the farthest in one hour?

Your answer (check it yourself)

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 \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 \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 > 1.92

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, $(3.6 \times 0.7 - 0.6) \times 2.2$ , 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.

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

Generated variants — 12

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