Practice · Bigger units express numbers more simply · Sensim Math

Variant 1 easy answer: 112 ft 6 in

A fence is made by joining $45$ rods, each $30\ \text{in}$ long, end to end without overlapping. Find the length of the fence in feet and inches. (Use $12\ \text{in} = 1\ \text{ft}$ .)

Show solution

1 · Understandwhat's really being asked

A fence is built by joining 45 rods end to end, each 30 inches long, with no overlap. Find the total length expressed in feet and inches, using 12 in = 1 ft.

Givens

There are 45 rods
Each rod is 30 in long
Rods are joined end to end with no overlap
12 in = 1 ft

Unknowns

The total fence length in feet and inches

Constraints

Total length in inches is 45 times 30
To convert inches to feet, divide by 12; the remainder is leftover inches (less than 12)

2 · Planchoose the strategy

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

This is a measurement-conversion problem: first find the total inches by multiplying, then convert to the larger unit of feet by dividing by 12, keeping the remainder as inches. Watching the units (inches to feet) guides the divide-by-12 step.

3 · Execute2 carry out the plan

1Find the total length in inches

#7 Identify Subproblems 4.NBT.B.5

Joining 45 rods of 30 in each gives a total of 45 x 30 = 1350 in.

45 \times 30 = 1350 \text{ in}

End-to-end with no overlap just means add up all the rod lengths, which is one multiplication.

2Convert inches to feet and inches

#8 Analyze the Units 4.MD.A.1

Divide the total inches by 12 because 12 in make 1 ft. 1350 / 12 = 112 with a remainder of 6, so the length is 112 ft and 6 in.

1350 \div 12 = 112 \text{ R } 6 \Rightarrow 112 \text{ ft } 6 \text{ in}

Grouping every 12 inches into a foot is exactly division with a remainder of leftover inches.

Answer: 112 ft 6 in

4 · Reviewdoes it hold up?

Convert back: 112 ft = 112 x 12 = 1344 in, plus 6 in = 1350 in, matching the total. The leftover 6 in is less than 12, so the conversion is proper.

Another way: Identify subproblems (tool 7): convert each rod first, since 30 in = 2 ft 6 in, then 45 rods give 90 ft and 45 x 6 = 270 in = 22 ft 6 in, and 90 + 22 = 112 ft 6 in, the same answer.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting the total inches into feet and inches using 12 in = 1 ft.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 45 rods by 30 in to get the total inches.

💡Takeaway. This only needs Grade 4 multiplying and dividing by 12 -- add the rods, then bundle every 12 inches into a foot!

Variant 2 easy answer: 137 ft 6 in

A fence is made by joining $50$ rods, each $33\ \text{in}$ long, end to end without overlapping. Find the length of the fence in feet and inches. (Use $12\ \text{in} = 1\ \text{ft}$ .)

Show solution

1 · Understandwhat's really being asked

A fence is built by joining 50 rods end to end, each 33 inches long, with no overlap. Find the total length expressed in feet and inches, using 12 in = 1 ft.

Givens

There are 50 rods
Each rod is 33 in long
Rods are joined end to end with no overlap
12 in = 1 ft

Unknowns

The total fence length in feet and inches

Constraints

Total length in inches is 50 times 33
To convert inches to feet, divide by 12; the remainder is leftover inches (less than 12)

2 · Planchoose the strategy

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

This is a measurement-conversion problem: first find the total inches by multiplying, then convert to the larger unit of feet by dividing by 12, keeping the remainder as inches. Watching the units (inches to feet) guides the divide-by-12 step.

3 · Execute2 carry out the plan

1Find the total length in inches

#7 Identify Subproblems 4.NBT.B.5

Joining 50 rods of 33 in each gives a total of 50 x 33 = 1650 in.

50 \times 33 = 1650 \text{ in}

End-to-end with no overlap just means add up all the rod lengths, which is one multiplication.

2Convert inches to feet and inches

#8 Analyze the Units 4.MD.A.1

Divide the total inches by 12 because 12 in make 1 ft. 1650 / 12 = 137 with a remainder of 6, so the length is 137 ft and 6 in.

1650 \div 12 = 137 \text{ R } 6 \Rightarrow 137 \text{ ft } 6 \text{ in}

Grouping every 12 inches into a foot is exactly division with a remainder of leftover inches.

Answer: 137 ft 6 in

4 · Reviewdoes it hold up?

Convert back: 137 ft = 137 x 12 = 1644 in, plus 6 in = 1650 in, matching the total. The leftover 6 in is less than 12, so the conversion is proper.

Another way: Identify subproblems (tool 7): convert each rod first, since 33 in = 2 ft 9 in, then 50 rods give 100 ft and 50 x 9 = 450 in = 37 ft 6 in, and 100 + 37 = 137 ft 6 in, the same answer.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting the total inches into feet and inches using 12 in = 1 ft.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 50 rods by 33 in to get the total inches.

💡Takeaway. This only needs Grade 4 multiplying and dividing by 12 -- add the rods, then bundle every 12 inches into a foot!

Variant 3 easy answer: 157 ft 6 in

A fence is made by joining $54$ rods, each $35\ \text{in}$ long, end to end without overlapping. Find the length of the fence in feet and inches. (Use $12\ \text{in} = 1\ \text{ft}$ .)

Show solution

1 · Understandwhat's really being asked

A fence is built by joining 54 rods end to end, each 35 inches long, with no overlap. Find the total length expressed in feet and inches, using 12 in = 1 ft.

Givens

There are 54 rods
Each rod is 35 in long
Rods are joined end to end with no overlap
12 in = 1 ft

Unknowns

The total fence length in feet and inches

Constraints

Total length in inches is 54 times 35
To convert inches to feet, divide by 12; the remainder is leftover inches (less than 12)

2 · Planchoose the strategy

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

This is a measurement-conversion problem: first find the total inches by multiplying, then convert to the larger unit of feet by dividing by 12, keeping the remainder as inches. Watching the units (inches to feet) guides the divide-by-12 step.

3 · Execute2 carry out the plan

1Find the total length in inches

#7 Identify Subproblems 4.NBT.B.5

Joining 54 rods of 35 in each gives a total of 54 x 35 = 1890 in.

54 \times 35 = 1890 \text{ in}

End-to-end with no overlap just means add up all the rod lengths, which is one multiplication.

2Convert inches to feet and inches

#8 Analyze the Units 4.MD.A.1

Divide the total inches by 12 because 12 in make 1 ft. 1890 / 12 = 157 with a remainder of 6, so the length is 157 ft and 6 in.

1890 \div 12 = 157 \text{ R } 6 \Rightarrow 157 \text{ ft } 6 \text{ in}

Grouping every 12 inches into a foot is exactly division with a remainder of leftover inches.

Answer: 157 ft 6 in

4 · Reviewdoes it hold up?

Convert back: 157 ft = 157 x 12 = 1884 in, plus 6 in = 1890 in, matching the total. The leftover 6 in is less than 12, so the conversion is proper.

Another way: Identify subproblems (tool 7): convert each rod first, since 35 in = 2 ft 11 in, then 54 rods give 108 ft and 54 x 11 = 594 in = 49 ft 6 in, and 108 + 49 = 157 ft 6 in, the same answer.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting the total inches into feet and inches using 12 in = 1 ft.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 54 rods by 35 in to get the total inches.

💡Takeaway. This only needs Grade 4 multiplying and dividing by 12 -- add the rods, then bundle every 12 inches into a foot!

Variant 4 medium answer: 125 ft 0 in

A fence is made by joining $60$ rods, each $25\ \text{in}$ long, end to end without overlapping. Find the length of the fence in feet and inches. (Use $12\ \text{in} = 1\ \text{ft}$ .)

Show solution

1 · Understandwhat's really being asked

A fence is built by joining 60 rods end to end, each 25 inches long, with no overlap. Find the total length expressed in feet and inches, using 12 in = 1 ft.

Givens

There are 60 rods
Each rod is 25 in long
Rods are joined end to end with no overlap
12 in = 1 ft

Unknowns

The total fence length in feet and inches

Constraints

Total length in inches is 60 times 25
To convert inches to feet, divide by 12; the remainder is leftover inches (less than 12)

2 · Planchoose the strategy

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

This is a measurement-conversion problem: first find the total inches by multiplying, then convert to the larger unit of feet by dividing by 12, keeping the remainder as inches. Watching the units (inches to feet) guides the divide-by-12 step.

3 · Execute2 carry out the plan

1Find the total length in inches

#7 Identify Subproblems 4.NBT.B.5

Joining 60 rods of 25 in each gives a total of 60 x 25 = 1500 in.

60 \times 25 = 1500 \text{ in}

End-to-end with no overlap just means add up all the rod lengths, which is one multiplication.

2Convert inches to feet and inches

#8 Analyze the Units 4.MD.A.1

Divide the total inches by 12 because 12 in make 1 ft. 1500 / 12 = 125 with a remainder of 0, so the length is 125 ft and 0 in.

1500 \div 12 = 125 \text{ R } 0 \Rightarrow 125 \text{ ft } 0 \text{ in}

Grouping every 12 inches into a foot is exactly division with a remainder of leftover inches.

Answer: 125 ft 0 in

4 · Reviewdoes it hold up?

Convert back: 125 ft = 125 x 12 = 1500 in, plus 0 in = 1500 in, matching the total. The leftover 0 in is less than 12, so the conversion is proper.

Another way: Identify subproblems (tool 7): convert each rod first, since 25 in = 2 ft 1 in, then 60 rods give 120 ft and 60 x 1 = 60 in = 5 ft 0 in, and 120 + 5 = 125 ft 0 in, the same answer.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting the total inches into feet and inches using 12 in = 1 ft.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 60 rods by 25 in to get the total inches.

💡Takeaway. This only needs Grade 4 multiplying and dividing by 12 -- add the rods, then bundle every 12 inches into a foot!

Variant 5 medium answer: 170 ft 6 in

A fence is made by joining $66$ rods, each $31\ \text{in}$ long, end to end without overlapping. Find the length of the fence in feet and inches. (Use $12\ \text{in} = 1\ \text{ft}$ .)

Show solution

1 · Understandwhat's really being asked

A fence is built by joining 66 rods end to end, each 31 inches long, with no overlap. Find the total length expressed in feet and inches, using 12 in = 1 ft.

Givens

There are 66 rods
Each rod is 31 in long
Rods are joined end to end with no overlap
12 in = 1 ft

Unknowns

The total fence length in feet and inches

Constraints

Total length in inches is 66 times 31
To convert inches to feet, divide by 12; the remainder is leftover inches (less than 12)

2 · Planchoose the strategy

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

This is a measurement-conversion problem: first find the total inches by multiplying, then convert to the larger unit of feet by dividing by 12, keeping the remainder as inches. Watching the units (inches to feet) guides the divide-by-12 step.

3 · Execute2 carry out the plan

1Find the total length in inches

#7 Identify Subproblems 4.NBT.B.5

Joining 66 rods of 31 in each gives a total of 66 x 31 = 2046 in.

66 \times 31 = 2046 \text{ in}

End-to-end with no overlap just means add up all the rod lengths, which is one multiplication.

2Convert inches to feet and inches

#8 Analyze the Units 4.MD.A.1

Divide the total inches by 12 because 12 in make 1 ft. 2046 / 12 = 170 with a remainder of 6, so the length is 170 ft and 6 in.

2046 \div 12 = 170 \text{ R } 6 \Rightarrow 170 \text{ ft } 6 \text{ in}

Grouping every 12 inches into a foot is exactly division with a remainder of leftover inches.

Answer: 170 ft 6 in

4 · Reviewdoes it hold up?

Convert back: 170 ft = 170 x 12 = 2040 in, plus 6 in = 2046 in, matching the total. The leftover 6 in is less than 12, so the conversion is proper.

Another way: Identify subproblems (tool 7): convert each rod first, since 31 in = 2 ft 7 in, then 66 rods give 132 ft and 66 x 7 = 462 in = 38 ft 6 in, and 132 + 38 = 170 ft 6 in, the same answer.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting the total inches into feet and inches using 12 in = 1 ft.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 66 rods by 31 in to get the total inches.

💡Takeaway. This only needs Grade 4 multiplying and dividing by 12 -- add the rods, then bundle every 12 inches into a foot!

Variant 6 medium answer: 168 ft 0 in

A fence is made by joining $72$ rods, each $28\ \text{in}$ long, end to end without overlapping. Find the length of the fence in feet and inches. (Use $12\ \text{in} = 1\ \text{ft}$ .)

Show solution

1 · Understandwhat's really being asked

A fence is built by joining 72 rods end to end, each 28 inches long, with no overlap. Find the total length expressed in feet and inches, using 12 in = 1 ft.

Givens

There are 72 rods
Each rod is 28 in long
Rods are joined end to end with no overlap
12 in = 1 ft

Unknowns

The total fence length in feet and inches

Constraints

Total length in inches is 72 times 28
To convert inches to feet, divide by 12; the remainder is leftover inches (less than 12)

2 · Planchoose the strategy

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

This is a measurement-conversion problem: first find the total inches by multiplying, then convert to the larger unit of feet by dividing by 12, keeping the remainder as inches. Watching the units (inches to feet) guides the divide-by-12 step.

3 · Execute2 carry out the plan

1Find the total length in inches

#7 Identify Subproblems 4.NBT.B.5

Joining 72 rods of 28 in each gives a total of 72 x 28 = 2016 in.

72 \times 28 = 2016 \text{ in}

End-to-end with no overlap just means add up all the rod lengths, which is one multiplication.

2Convert inches to feet and inches

#8 Analyze the Units 4.MD.A.1

Divide the total inches by 12 because 12 in make 1 ft. 2016 / 12 = 168 with a remainder of 0, so the length is 168 ft and 0 in.

2016 \div 12 = 168 \text{ R } 0 \Rightarrow 168 \text{ ft } 0 \text{ in}

Grouping every 12 inches into a foot is exactly division with a remainder of leftover inches.

Answer: 168 ft 0 in

4 · Reviewdoes it hold up?

Convert back: 168 ft = 168 x 12 = 2016 in, plus 0 in = 2016 in, matching the total. The leftover 0 in is less than 12, so the conversion is proper.

Another way: Identify subproblems (tool 7): convert each rod first, since 28 in = 2 ft 4 in, then 72 rods give 144 ft and 72 x 4 = 288 in = 24 ft 0 in, and 144 + 24 = 168 ft 0 in, the same answer.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting the total inches into feet and inches using 12 in = 1 ft.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 72 rods by 28 in to get the total inches.

💡Takeaway. This only needs Grade 4 multiplying and dividing by 12 -- add the rods, then bundle every 12 inches into a foot!

Variant 7 medium answer: 175 ft 6 in

A fence is made by joining $78$ rods, each $27\ \text{in}$ long, end to end without overlapping. Find the length of the fence in feet and inches. (Use $12\ \text{in} = 1\ \text{ft}$ .)

Show solution

1 · Understandwhat's really being asked

A fence is built by joining 78 rods end to end, each 27 inches long, with no overlap. Find the total length expressed in feet and inches, using 12 in = 1 ft.

Givens

There are 78 rods
Each rod is 27 in long
Rods are joined end to end with no overlap
12 in = 1 ft

Unknowns

The total fence length in feet and inches

Constraints

Total length in inches is 78 times 27
To convert inches to feet, divide by 12; the remainder is leftover inches (less than 12)

2 · Planchoose the strategy

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

This is a measurement-conversion problem: first find the total inches by multiplying, then convert to the larger unit of feet by dividing by 12, keeping the remainder as inches. Watching the units (inches to feet) guides the divide-by-12 step.

3 · Execute2 carry out the plan

1Find the total length in inches

#7 Identify Subproblems 4.NBT.B.5

Joining 78 rods of 27 in each gives a total of 78 x 27 = 2106 in.

78 \times 27 = 2106 \text{ in}

End-to-end with no overlap just means add up all the rod lengths, which is one multiplication.

2Convert inches to feet and inches

#8 Analyze the Units 4.MD.A.1

Divide the total inches by 12 because 12 in make 1 ft. 2106 / 12 = 175 with a remainder of 6, so the length is 175 ft and 6 in.

2106 \div 12 = 175 \text{ R } 6 \Rightarrow 175 \text{ ft } 6 \text{ in}

Grouping every 12 inches into a foot is exactly division with a remainder of leftover inches.

Answer: 175 ft 6 in

4 · Reviewdoes it hold up?

Convert back: 175 ft = 175 x 12 = 2100 in, plus 6 in = 2106 in, matching the total. The leftover 6 in is less than 12, so the conversion is proper.

Another way: Identify subproblems (tool 7): convert each rod first, since 27 in = 2 ft 3 in, then 78 rods give 156 ft and 78 x 3 = 234 in = 19 ft 6 in, and 156 + 19 = 175 ft 6 in, the same answer.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting the total inches into feet and inches using 12 in = 1 ft.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 78 rods by 27 in to get the total inches.

💡Takeaway. This only needs Grade 4 multiplying and dividing by 12 -- add the rods, then bundle every 12 inches into a foot!

Variant 8 hard answer: 154 ft 0 in

A fence is made by joining $84$ rods, each $22\ \text{in}$ long, end to end without overlapping. Find the length of the fence in feet and inches. (Use $12\ \text{in} = 1\ \text{ft}$ .)

Show solution

1 · Understandwhat's really being asked

A fence is built by joining 84 rods end to end, each 22 inches long, with no overlap. Find the total length expressed in feet and inches, using 12 in = 1 ft.

Givens

There are 84 rods
Each rod is 22 in long
Rods are joined end to end with no overlap
12 in = 1 ft

Unknowns

The total fence length in feet and inches

Constraints

Total length in inches is 84 times 22
To convert inches to feet, divide by 12; the remainder is leftover inches (less than 12)

2 · Planchoose the strategy

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

This is a measurement-conversion problem: first find the total inches by multiplying, then convert to the larger unit of feet by dividing by 12, keeping the remainder as inches. Watching the units (inches to feet) guides the divide-by-12 step.

3 · Execute2 carry out the plan

1Find the total length in inches

#7 Identify Subproblems 4.NBT.B.5

Joining 84 rods of 22 in each gives a total of 84 x 22 = 1848 in.

84 \times 22 = 1848 \text{ in}

End-to-end with no overlap just means add up all the rod lengths, which is one multiplication.

2Convert inches to feet and inches

#8 Analyze the Units 4.MD.A.1

Divide the total inches by 12 because 12 in make 1 ft. 1848 / 12 = 154 with a remainder of 0, so the length is 154 ft and 0 in.

1848 \div 12 = 154 \text{ R } 0 \Rightarrow 154 \text{ ft } 0 \text{ in}

Grouping every 12 inches into a foot is exactly division with a remainder of leftover inches.

Answer: 154 ft 0 in

4 · Reviewdoes it hold up?

Convert back: 154 ft = 154 x 12 = 1848 in, plus 0 in = 1848 in, matching the total. The leftover 0 in is less than 12, so the conversion is proper.

Another way: Identify subproblems (tool 7): convert each rod first, since 22 in = 1 ft 10 in, then 84 rods give 84 ft and 84 x 10 = 840 in = 70 ft 0 in, and 84 + 70 = 154 ft 0 in, the same answer.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting the total inches into feet and inches using 12 in = 1 ft.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 84 rods by 22 in to get the total inches.

💡Takeaway. This only needs Grade 4 multiplying and dividing by 12 -- add the rods, then bundle every 12 inches into a foot!

Variant 9 hard answer: 180 ft 0 in

A fence is made by joining $90$ rods, each $24\ \text{in}$ long, end to end without overlapping. Find the length of the fence in feet and inches. (Use $12\ \text{in} = 1\ \text{ft}$ .)

Show solution

1 · Understandwhat's really being asked

A fence is built by joining 90 rods end to end, each 24 inches long, with no overlap. Find the total length expressed in feet and inches, using 12 in = 1 ft.

Givens

There are 90 rods
Each rod is 24 in long
Rods are joined end to end with no overlap
12 in = 1 ft

Unknowns

The total fence length in feet and inches

Constraints

Total length in inches is 90 times 24
To convert inches to feet, divide by 12; the remainder is leftover inches (less than 12)

2 · Planchoose the strategy

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

This is a measurement-conversion problem: first find the total inches by multiplying, then convert to the larger unit of feet by dividing by 12, keeping the remainder as inches. Watching the units (inches to feet) guides the divide-by-12 step.

3 · Execute2 carry out the plan

1Find the total length in inches

#7 Identify Subproblems 4.NBT.B.5

Joining 90 rods of 24 in each gives a total of 90 x 24 = 2160 in.

90 \times 24 = 2160 \text{ in}

End-to-end with no overlap just means add up all the rod lengths, which is one multiplication.

2Convert inches to feet and inches

#8 Analyze the Units 4.MD.A.1

Divide the total inches by 12 because 12 in make 1 ft. 2160 / 12 = 180 with a remainder of 0, so the length is 180 ft and 0 in.

2160 \div 12 = 180 \text{ R } 0 \Rightarrow 180 \text{ ft } 0 \text{ in}

Grouping every 12 inches into a foot is exactly division with a remainder of leftover inches.

Answer: 180 ft 0 in

4 · Reviewdoes it hold up?

Convert back: 180 ft = 180 x 12 = 2160 in, plus 0 in = 2160 in, matching the total. The leftover 0 in is less than 12, so the conversion is proper.

Another way: Identify subproblems (tool 7): convert each rod first, since 24 in = 2 ft 0 in, then 90 rods give 180 ft and 90 x 0 = 0 in = 0 ft 0 in, and 180 + 0 = 180 ft 0 in, the same answer.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting the total inches into feet and inches using 12 in = 1 ft.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 90 rods by 24 in to get the total inches.

💡Takeaway. This only needs Grade 4 multiplying and dividing by 12 -- add the rods, then bundle every 12 inches into a foot!

Variant 10 hard answer: 152 ft 0 in

A fence is made by joining $96$ rods, each $19\ \text{in}$ long, end to end without overlapping. Find the length of the fence in feet and inches. (Use $12\ \text{in} = 1\ \text{ft}$ .)

Show solution

1 · Understandwhat's really being asked

A fence is built by joining 96 rods end to end, each 19 inches long, with no overlap. Find the total length expressed in feet and inches, using 12 in = 1 ft.

Givens

There are 96 rods
Each rod is 19 in long
Rods are joined end to end with no overlap
12 in = 1 ft

Unknowns

The total fence length in feet and inches

Constraints

Total length in inches is 96 times 19
To convert inches to feet, divide by 12; the remainder is leftover inches (less than 12)

2 · Planchoose the strategy

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

This is a measurement-conversion problem: first find the total inches by multiplying, then convert to the larger unit of feet by dividing by 12, keeping the remainder as inches. Watching the units (inches to feet) guides the divide-by-12 step.

3 · Execute2 carry out the plan

1Find the total length in inches

#7 Identify Subproblems 4.NBT.B.5

Joining 96 rods of 19 in each gives a total of 96 x 19 = 1824 in.

96 \times 19 = 1824 \text{ in}

End-to-end with no overlap just means add up all the rod lengths, which is one multiplication.

2Convert inches to feet and inches

#8 Analyze the Units 4.MD.A.1

Divide the total inches by 12 because 12 in make 1 ft. 1824 / 12 = 152 with a remainder of 0, so the length is 152 ft and 0 in.

1824 \div 12 = 152 \text{ R } 0 \Rightarrow 152 \text{ ft } 0 \text{ in}

Grouping every 12 inches into a foot is exactly division with a remainder of leftover inches.

Answer: 152 ft 0 in

4 · Reviewdoes it hold up?

Convert back: 152 ft = 152 x 12 = 1824 in, plus 0 in = 1824 in, matching the total. The leftover 0 in is less than 12, so the conversion is proper.

Another way: Identify subproblems (tool 7): convert each rod first, since 19 in = 1 ft 7 in, then 96 rods give 96 ft and 96 x 7 = 672 in = 56 ft 0 in, and 96 + 56 = 152 ft 0 in, the same answer.

Standardsmin grade 4

4.MD.A.1 Know relative sizes of measurement units and convert larger to smaller units — Converting the total inches into feet and inches using 12 in = 1 ft.
4.NBT.B.5 Multiply a whole number of up to four digits by a one-digit whole number — Multiplying 96 rods by 19 in to get the total inches.

💡Takeaway. This only needs Grade 4 multiplying and dividing by 12 -- add the rods, then bundle every 12 inches into a foot!

Bigger units express numbers more simply · 10 practice problems

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