Problem
Bigger units express numbers more simply
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.
Measurement & data
Your answer
Watch out Don't stop at the raw total in inches — the question asks for the length in feet and inches, so 2106 must still be converted using 12 in = 1 ft.
How to solve
Strategy Analyze the Units — 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.
1STEP 1
Find the total length in inches
Joining 78 rods of 27 in each gives a total of 78 x 27 = 2106 in.
78 × 27 = 2106 in
End-to-end with no overlap just means add up all the rod lengths, which is one multiplication.
4.NBT.B.5Identify Subproblems2STEP 2
Convert inches to feet and inches
Divide by 12 since 12 in make 1 ft: 2106 / 12 = 175 R 6, so the length is 175 ft 6 in.
2106 ÷ 12 = 175 R 6 → 175 ft 6 in
Grouping every 12 inches into a foot is exactly division with a remainder of leftover inches.
4.MD.A.1Analyze The UnitsThe 2106 inches of fence equal 175 feet and 6 inches.
Why?
A foot is exactly 12 inches, so each foot in the fence is one equal group of 12 inches taken from the 2106.
Why?
A foot is just 12 inches bundled together, which is one equal group of 12.
🧱Multiplication as equal groupsa times b means a equal groups of b — it is just repeated adding of the same amount.
Why?
Asking how many whole groups of 12 inches fit inside 2106 is dividing 2106 by 12, and that division gives 175 feet.
Why?
Building 175 feet back up from 12-inch groups is a multiplication, so finding the number of groups from the total reverses that multiplication, which is division.
🧱Inverse operationsSubtraction undoes addition and division undoes multiplication — they reverse each other.
Why?
The 6 inches that are left cannot make another full foot, so they stay as leftover inches, and the whole length is 175 feet plus those 6 inches.
Why?
The total length breaks with no gaps or overlaps into the part that forms whole feet and the leftover part, so the two parts add back to the whole.
🧱Whole is the sum of its partsBreak a thing into pieces with no gaps or overlaps and the pieces add back to the whole.
Answer
175 ft 6 in
2106 ÷ 12 = 175 R 6 → 175 ft 6 in
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.
Takeaway
This only needs Grade 4 multiplying and dividing by 12 -- add the rods, then bundle every 12 inches into a foot!
- Find the total length in inches
- Convert inches to feet and inches
Where next?
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