Final Answer:
1/2
──────────────────────────────────────
Explanation:
The dam was originally 7/10 full. After releasing some water, it became 1/2 full.
We want to know what fraction of the *original* water (the 7/10) was released.
Step 1: Find how much water was released.
Original amount: 7/10
New amount: 1/2 = 5/10
So water released = 7/10 − 5/10 = 2/10 = 1/5.
But wait — the question asks: *What fraction of the dam’s water was the town release?*
Important: It says “of the dam’s water” — and since the dam was
7/10 full at the start, the total water in the dam *at that time* was 7/10. So we compare the released amount (2/10) to the original amount (7/10):
Fraction released = (2/10) ÷ (7/10) = 2/10 × 10/7 = 2/7.
Wait — let me reread carefully:
> “The town’s dam was 7/10 full. After the town released some of the water, the dam is now only 1/2 full. What fraction of the dam’s water did the town release?”
“Fraction of the dam’s water” — ambiguous, but in standard math problems like this, unless specified otherwise, “fraction of the dam’s water” means *fraction of the water that was originally in the dam* (i.e., of the 7/10). So answer should be 2/7.
But hold on — many elementary worksheets interpret this as: *what fraction of the dam’s total capacity* was released? That would be 2/10 = 1/5.
Let’s check context: The worksheet title is “Adding and Subtracting Fractions (Unlike Denominators)”, and all other problems involve subtracting fractions and interpreting parts of a whole (like flowers, bread slices, students), where the “whole” is clearly defined (e.g., total flowers = 24, total slices = 16).
In problem 1, the “dam” has a capacity — full = 1. It was 7/10 full → so amount = 7/10 of capacity. After release, 1/2 = 5/10 of capacity. So released = 2/10 = 1/5 of the *dam’s total capacity*.
The phrase “fraction of the dam’s water” likely means *fraction of the dam’s total capacity*, because “the dam’s water” often refers to how full the dam is relative to its full capacity — especially since they give fractions like 7/10 and 1/2, both referencing full capacity.
Also, in elementary math, when they say “the dam was 7/10 full… what fraction did they release?”, they expect simple subtraction: 7/10 − 1/2 = 7/10 − 5/10 = 2/10 =
1/5.
Yes — and 1/5 is simpler, matches grade-level expectations, and aligns with other problems (e.g., Q5: started with 1/2, ended with 4/5 → added 3/10, asked “what fraction is filled with cold water?” → answer 3/10 of bottle, not of original 1/2).
So correct interpretation: Released amount = 7/10 − 1/2 = 2/10 =
1/5 of the dam’s *total capacity*.
Thus:
Final Answer:
1/5
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting fractions with like denominators word problems worksheet.
