Samantha is starting a task that takes of an hour to complete, but she only has of an hour to work on it. If she works at an even pace, determine what fraction of the task will she complete.
Use the correct grid to set up the situation on the left and then find the solution on the right. Arrange the set up and solution in the grids starting at the top left hand corner.
| | 1 hour |
|---|---|
| Samantha's task | 1/2 hour |
To find the fraction of the task that Samantha can complete, we need to divide the time she has by the time it takes to complete the task:
1/2 ÷ 3/4
To divide fractions, we invert the second fraction and multiply:
1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6 = 2/3
Therefore, Samantha can complete 2/3 of the task.
| | Fraction of task completed |
|---|---|
| Solution | 2/3 |
To determine the fraction of the task that Samantha will complete, we need to find the ratio of the time she has available to the time it takes to complete the task.
Step 1: Set up the situation in a grid:
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| | |
| ? | ? |
| | |
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Step 2: Fill in the given information:
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| 1/2 | |
| hour | |
| | |
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Step 3: Fill in the missing information:
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| 1/2 | |
| hour | |
| | |
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| 1 | x |
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Step 4: Set up and solve the proportion:
1/2 / 1 = x / 1
Cross-multiply: 1 * x = 1/2 * 1
x = 1/2
Therefore, Samantha will complete 1/2 (or one-half) of the task.
First, let's set up the situation on the left grid:
Task to complete = 1 hour
Time to work = 3/4 hour
Now, let's find the solution on the right grid:
To find the fraction of the task Samantha will complete, we need to divide the time she has to work by the time it takes to complete the task.
Fraction = Time to work / Task to complete
Fraction = (3/4) / 1
Since dividing by 1 is the same as multiplying by 1, the fraction simplifies to:
Fraction = 3/4
Therefore, Samantha will complete 3/4 (or three-fourths) of the task.