Answer: 7÷12 (choice C)
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Step-by-step explanation:
The given fractions are
1÷2 and 2÷3
Use a calculator, or long division to find these decimal values
- 1÷2 = 0.5 exactly, which we can think of as 0.500
- 2÷3 = 0.667 approximately
So we want to find a fraction where it's decimal value is between 0.500 and 0.667; we can think of it like finding something between 500 and 667, then stick a decimal point to the left end.
Use a calculator or long division to compute the following values
- 3÷6 = 0.500 exactly
- 4÷5 = 0.800 exactly
- 7÷12 = 0.583 approximately
- 1÷3 = 0.333 approximately
Of those choices, only 7÷12 = 0.583 is between 0.500 and 0.667 (since 583 is between 500 and 667).
Therefore, 7÷12 is between 1÷2 and 2÷3
We can write that as the compound inequality
1÷2 < 7÷12 < 2÷3
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Another approach
Rewrite all of the fractions so that they have the LCD 60
- 1÷2 = 30÷60
- 2÷3 = 40÷60
- 3÷6 = 30÷60
- 4÷5 = 48÷60
- 7÷12 = 35÷60
- 1÷3 = 20÷60
Since we want a fraction between 1÷2 and 2÷3, this is equivalent to finding a fraction between 30÷60 and 40÷60
The denominators are the same, so we compare the numerators. We want a numerator between 30 and 40.
Of the choices listed, only 35÷60 is between 30÷60 and 40÷60 (since 35 is between 30 and 40)
35÷60 then reduces back to 7÷12 which is the final answer
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Below is a diagram showing a number line. Marked on it has the locations of each fraction mentioned. The fraction 7÷12 is between the markers 1÷2 and 2÷3, while the other choices are outside those boundaries.