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10. Which fraction lies in between 1÷2and2÷3 A 3÷6 B 4÷5 C 7÷12 D 1÷3​

User Chaine
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Answer: 7÷12 (choice C)

================================================

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.

10. Which fraction lies in between 1÷2and2÷3 A 3÷6 B 4÷5 C 7÷12 D 1÷3​-example-1
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