<h3>Answer:</h3>
- 8/3
- 3/2
- 4
<h3>Explanation:</h3>
For these problems, it can be convenient to multiply both numbers by the largest denominator, then do the division.
1. (2×4) / (3/4 × 4) = 8/3
2. (3/4 × 4) / (1/2 × 4) = 3/2
3. (1 1/2 × 8) / (3/8 × 8) = 12/3 = 4
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<em>Converting mixed numbers to fractions</em>
To convert a mixed number to an improper fraction, first determine the denominator of the fraction. For the mixed number 1 1/2, that denominator is 2.
Then, multiply the integer by that denominator, and add the numerator of the fraction. Here that means 1 (integer) ×2 + 1 (numerator of 1/2) = 2+1 = 3.
Finally, express the result over the denominator:
... 1 1/2 = 3/2
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<em>Dividing fractions</em>
A relatively simple mantra to remember for dividing fractions is "invert and multiply". What gets inverted is the denominator.
For your problems, this looks like
... (2)/(3/4) = (2/1) / (3/4) = (2/1) × (4/3) . . . . . . 4/3 is 3/4 inverted
... (3/4) / (1/2) = (3/4) × (2/1)
... (1 1/2) / (3/8) = (3/2) × (8/3)
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Another way to divide fractions is to make use of a common denominator. If you express both fractions using the same denominator, then those denominators effectively cancel. (This is more obvious if you "invert and multiply".)
In letters, this looks like ....
... (a/c) / (b/c) = a/b
If you invert and multiply, you get the same result.
... (a/c) / (b/c) = (a/c) × (c/b) = (ac)/(bc) = a/b
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In the above problems, the common denominator we used was the largest of the denominators of the numbers given. This worked because that was, in fact, the least common denominator of those numbers. For different numbers, you might have to make a different choice.
