3/4 ___ - 5/6
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- 1 3/4 ___ 3/4
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2 3/4 ___ 2 4/6
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PLEASE HELP
3/4 > -5/6
-1 3/4 < 3/4
2 3/4 > 2 4/6
3 / 4 = 0.75
- 5 / 6 = - 0.833
0.75 > - 0.833
3 / 4 > - 5 / 6
- 1 3/4 = - 1.75
3 / 4 = 0.75
- 1.75 < 0.75
- 1 3/4 < 3 / 4
2 3/4 = 2.75
2 4/6 = 2 2/3 = 2.666
2.75 > 2.666
2 3/4 > 2 4/6
To compare the fractions, we need to find a common denominator for each pair of fractions.
For the first comparison (3/4 ___ 5/6), we can find a common denominator by multiplying the denominators together, which gives us 4 * 6 = 24.
Now we need to convert both fractions to have a denominator of 24. To do this, we multiply the numerator and the denominator of each fraction by the same number that will turn the denominator into 24.
For the first fraction, we multiply by 6/6, and for the second fraction, we multiply by 4/4, since 6/6 and 4/4 both equal 1 and won't change the value of the fractions.
The first fraction becomes (3*6)/(4*6) = 18/24, and the second fraction becomes (5*4)/(6*4) = 20/24.
Now we can compare the fractions: 18/24 ___ 20/24.
Let's simplify both fractions:
18/24 can be reduced by dividing both the numerator and denominator by their greatest common factor, which is 6. We get (18/6)/(24/6) = 3/4.
20/24 can also be reduced by dividing both the numerator and denominator by their greatest common factor, which is 4. We get (20/4)/(24/4) = 5/6.
So, the comparison is now 3/4 ___ 5/6.
To determine the relationship between these two fractions, we compare the numerators:
3 is less than 5, so 3/4 is less than 5/6.
Therefore, the first comparison is < (less than).
For the second comparison (-1 3/4 ___ 3/4), we can convert the mixed number -1 3/4 into an improper fraction.
To do this, we multiply the whole number (-1) by the denominator (4), and then add the numerator (3). The result is -1*4 + 3 = -4 + 3 = -1.
So, -1 3/4 as an improper fraction is -1 3/4 = -7/4.
Now we can compare the fractions: -7/4 ___ 3/4.
To determine the relationship, we can see that the two fractions have the same denominator (4), so we only need to compare the numerators.
-7 is less than 3, so -7/4 is less than 3/4.
Therefore, the second comparison is < (less than).
For the third comparison (2 3/4 ___ 2 4/6), let's convert the mixed numbers into improper fractions.
2 3/4 as an improper fraction is 2 3/4 = (2*4 + 3)/4 = 11/4.
2 4/6 as an improper fraction is 2 4/6 = (2*6 + 4)/6 = 16/6.
Now we can compare the fractions: 11/4 ___ 16/6.
To find a common denominator, we multiply the denominators 4 and 6 to get 24.
Now we convert both fractions to have 24 as the denominator:
11/4 * 6/6 = 66/24.
16/6 * 4/4 = 64/24.
So, the comparison becomes 66/24 ___ 64/24.
To compare the numerators:
66 is greater than 64, so 66/24 is greater than 64/24.
Therefore, the third comparison is > (greater than).
To summarize:
- 3/4 < 5/6
- -1 3/4 < 3/4
- 2 3/4 > 2 4/6