Explain how you know that [tex]\frac{7}{12}[/tex] is greater than [tex]\frac{1}{3}[/tex] but less than [tex]\frac{2}{3}[/tex].
Answer (3)
7/12 1/3=4/12 2/3=8/12
7/12>1/3 7/12<2/3
The easiest way to compare fractions is by having a common denominator for both fractions.
This is because , when the denominator is the same in both fractions, we will simply compare the numerators and the greater fraction will be the one having greater numerator
Part 1:
The first given fraction is 12 7
The second given fraction is 3 1
We can make the denominator in the second one equal to 12 by multiplying it by 4.
However, to preserve the value of the fraction, we will multiply it by 4 4
This will give us:
3 1 * 4 4 = 12 4
Now, the two fractions became 12 4 and 12 7
The denominator is the same, so we will compare numerators.
Since 7 is greater than 4, therefore:
12 7 is the greater fraction
Part 2:
The first given fraction is 12 7
The second given fraction is 3 2
We can make the denominator in the second one equal to 12 by multiplying it by 4.
However, to preserve the value of the fraction, we will multiply it by 4 4
This will give us:
3 2 * 4 4 = 12 8
Now, the two fractions became 12 8 and 12 7
The denominator is the same, so we will compare numerators.
Since 8 is greater than 7, therefore:
12 8 is the greater fraction
Hope this helps :)
The fraction 12 7 is greater than 3 1 because, after converting 3 1 to 12 4 , 7 is greater than 4. Conversely, 12 7 is less than 3 2 since 3 2 converts to 12 8 , and 7 is less than 8. Therefore, 3 1 < 12 7 < 3 2 .
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