manuel says that you can use one of the denominators of 5/6 and 11/30 when renaming these fraction using a common denominator. why is this true
30 is a multiple of 6.
Manuel says that you can use of the denominators of 5/6 and 11/30 when renaming these fractions using a common denominator. Why is the true?
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MAnUel SayS ThAt yOu cAn uSe oF tHe DeNomiNatOrs of 5/6 and 11/30 WheN reNamIng theSe FracTionS uSiNg a coMmoN DenoMiNaTor. Why is thE tRue?
Manuel is correct in saying that you can use one of the denominators of 5/6 and 11/30 when renaming these fractions using a common denominator. To understand why this is true, let's first define what a common denominator is.
A common denominator is a number that can be used as the denominator for two or more fractions so that they have equivalent fractions with the same denominator. The goal of finding a common denominator is to make it easier to compare and perform operations on fractions.
In this case, we have the fractions 5/6 and 11/30. To find a common denominator, we need to determine the least common multiple (LCM) of the denominators 6 and 30. The LCM is the smallest number that both 6 and 30 divide evenly into.
To find the LCM of 6 and 30, we can list their multiples and look for the smallest common multiple:
Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, ...
Multiples of 30: 30, 60, 90, 120, ...
From the above lists, we can see that the smallest common multiple (LCM) of 6 and 30 is 30. Therefore, 30 is a common denominator for 5/6 and 11/30.
Now, why is it valid to choose 30 as the common denominator?
This is because any fraction can be multiplied or divided by 1 without changing its value. In this case, the fraction 5/6 can be multiplied by 5/5 (which is equal to 1) to give us an equivalent fraction with a denominator of 30. Similarly, the fraction 11/30 can be multiplied by 6/6 (which is equal to 1) to give us an equivalent fraction with a denominator of 30.
By multiplying the numerator and denominator of each fraction by these appropriate values, the fractions 5/6 and 11/30 become 25/30 and 66/30, respectively.
As a result, both fractions are now expressed with a common denominator of 30, allowing for easier comparison or mathematical operations.