equivalent fractions or proportions

[bobisaka]

Hi, can you show me the process of equivalent fractions?
I have forgotten how to do it.. what steps should i take to come to 114/8?

In a complex fraction, the highlighted part is where i stop, as i forget how to do the next steps to get the answer for why they are the same proportions. Sometimes i get it, but most of the time i get a brain freeze..

230/16 = 345/24

115/8 = 115/8

 

[pka]

In over sixty years in the profession I have never seen equivalent fractions. It must be a mathEd thing?
\(230=2\cdot 5\cdot 23\\16=2^4\\345=3\cdot 5\cdot 23\\24=2^3\cdot 3\)

 

[Steven G]

You just divide the numerator and denominator by (hopefully) the largest number that goes evenly into both.

 

[Otis]

… the highlighted part is where i stop, as i forget how to [show] why they are [equivalent fractions] …

230/16 = 345/24

Hi bobisaka. We can show they're equivalent, by confirming that 230×24 is the same as 16×345.

In a true proportion statement A/B=C/D, we know that A×D=B×C always.

For reducing fractions to lowest terms, we can use prime factorizations (like pka showed) to cancel common factors and multiply what's left. Alternately, we can try some division rules for Whole numbers:

Even numbers are divisible by 2
Numbers whose digits add to make a multiple of 3 are divisible by 3
Numbers ending in 0 or 5 are divisible by 5

Both numbers in 230/16 are even, so we divide each by 2. The result is 115/8. We know that 115 is not in the multiplication table, so 115 cannot have any factors common to 8; therefore, 115/8 cannot be reduced further.

Both numbers in 345/16 are not even, so we can't divide each by 2. Are they both divisible by 3? Let's check. The digits in 345 add up to 12, and 12 is a multiple of 3, so 345 is divisible by 3. The digits in 24 add up to 6 -- another multiple of 3 -- so we divide 345 and 24 by 3. The result is 115/8.

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