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CCSS.Math:

rewrite each fraction with a denominator of ten so we have two fractions three fifths and seven halves and we want to take their denominators of five and two and change them to be a common denominator of 10 so let's start with three-fifths and we can look at this visually here we can use this rectangle to represent a whole one whole and to show three fifths of that whole we're going to need to divide it into fifths or five equal pieces so let's do that we try to make these as equal as possible and so we have three pieces and then finally there we go so these should represent five equal pieces or fifths and to show three fifths we need to shade three of those five pieces so one two three of those five pieces should be shaded in to show three-fifths but we've decided we don't want fifths any more now we want tenths we want a new denominator of ten so to change this fraction over here to change this to be tenths we need to split each of these fifths in half we need to double the amount of pieces so we can do that here and now instead of fifths or five equal sized pieces we have tenths we have one two three four five six seven eight nine ten so we found a way to have tents without changing the amount that's represented the same amount is still shaded but now we have tenths so our denominator doubled we multiplied it by two we have twice as many pieces but look at what happened to our numerator instead of three pieces now we have one two three four five six pieces it also doubled it also was multiplied by two - because if we double all of the pieces well then the shaded ones will also double each of those pieces also split in two so now there's twice as many shaded pieces so three fifths can be re-written as six tenths three fifths is equal to six tenths and again we didn't change the fraction we didn't change how much was shaded three fifths and six tenths represented the same amount we just changed the denominator and wrote it a different way so three fifths can be re-written in tenths as six tenths and now for seven halves we again we want a denominator of ten so we could draw it out or we could try to use this pattern we just noticed up here to figure out how to make halves turn into tenths to get from fifths two tenths we had to double or multiply by 2 to get from halves to tents we'd have to multiply each of our pieces times five times five each of our halves would be split into five pieces so we'd multiply two times 5 to get tenths and like the pattern showed us up here if the denominator is multiplied by a number we multiply the numerator by the same number because those shaded pieces would also be split five times so we'd multiply our seven times five also these should match the numerator and denominator multiplied by the same number and seven times five is thirty-five so thirty-five tenths is equal to seven halves so to change these two fractions to have a common denominator of 10 three-fifths will become six tenths and seven halves will become 35 tenths