WEBVTT
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Last week, Michael and Elizabeth exercised by running, cycling, and swimming.
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The table shows the fraction of the total exercise time that they spent on each activity.
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Find the missing fraction for each person.
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Let’s let running be pink, cycling be yellow, and swimming be blue.
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And then, we can sketch a visual for the information we were given.
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If we start with Elizabeth, she spent four-sevenths of her time running and one-seventh of her time swimming.
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If this box represents all the time she spent exercising, we can divide that time up into seven pieces.
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Four out of the seven she spent running.
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One out of the seven she spent swimming.
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And the remaining time is how much she spent cycling.
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And so, we can say that two-sevenths of her exercise time went to cycling.
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Four-sevenths plus one-seventh plus two-sevenths equals seven-sevenths, or one whole, the total time Elizabeth was exercising.
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If we try to use this same process for Michael’s exercise time, it won’t be as simple.
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We can make a bar that represents Michael’s total exercise time, and then we could divide this bar in half.
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Because we know that half of the time Michael spent cycling.
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But then we tried to divide this up into fifths because Michael spent one-fifth of his time swimming.
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We know the rest of the time was spent running, but how can we find out what fraction this is?
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It looks like Michael was running one and a half-fifths.
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But we don’t usually use decimals with our fractions.
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To fix this problem, we can divide Michael’s total exercise time into tenths, into 10 equal pieces.
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One-half equals five-tenths.
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We thought we had one and a half-fifths.
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That would have been the time he spent running.
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And we can write that as three out of 10.
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And we could say that one-fifth, the time he spent swimming, is equal to two-tenths.
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Five-tenths plus three-tenths plus two-tenths equals ten-tenths, the whole amount of time Michael was exercising.
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And so, we can say that Michael was running three-tenths of his total exercise time.