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