Mixed numbers, plus and minus

Mei Ling has 3 and one third metres of cloth. She uses 1 and three quarters metres of it to make a bag. How much cloth is left? Give your answer as a mixed number. Try it first. Pause if you like. Here's her cloth, as one long strip. Every box along it is one whole metre. 3 whole metres, and one third of a metre over: the 3 and one third metres she starts with. And underneath, the cloth she uses: 1 whole metre and three quarters of a metre. The whole metres come off first, because a whole metre needs no cutting up. She uses 1 whole metre, so that first metre of the strip is gone. Three quarters of a metre still has to come off. So what's left to work out is 2 and one third minus three quarters. One third and three quarters aren't the same size of part, so we can't subtract them yet. The lowest common multiple of 3 and 4 is 12, so both are written in twelfths. Each third splits into 4 equal parts, so one third is 4 twelfths. Each quarter splits into 3, so three quarters is 9 twelfths. Count them: 9 twelfths coming off, 4 twelfths to take them from. 9 is bigger than 4, so one of the whole metres has to be opened up. Cut it into the same parts, and one whole metre is 12 twelfths. Those 12 sit next to the 4 already there: 16 twelfths. So 2 and 4 twelfths is the same length as 1 and 16 twelfths. Now the 9 twelfths can come off. 9 of those 16 parts went into the bag. 16 twelfths minus 9 twelfths is 7 twelfths. And the 1 whole metre beside them was never touched. So 1 and 7 twelfths metres of cloth are left. One third of a metre is 4 twelfths, and three quarters is 9 twelfths. 9 is more than 4, so the whole metre beside them was opened. One whole metre is 12 twelfths, and 12 and 4 make 16. 16 minus 9 is 7, so 1 and 7 twelfths metres are left. When the fraction you subtract is bigger than the fraction you have, change one whole into the same parts first.