1. **State the problem:** Ann and Bob share 240 in the ratio 3:5. Ann gives half of her share to Colin, and Bob gives a tenth of his share to Colin. We need to find the fraction of 240 that Colin receives. 2. **Find Ann's and Bob's shares:** The ratio 3:5 means Ann gets 3 parts and Bob gets 5 parts out of a total of 3+5=8 parts. Ann's share = $$\frac{3}{8} \times 240 = 90$$ Bob's share = $$\frac{5}{8} \times 240 = 150$$ 3. **Calculate what Ann gives to Colin:** Ann gives half of her share to Colin. Amount from Ann to Colin = $$\frac{1}{2} \times 90 = 45$$ 4. **Calculate what Bob gives to Colin:** Bob gives a tenth of his share to Colin. Amount from Bob to Colin = $$\frac{1}{10} \times 150 = 15$$ 5. **Total amount Colin receives:** $$45 + 15 = 60$$ 6. **Find the fraction of 240 that Colin receives:** $$\frac{60}{240} = \frac{\cancel{60}}{\cancel{240}} = \frac{1}{4}$$ **Final answer:** Colin receives $$\frac{1}{4}$$ of the 240.