1.In recent years,the chinese government has made fuether efforts to increase its investment in the construction of gymnasiums to better meet people's fast-growing fitness needs.
近年来，中国政府进一步加大体育馆建设投资，以更好的满足人们快速增长的健身需求。
“近一步加大”：has made further efforts to increase.
“体育馆建设投资”:investment in the construction of gymnasiums.
“满足某人的需求”:meet one's needs
“快速增长”:(fast-growing/rapidly-growing)
“健身需求”:fitness needs
2.Besides building new gymnasiums,many cities have taken measures such as renovating old factories and commercial buildings to increase the number of local gymnasiums.
除了新建体育馆外，许多城市还采取了改造旧工厂和商业建筑等措施，来增加当地体育馆的数量。
“除了…之外(还有)”：besides
“采取措施”：take/adopt measures
“列举；例如”：such as
“改造”：renovate
3.With the support of government grants,an increasing number of gymnasiums are open to the public free of charge pr for a low fee.
在政府资金的支持下，越来越多的体育馆向公众免费开放，或者只收取少量费用。
“在…的支持下”：with the support of/with the help of.
“政府资金”：government grants/goverment funds.
“向…开放”：be open to.
“免费开放”：free of charge/for free.
“只收取少量费用”：for a low free.
4.Many gymnasiums have greatly improved their services through modern information technology,which enables people to book space and pay online at their convenience.
许多体育馆通过运用现代信息技术大大提高了服务质量。人们可以方便的在线预订场地和付费。
“通过运用现代信息技术”：through modern information technology.
“提高服务质量”：improve services.
“方便的”：conveniently/at one's convenience.
“在线预订场地和付费”：book space and pay online.
“预订”：book.
5.It can be predicted that with the continuous improvement of sports facilities,more and more people will take exercises in gymnasiums.
“可以预见…”：It can be predicted that….
“随着运动设施的不断完善”：with the continuous improvement of sports facilities.
“运动设施”：support facilities.
“不断改善”：continuous improvement.
“将会去体育馆健身”：will take exercises in gymnasiums./will go to the gymnasiums to work out.