The economic value of having colonies in the first place was for 3 main reasons
1) attain cheap labour from the native peoples
2) acquire cheap raw materials to bring to the homeland (Europe)
3) open up new markets to trade with
the first two were vital in Britains industrial revolution. Without cheap raw materials, and cheap labourers, the factories and refineries in Britain would have costed far more to maintain and keep supplied. This, in turn, would have slowed down production considerably. There is no doubt in my mind that the industrial revolution would still have taken place in Britain with or without the colonies, but WITH the colonies the process was sped up considerably.
Overall, cheap labour and raw materials attained through Britains colonial interests sped up the industrialisation of the UK.
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Muslim mathematicians calculated the time of day needed to pray five times daily
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