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Without photosynthesis there would be no glucose or oxygen for respiration. Without respiration there would be no carbon dioxide for photosynthesis.
Cellular respiration is the process of putting energy from glucose into a usable form in a molecule called ATP. It is a series of complex biochemical reactions where all the energy stored in glucose (which stores a lot) is transferred to other molecules, which can use it more efficiently.
The equation of respiration is
##C_6H_12O_6 + 6O_2 -> 6CO_2 + 6H_2O + “energy in ATP”##
Photosynthesis can be thought of as the opposite reaction. Photosynthesis absorbs energy, rather than emits energy. Plant cells which photosynthesise take in ##CO_2## and ##H_2O## from and light energy from the sun, and undergo the reaction
##6CO_2 + 6H_2O + “energy from sun” -> C_6H_12O_6 + 6O_2##
The two are clearly dependent on each other. Without photosynthesis, there wouldn’t be any glucose or oxygen which kick off the respiration reaction. Without respiration, plants would use up all the ##CO_2## and starve to death.
Photosynthesis requires the products from respiration, and respiration requires the products from photosynthesis.