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The phrase "approximately equal amount of" is correct and usable in written English.
It can be used when discussing quantities that are similar but not exactly the same, often in scientific or mathematical contexts.
Example: "In the experiment, we used an approximately equal amount of both solutions to ensure accurate results."
Alternatives: "roughly the same quantity of" or "about the same amount of".
Exact(10)
Moreover, mixed grain boundaries with approximately equal amount of tilt and twist components do not exhibit high energies.
An effect of composition induced optical transparency, due to the strong modification of the density of states, was observed for symmetrical compositions with approximately equal amount of components.
We found that state effects were as important as trait effects in shaping individual functional connectivity patterns, each explaining an approximately equal amount of variance.
In multi-level heterogeneous networks, the hierarchy levels are formed based on the energy of the nodes, such that nodes in the same level have an approximately equal amount of energy.
In particular, while storms cause a transfer of C from biomass to DOM pools (from where it will decompose unless salvage logged), fires cause an approximately equal amount of direct emission (of CO2 to the atmosphere) and indirect emission (i.e. C moved from living biomass to DOM from where it will decompose).
NEs used in the pull-down reactions show an approximately equal amount of CARM1 was present in all of the NEs (Fig. 5G).
Similar(50)
Burning a gallon of gasoline or of jet fuel produces approximately equal amounts of carbon dioxide.
The individual segments of the caldera ring fault radiated approximately equal amounts of energy.
Sugars, starches, and cellulose produce approximately equal amounts of methane and carbon dioxide.
To examine this phenomenon, I developed a videotape composed of actual footage of approximately equal amounts of violence committed by Israel and the Palestine Liberation Organization.
Commercial "stearic acid" is a mixture of approximately equal amounts of stearic and palmitic acids and small amounts of oleic acid.
More suggestions(2)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com