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The phrase "on different ways" is grammatically correct and can be used in written English.
It can be used to indicate various methods or approaches that can be taken in a certain situation. Example: "The teacher explained the concept to the students in different ways, using visual aids, real-life examples, and hands-on activities to ensure that every student understood."
Exact(60)
Another reason for the differences are is that the two services rely on different ways of getting their numbers.
On one version, defended by Peter Singer (1973, pp. 30-41), when people insist on different ways of arranging matters properly, each person in a sense claims a right to be dictator over their shared lives.
We thus focused on different ways that executives could frame the consequences of competition.
Thus discussion focused on different ways to modernise, but did not question the goal itself.
These three hybrid algorithms are based on different ways of combining two individual heuristics.
The national focus on the Living Wage rightly focused attention on different ways of reducing poverty and inequality.
The gemologists worked on different ways to cut the stone while designers worked on creating the band.
This paper presents a physical model for work materials, balls, and vial collisions based on different ways of motions.
Damon wasn't solely focused on different ways to flex his acting muscles: he gained weight – and an entirely unflattering new look – for Steven Soderbergh's underrated corporate comedy.
Scientists around the world are working on different ways to get drugs into specific cells without negatively impacting the rest of the body.
In the Back-to-School issue of Local Living, we sought out experts for advice on different ways to prepare for the school year.
More suggestions(15)
on different means
on several ways
on different solutions
on other ways
on different characteristics
on different techniques
on certain ways
on different angles
on various ways
on different pathways
on different varieties
on different approaches
on different understandings
on different considerations
on different strategies
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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