The difference between Improve and Shape up
When used as verbs, improve means to make (something) better, whereas shape up means to improve.
check bellow for the other definitions of Improve and Shape up
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Improve as a verb (transitive):
To make (something) better; to increase the value or productivity (of something).
Examples:
"Painting the woodwork will improve this house."
"Buying more servers would improve performance."
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Improve as a verb (intransitive):
To become better.
Examples:
"I have improved since taking the tablets."
"The error messages have improved since the last version, when they were incomprehensible."
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Improve as a verb (obsolete):
To disprove or make void; to refute.
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Improve as a verb (obsolete):
To disapprove of; to find fault with; to reprove; to censure.
Examples:
"to improve negligence"
"rfquotek Chapman"
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Improve as a verb (dated):
To use or employ to good purpose; to turn to profitable account.
Examples:
"to improve one's time;  to improve his means"
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Shape up as a verb (intransitive, idiomatic):
To improve; to correct one's bad habits or behavior.
Examples:
"He'd better shape up soon, or he'll fail the class."
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Shape up as a verb (intransitive, idiomatic):
To take shape; to transform into or become.
Examples:
"The fog has vanished and it's shaping up to be a beautiful day."