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=== Others === Arithmetic is relevant to many fields. In [[daily life]], it is required to calculate change when shopping, manage [[personal finances]], and adjust a cooking recipe for a different number of servings. Businesses use arithmetic to calculate profits and losses and [[Marketing research|analyze market trends]]. In the field of [[engineering]], it is used to measure quantities, calculate loads and forces, and design structures.<ref>{{multiref | {{harvnb|Lockhart|2017|pp=1β2}} | {{harvnb|Bird|2021|p=3}} | {{harvnb|Aubrey|1999|p=[https://books.google.com/books?id=_NhpY_VPdCsC&pg=PA49 49]}} }}</ref> [[Cryptography]] relies on arithmetic operations to protect sensitive information by [[encrypt]]ing data and messages.<ref>{{multiref | {{harvnb|Omondi|2020|p=[https://books.google.com/books?id=_m7NDwAAQBAJ&pg=PR8 viii]}} | {{harvnb|Paar|Pelzl|2009|p=[https://books.google.com/books?id=f24wFELSzkoC&pg=PA13 13]}} }}</ref> Arithmetic is intimately connected to many branches of mathematics that depend on numerical operations. [[Algebra]] relies on arithmetic principles to solve [[equation]]s using variables. These principles also play a key role in [[calculus]] in its attempt to determine [[rates of change]] and areas under [[curve]]s. [[Geometry]] uses arithmetic operations to measure the properties of shapes while [[statistics]] utilizes them to analyze numerical data.<ref>{{multiref | {{harvnb|Musser|Peterson|Burger|2013|p=[https://books.google.com/books?id=8jh7DwAAQBAJ&pg=PA17 17]}} | {{harvnb|Kleiner|2012|p=[https://books.google.com/books?id=7NcEIteAfyYC&pg=PA255 255]}} | {{harvnb|Marcus|McEvoy|2016|p=[https://books.google.com/books?id=x29VCwAAQBAJ&pg=PA285 285]}} | {{harvnb|Monahan|2012}} }}</ref> Due to the relevance of arithmetic operations throughout mathematics, the influence of arithmetic extends to most sciences such as [[physics]], [[computer science]], and [[economics]]. These operations are used in calculations, [[problem-solving]], [[data analysis]], and algorithms, making them integral to scientific research, technological development, and economic modeling.<ref>{{multiref | {{harvnb|Gallistel|Gelman|2005|pp=559β560}} | {{harvnb|Ali Rahman|Shahrill|Abbas|Tan|2017|pp=373β374}} | {{harvnb|Li|Schoenfeld|2019|loc=Abstract, Introducation}} | {{harvnb|Asano|2013|pp=xiiiβxv}} }}</ref>
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