Sure. There are other applications of arithmetic, but algebra without arithmetic is impossible. A broad knowledge of arithmetic is essential for mastery of algebra.
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No, algebra is not arithmetic. While both algebra and arithmetic involve numbers and mathematical operations, algebra is a branch of mathematics that goes beyond the basic arithmetic operations (addition, subtraction, multiplication, and division) to include variables, equations, and abstract mathematical concepts.
arithmetic
Arithmetic, algebra
The study of algebra is commonly referred to as arithmetic. This is a branch of mathematics which is a broad science.
Of course. Formulas are not encountered until the student progresses from arithmetic to algebra.