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  1. Multiplication builds on the concept of addition 
  2. Division builds on the concept of subtraction 
  3. Integers build on the concept of natural numbers 
  4. Fractions build on the concept of decimals 
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Option 4 : Fractions build on the concept of decimals 

The mathematical concepts are hierarchical which adds on the practical and conceptual knowledge from one class to the next class so that the mathematical concepts are taught in a pre-defined order like first the teaching of arithmetic and then the algebra, trigonometry, and calculus are taught. Fractions built on the concepts of decimals are not correct in the context of a hierarchy of mathematical concepts because fractions are a basic concept and children first learn fractions and then they proceed to decimals.

  • If children are taught decimals first then they may face problems understanding because they don't have a basic idea about fractions.
  • The correct hierarchical order of mathematical concepts is first teaching fractions and then proceeding toward decimals.
  • When students have first introduced to fractions then they have a basic understanding of numerators and denominators which may lead to the idea of decimal fractions.
Hence fractions built on the concepts of decimals are not correct in the context of a hierarchy of mathematical concepts. 
On the other hand, all the remaining options are correct as they follow the correct hierarchical order regarding the concepts in mathematics.
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