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English: GROUP NAMES: COUPLERS combine two numbers. SIZERS scale the original number. Couples need matching names (in math). That's why we line up #placevalue positions. That's why fraction names (de-name-inators) need to match. Not so with Sizers in most contexts. Sizers simply change the size of the original number. The unit name stays the same (except when working with compound units or conversions). Sizers combine numbers too (identical numbers). However, their defining feature is 'making copies' of the Base (original value) or 'splitting it' into equal parts.

OPERATIONS: SUBTRACTION is finding the difference. Start at either side. ADDITION is the # spaces to the right (sometimes need to resolve combo symbols to determine if +). MULTIPLICATION always increases the size of the Base/original number (zero and 1 misbehave as usual). When you multiply by a fraction or decimal you are dividing. Multiplication by a fraction is 2 steps: multiply by the top # and divide by the bottom. The denominator is always larger. It has a larger effect. If you gave a descriptive name to this process one would call it..Division. (Focusing on the smaller or minor part can distort the overall meaning and lead to mislabeling. Using accurate, logical nomenclature from the start gives multiplication a consistent meaning: Multiplication increases the size of the Base value.) Decimals - same principle as fractions. The decimal’s 'denominator' is conveyed by its Place Value and its ‘denominator’ is always larger.

Last but not least, DIVISION decreases the size of the Base value (except 0, 1).