What is Proportionality table? — Mathematics

Definition 49.1 Primary & Middle School Mathematics · Chapter 49 — Proportionality

A table of two rows is a proportionality table when the numbers of the second row are those of the first multiplied by one fixed number, the coefficient. Equivalently: all column quotients $\frac{\text{bottom}}{\text{top}}$ are equal.

Examples

Example 49.2

top	$4$	$10$	$14$
bottom	$6$	$15$	$21$

Quotients: $\frac64 = 1.5$ , $\frac{15}{10} = 1.5$ , $\frac{21}{14} = 1.5$ : proportional, coefficient $1.5$ .

Example 49.4 (Fourth proportional)

If $7$ identical books weigh $2.8$ kg, how much do $12$ such books weigh? Table and cross rule:

books	$7$	$12$
kg	$2.8$	$m$

7 \times m = 2.8 \times 12 \quad\Longrightarrow\quad m = \frac{2.8 \times 12}{7} = \frac{33.6}{7} = 4.8 \text{ kg}.

Check by the unit: one book weighs $0.4$ kg, twelve weigh $4.8$ kg.

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