Pace Work. Math

Дата: 27.04.2020

Тема уроку: Пропорції

Зміст уроку: Складання пропорцій. Розв'язання задач. Тренувальні вправи

1. Study the theory block: 

A ratio is one thing or value compared with or related to another thing or value; it is just a statement or an expression, and can only perhaps be simplified or reduced.

On the other hand, a proportion is two ratios which have been set equal to each other; a proportion is an equation that can be solved.

When I say that a proportion is two ratios that are equal to each other, I mean this in the sense of two fractions being equal to each other. For instance, $\small{ \frac{5}{10} }$ equals $\small{ \frac{1}{2} }$.

Solving a proportion means that we have been given an equation containing two fractions which have been set equal to each other, and we are missing one part of one of the fractions; we then need to solve for that one missing value. For instance, suppose we are given the following equation:

$\small{ \dfrac{x}{10} = \dfrac{1}{2} }$

We already know, by just looking at this equation and comparing the two fractions, that x must be equal to 5, but let's suppose for the moment that we hadn't noticed this. We can solve the given equation by multiplying through on both sides by 10 (or, if one prefers, $\small{ \frac{10}{1} }$) to clear the denominators:

$\small{ \dfrac{x}{10} = \dfrac{1}{2} }$

$\small{ \dfrac{10}{1}\left(\dfrac{x}{10}\right) = \dfrac{10}{1}\left(\dfrac{1}{2}\right) }$

$\small{ \dfrac{\cancel{10}}{1}\left(\dfrac{x}{\cancel{10}}\right) = \dfrac{{}^5\bcancel{10}}{1}\left(\dfrac{1}{\bcancel{2}_1}\right) }$

$\small{ x = 5 }$

$2.\; Do\; the\; task:$