What Is A Ratio Table

In this explainer, nosotros volition learn how to use equivalent ratios to complete ratio tables and solve problems in real-life situations.

First, let'south learn some vocabulary associated with ratios.

Definition: Antecedent and Consequent

A ratio compares two numbers. Allow's phone call these numbers and . The ratio can exist written as or . Here, is called the kickoff term, or antecedent of the ratio, and the second term, or consequent.

Ii ratios are equivalent when they can exist simplified to the same ratio. Tables of equivalent ratios are very useful to find values of two quantities knowing that their ratios are equivalent.

For example, let's consider a typical example of equivalent ratios when we buy a different number of items and each item has the same price. Let's imagine that one bag of apples costs $1.l. Ii numberless of apples, then, price $three, three bags cost $4.fifty, and and then on. Nosotros can put these values in a table, equally shown here.

Number of Bags	i	2	3	4	5
Price ($)	1.l	iii.00	4.50	6.00	7.50

All the ratios of the price to the number of bags are equivalent:

This means that, in the table, the numbers in the same column are obtained, one from the other, by multiplying or dividing by 1.50.

This as well means that, given 1 pair of numbers in one cavalcade of the table, whatsoever other pair tin be institute by multiplying both numbers by the same number. For instance, we come across that we can get from "2 numberless price $3" to "four bags price $six" past multiplying the two and the 3 past 2.

Note that the cost of 5 bags is given by the cost of iii bags plus the price of 2 bags.

Let'south check our understanding.

Example i: Identifying the Antecedent and Consequent of a Ratio

Complete the following tabular array:

Offset Number (Antecedent)	Second Number (Consequent)	Forms of Expressing the Ratio
3	four	or
		or

Answer

Here, we are given a ratio, , written likewise as . Nosotros need to identify the antecedent and the consequent of the ratio. As nosotros know that the antecedent is the commencement term, it is 31. The consequent is the 2d term, 35.

Example 2: Finding a Ratio Using a Ratio Table

Using the ratio table, determine how many people viii pizzas would serve.

Number of Pizzas	iii	four	7	8
People Served	9	12	21	?

Answer

We can cheque that the ratios of the number of pizzas to the number of people served, every bit given in the tabular array, are equivalent, by looking at the ratios , , and . They are indeed all equal to 3 (which means that i pizza serves 3 people).

Having found that one pizza serves iii people, we can find that eight pizzas serve people. We could also say that 8 is double four, and and then the number of people served is double 12, that is, 24.

Example 3: Finding the Consistent Having the Antecedent and 1 Equivalent Ratio

Sameh bought forty packs of baseball game cards for a discounted price of $96. If he sells x packs to a friend at the aforementioned cost, how much should he accuse?

Number of Baseball game Card Packs	10	40
Toll in Dollars		96

Answer

Hither, we know that 40 cards have cost Sameh $96, and we desire to find the price of 10 cards at the same cost, meaning when the ratio of the price to the number of cards is the same in both cases (which means that the price per card is the same).

Since 10 is one quarter of forty, that is, or , the toll of 10 cards is obtained by dividing the price of forty cards by 4 likewise. The price of x cards is dollars.

We could likewise have calculated first the price of one card and so multiplied this by x to get the cost of 10 cards: . This is of course exactly the aforementioned as .