# RATIOS RATES TABLES AND GRAPHS

In this section, you will learn how to determine the ratio or rate of change of a relation from a table or graph. Students will also compare and contrast ratios, rates, and rates of change.

Example 1 :

Students in Mr. Webster’s science classes are doing an experiment that requires 250 milliliters of distilled water for every 5 milliliters of ammonia. The table shows the amount of distilled water needed for various amounts of ammonia.

Question (i) :

Use the numbers in the first column of the table to write a ratio of distilled water to ammonia.

100 ml distilled water/2 ml ammonia  (or)  100 : 2

Question (ii) :

How much distilled water is used for 1 milliliter of ammonia?

From the first column of the table, the ratio  of distilled water to ammonia is

100 ml water/2 ml ammonia

To find the quantity of distilled water used for 1 milliliter of ammonia, we have to make the second quantity (ammonia) as 1.

100 ml distilled water : 2 ml ammonia = (100 ÷ 2)/(2 ÷ 2)

100 ml distilled water : 2 ml ammonia = 50/1

That is,

50 ml distilled water / 1 ml ammonia

The quantity of distilled water used for 1 milliliter of ammonia is 50 ml.

Question (iii) :

Use your answer from question 2, write another ratio of distilled water to ammonia.

To write another ratio from the answer of question 2, we have find an equivalent ratio to 50 : 1.

To find equivalent ratio of the given ratio, we have to multiply both the terms of the ratio by the same non zero number, say "2".

Then, we have

(50 x 2) : (1 x 2) = 100 : 2

Therefore, another ratio of distilled water to ammonia is 100 : 2

Question (iv) :

Check whether the two ratios from answers of question 1 and question 2 are equivalent or not equivalent.

The two ratios from the answers of question 1 and 2 are

100 : 2 and 50 : 1

Let us check, whether two rations 100 : 2 and 50 : 1 are equivalent or not equivalent.

From the above working, it is clear that the two ratios 100 : 2 and 50 : 1 are equivalent.

Question (v) :

Complete the table. What are the equivalent ratios shown in the table?

For the first blank :

(100 ÷ 2)/(2 ÷ 2) = 50/1

(50 x 3)/(1 x 3) = 150/3

For the second blank :

(100 ÷ 2)/(2 ÷ 2) = 50/1

(50 ÷ 2)/(1 ÷ 2) = 25/0.5

(25 x 7)/(0.5 x 7) = 175/3.5

For the third blank :

(100 x 2)/(2 x 2) = 200/4

Then, we have

Example 2 :

Look at the picture given below.

An express train travels from Webster to Washington, D.C., at a constant speed and makes the trip in 2 hours.

Question (i) :

Make a table to show the distance the train travels in various amounts of time.

Write a ratio of distance to time to find the rate.

Use the unit rate to make a table.

Question (ii) :

Graph the information from the table.

Write ordered pairs with time as the x-coordinate and distance as the y-coordinate.

(1, 60), (2, 120), (3, 180), (4, 240), (5, 300)

Graph the ordered pairs. Fractions and decimals can represent times and distances, so connect the points.

Question (iii) :

Use the graph to find how long the train takes to travel 90 miles.

When we look at the graph carefully, the value on y - axis which is corresponding to 1.5 on x-axis  is 90.

Look at the graph given below.

When we look at the above graph carefully, the value on y- axis which is corresponding to the value 1.5 on x-axis is 90.

The point (1.5, 90) is on the graph, so the train takes 1.5 hours.

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