Representing Ratios Practice
1. The ratio of boys to girls in a classroom is 2:3. If there are 12 boys in the classroom, how many girls are there?
Solution:
The ratio of boys to girls is given as 2:3.
So, the ratio can be written as boys/girls = 2/3.
We are given that there are 12 boys.
Let the number of girls be x.
According to the given ratio, we can set up the equation:
12/x = 2/3.
Cross-multiplying, we get:
12 * 3 = 2 * x.
Simplifying, we have:
36 = 2x.
Dividing both sides by 2, we get:
18 = x.
Therefore, there are 18 girls in the classroom.
2. The ratio of the lengths of two sides of a rectangle is 3:4. If the length is 15 cm, what is the width of the rectangle?
Solution:
The ratio of the lengths of the sides is given as 3:4.
So, the ratio can be written as length/width = 3/4.
We are given that the length is 15 cm.
Let the width be x cm.
According to the given ratio, we can set up the equation:
15/x = 3/4.
Cross-multiplying, we get:
15 * 4 = 3 * x.
Simplifying, we have:
60 = 3x.
Dividing both sides by 3, we get:
20 = x.
Therefore, the width of the rectangle is 20 cm.
3. The ratio of the number of red marbles to the number of blue marbles in a jar is 5:2. If there are 35 red marbles, how many blue marbles are there?
Solution:
The ratio of red marbles to blue marbles is given as 5:2.
So, the ratio can be written as red/blue = 5/2.
We are given that there are 35 red marbles.
Let the number of blue marbles be x.
According to the given ratio, we can set up the equation:
35/x = 5/2.
Cross-multiplying, we get:
35 * 2 = 5 * x.
Simplifying, we have:
70 = 5x.
Dividing both sides by 5, we get:
14 = x.
Therefore, there are 14 blue marbles in the jar.
Sure! I can help you with practicing representing ratios. Here's a step-by-step guide:
Step 1: Understand what a ratio is
A ratio represents a comparison between two or more quantities. It shows the relationship between the quantities using a colon (:) or a fraction.
Step 2: Identify the quantities you want to compare
In order to represent a ratio, you need to identify the two or more quantities that you want to compare. These quantities should have the same units or be able to be converted to the same units.
Step 3: Write the ratio using a colon
To represent a ratio using a colon, simply write the quantities being compared with a colon between them. For example, if you want to compare the number of boys to the number of girls in a class, you would write it as "boys:girls".
Step 4: Simplify the ratio
If the quantities being compared have a common factor, you can simplify the ratio by dividing both quantities by the common factor. For example, if you have a ratio of 12:18, you can simplify it to 2:3 by dividing both quantities by 6.
Step 5: Represent the ratio as a fraction
Another way to represent a ratio is to write it as a fraction. To do this, simply write the quantities being compared as the numerator and denominator of the fraction. For example, if you have a ratio of 2:5, you can represent it as 2/5.
Step 6: Convert the ratio to a different unit
If the quantities being compared have different units, you may need to convert one or both of them to the same unit before representing the ratio. This can usually be done by using conversion factors.
Step 7: Use the ratio to solve problems
Once you have represented the ratio, you can use it to solve problems. For example, if you have a ratio of 3:5 representing the number of red to blue marbles in a bag, and you know there are 60 red marbles, you can use the ratio to find out how many blue marbles there are.
I hope this step-by-step guide helps you practice representing ratios! Let me know if you have any further questions.