How do you solve problems involving percentages and ratios?

Percentage and ratio problems can be challenging, but there are some tips and tricks that can help you solve them. One important thing to remember is that percentages are simply ratios that have been multiplied by 100. With that in mind, you can approach percentage and ratio problems in a similar way.

• Convert percentages to fractions or decimals: This can make the problem easier to solve. For example, 25% can be written as 0.25 or 1/4.
• Use the unitary method: The unitary method involves setting up a proportion using a single unit. For example, if you know that 20% of a number is 30, you can set up the proportion 20/100 = 30/x and solve for x.
• Use cross-multiplication: If you have a proportion with two fractions, you can use cross-multiplication to solve for the missing value. For example, if you know that 3/4 is equal to 75/x, you can cross-multiply to get 3x = 75 x 4, and then solve for x.

When solving ratio problems, it's important to remember that ratios are simply comparisons of two quantities. One useful technique is to use a common denominator to make the ratios easier to compare. For example, if you are comparing the ratios of boys to girls in a class and you know that there are 15 boys and 20 girls, you can find the ratio of boys to girls by dividing both numbers by the smaller number (in this case, 15). This gives you a ratio of 1:1.33 or 3:4.

There are a few different ways to solve problems involving percentages and ratios. One way is to use the basic percent equation:

Percent = (part / whole) * 100

For example, if you want to find 20% of 100, you would use the following equation:

20% = (part / 100) * 100

20 = (part / 100)

2 = part

Another way to solve problems involving percentages and ratios is to use the proportion method. To do this, you would write two ratios: one ratio that represents the percent, and one ratio that represents the amount-to-base ratio. For example, if you want to find 60% of 12, you would write the following proportions:

60% = 60 / 100

60 = amount / 12

To solve for the amount, you would cross-multiply:

60 * 12 = 100 * amount

720 = 100 * amount

7.2 = amount

Therefore, 60% of 12 is 7.2.

Finally, you can also solve problems involving percentages and ratios by using a table. To do this, you would list the percent, the amount, and the base in separate columns. Then, you would multiply the percent and the base to find the total. Finally, you would divide the total by the base to find the amount. For example, if you want to find 60% of 12, you would use the following table:

Percent | Amount | Base | Total | Amount | | | | 60% | 12 | 100 | 720 | 7.2

Once you have found the amount, you can use it to answer the question that was asked.