Recall that a percent is a ratio where the denominator is $100$100. Because of this definition, we can use proportional reasoning strategies to solve problems with percents.
Proportions can be used to represent percent problems as follows:
$\frac{\text{percent}}{100}$percent100  $=$=  $\frac{\text{part}}{\text{whole}}$partwhole 
Evaluate: Use a proportion to answer the question, "What percent of 20 is 3?"
Think: We can translate the statement to a proportion. Then use proportional reasoning to solve for the unknown.
The percent is the unknown. So we can use the variable $x$x to represent it.
The number $3$3 is the part and $20$20 is the whole.
Do:
$\frac{\text{percent}}{100}$percent100  $=$=  $\frac{\text{part}}{whole}$partwhole 

$\frac{x}{100}$x100  $=$=  $\frac{3}{20}$320 
$x$x is the unknown percent. $20$20 is the whole. 
$\frac{x}{100}$x100  $=$=  $\frac{3\times5}{20\times5}$3×520×5 
Multiplying the fraction by $\frac{5}{5}$55 gives us a common denominator of $100$100. 
$\frac{x}{100}$x100  $=$=  $\frac{15}{100}$15100 

$x$x  $=$=  $15$15 
If the denominators in a proportion are the same, the numerators must also be the same. 
So the number $3$3 is $15%$15% of $20$20.
Reflect: Is there another method that we might use to check our solution?
Suppose we want to check our solution to the first worked example using a different method. Let's see how we can apply proportional reasoning to percents in a different way.
Evaluate: Find $15%$15% of $20$20.
Think: It might be easiest to find $10%$10% of $20$20.
We can then use half of that amount to find $5%$5% of $20$20. If we add the two amounts, that will give us $15%$15% of $20$20.
Do: First, find $10%$10% of $20$20.
$10%$10% of $20$20  $=$=  $0.10\times20$0.10×20 
Since $10%=0.10$10%=0.10 
$=$=  $2$2 
Evaluate 



$5%$5% of $20$20  $=$=  $\frac{1}{2}\times2$12×2 
Since $5%$5% is half of $10%$10% 
$=$=  $1$1  
$15%$15%  $=$=  $10%+5%$10%+5%  
$=$=  $2+1$2+1  
$=$=  $3$3 
So $15%$15% of $20$20 is $3$3.
Reflect: What other percents can we calculate using the benchmark of $10%$10%?
Translate the following percentage problem to a proportion. Do not solve or simplify the proportion.
'What percent of $92$92 is $23$23?'
Let the unknown number be $x$x.
Translate the following percentage problem to a proportion. Do not solve or simplify the proportion.
'$60%$60% of what number is $144$144?'
Let the unknown number be $x$x.
We want to find $45%$45% of $5$5 hours.
How many minutes are there in $5$5 hours?
What is $10%$10% of $300$300 minutes?
What is $5%$5% of $300$300 minutes?
Hence find $45%$45% of $300$300 minutes.
Use ratio reasoning with equivalent wholenumber ratios to solve realworld and mathematical problems by:• Creating and using a table to compare ratios.• Finding missing values in the tables. • Using a unit ratio. • Converting and manipulating measurements using given ratios. • Plotting the pairs of values on the coordinate plane.
Use ratio reasoning to solve realworld and mathematical problems with percents by: • Understanding and finding a percent of a quantity as a ratio per 100. • Using equivalent ratios, such as benchmark percents (50%, 25%, 10%, 5%, 1%), to determine a part of any given quantity. • Finding the whole, given a part and the percent.