Compare and Order Fractions, Decimals, and Percents

We are given two fractions and two percents. 2/5, 46 %, 3/8, 38 % In order to compare these numbers, we need to rewrite them to be in the same form. Let's rewrite the fractions into percents. We will start with 25. First, divide the numerator by the denominator by using long division.

Next, multiply the decimal number by 100 and add a percent sign. 0.4* 100=40 % We can rewrite 38 as a percent in a similar fashion. Let's divide 3 by 8.

Now, multiply the decimal number by 100 and add a percent sign. 0.375* 100=37.5 % As we can see, 38 is equivalent to 37.5 %. All the numbers are now written in percent form! cccc 2/5, & 46 %, & 3/8, & 38 % [0.2cm] ↓ & ↓ & ↓ & ↓ [0.2cm] 40 %, & 46 %, & 37.5 %, & 38 % Finally, we can order the number from least to greatest by comparing their percent form. cccc 37.5 % &< & 38 % &< & 40 % &< & 46 % [0.2cm] ↑ & & ↑ & & ↑ & & ↑ [0.2cm] 3/8, & & 38 %, & & 2/5, & & 46 %

We are given four different numbers. 48 %, 227 %, 0.65, 3.1 Two of these numbers are percents and two are decimal numbers. We need to rewrite them so that they are in the same form in order to be able to compare them. Percents:& 48 %, 227 % Decimals:& 0.65, 3.1 Let's rewrite the numbers as decimals. To do this, divide the percents by 100 and remove the percent signs. We will start with 48 %. Move the decimal point two places to the left to divide it by 100.

As we can see, 48 % is equivalent to 0.48. 48 %÷ 100=0.48 We can rewrite 227 % as a percent in a similar manner. Let's move the decimal point two places to the left.

We can see that 227 % is the same as 2.27. 227 %÷ 100=2.27 All the numbers are now written in decimal form! cccc 48 % & 227 % & 0.65 & 3.1 [0.2cm] ↓ & ↓ & ↓ & ↓ [0.2cm] 0.48 & 2.27 & 0.65 & 3.1 Finally, let's compare these numbers and order them from greatest to least. ccccccc 3.1 &> & 2.27 &> & 0.65 &> & 0.48 [0.2cm] ↓ & & ↓ & & ↓ & & ↓ [0.2cm] 3.1, & & 227 %, & & 0.65, & & 48 % [0.2cm] ↓ & & ↓ & & ↓ & & ↓ [0.2cm] Racing car & & Railway car & & Tiger & & Horse Therefore, the racing car is the fastest, followed by the railway car, the tiger, and, finally, the horse.

The boys need to compare two numbers, a mixed number and a percent. 4 59 and 462 % Let's analyze each solution step by step.

Tearrik's Solution

Tearrik decides to rewrite the mixed number as a percent to be able to compare the numbers. First, he converts the mixed number into an improper fraction by applying the corresponding formula. a bc=a* c+b/c Let's check if he applied the formula correctly.

The improper fraction that corresponds to 4 59 is 419. Tearrik calculated this step correctly. Next, he divides the numerator by the denominator using long division.

The quotient is about 4.55. Next, Tearrik needs to multiply this decimal number by 100 and add a percent sign. 4.55* 100=455 % This means that the mixed number is equivalent to about 455 %. Finally, Tearrik compares the percents and concludes that 462 % is greater than 455 %. 455 % < 462 % Tearrik's solution is absolutely correct!

Ali's Solution

Let's now consider Ali's solution. His first step is the same as Tearrik's. He rewrites the mixed number as an improper fraction. 4 59=41/9 ✓ Next, Ali rewrites the fraction as a percent. For this, he divides the numerator by the denominator. 41/9=4.55 He rounds the number to one decimal place and writes 4.6 %. However, he does not realize that he only found the corresponding decimal, and not the percent. To find the percent, he would also need to multiply the result by 100. This means that this step is incorrect. 41/9≈ 4.6 % * Therefore, Ali's solution is incorrect. Only Tearrik is correct.