Percents

We are asked to rewrite the mixed number of 34 57 as a percent. The fraction part is 57. We can write it as a decimal by dividing the numerator by the denominator. Let's use long division to divide to three decimal places.

The quotient is 0.714. Since the last digit is less than 5, we can round this number to 0.71. Now let's add the integer part 34 to the decimal part 0.71. This results in the number 34.71. 34 57≈ 34.71 Finally, we will multiply this number by 100 and add a percent sign to rewrite it as a percent. 34.71* 100=3471 % Therefore, the mixed number 34 57 corresponds to 3471 %.

We want to rewrite 482 % into a mixed number. Let's start by recalling the definition of a percent. It is the ratio of a number to 100. n % =n/100 We can use this formula to rewrite 482 % as a fraction. 482 % =482/100 Next, divide the numerator by the denominator to rewrite this improper fraction as a mixed number. Recall that a mixed number consists of an integer part and a fraction part. Use long division to find the integer quotient and remainder.

The quotient is 4. This is the integer part of the mixed number. The remainder is 82, so this will be the numerator of the fraction part. The denominator of the fraction part of the mixed number is the same as the denominator of the fraction. 482/100= 4 82 100 Finally, let's simplify the fraction part. We will begin by splitting the numerator and denominator into prime factors. 82&= 2* 41 100&= 2* 2* 5* 5 The numbers share only one common factor, 2, which makes it their GCF. We can simplify the fraction by dividing its numerator and denominator by their GCF.

We found that 482 % is equivalent to the mixed number 4 4150.

We know that after working for half an hour, Emily and Dylan correctly placed 34 puzzle pieces. There are 250 pieces in total. This means that they put together 34 250 of the whole puzzle. 34/250 Let's convert this fraction into a percent. First, let's divide the numerator by the denominator by using long division.

The quotient is 0.136. Next, multiply the result by 100 to rewrite the decimal number as a percent. We can do this by moving the decimal point two places to the right. 0.136* 100=13.6 The result is 13.6. This means that Emily and Dylan completed 13.6 % of the puzzle after half an hour of working on it.

We are asked to determine how many pieces Emily and Dylan successfully put together if they completed 60 % of the puzzle. We can do this by writing the corresponding fraction with the denominator of 250. The numerator will indicate the number of placed pieces. 60 %=?/250 Let's begin by recalling the definition of a percent. It is a ratio of a number to 100. n %=n/100 We can apply this formula to 60 %. 60 %=60/100 The next step would be to simplify the fraction. However, we want to write it with a denominator of 250, so instead of simplying, we will expand the fraction. We can find the factor we want to expand the fraction by if we divide 250 by 100. To do so, move the decimal point two places to the left. 250÷ 100=2.5 Finally, let's multiply both the numerator and denominator by 2.5.

Therefore, Emily and Dylan put together 150 pieces after completing 60 % of the puzzle.

Let's consider each percent one at a time.

First Percent: 715 %

The first percent is 715 %. This percent is greater than 100 %, which indicates that it might correspond to a mixed number or an improper fraction. Let's first rewrite it as a mixed number. Recall the definition of a percent. n % =n/100 We can use this formula to rewrite 715 % as a fraction. 715 % =715/100 Next, we need to rewrite this improper fraction as a mixed number. Recall that a mixed number consists of an integer part and a fraction part. We can find these parts by dividing the numerator by the denominator using long division.

The quotient is 7, which makes it the integer part of the mixed number. The remainder is 15, so 15 is the numerator of the fraction part. The denominator of the fraction part of the mixed number is the same as the denominator of the fraction. 715/100= 7 15 100 Finally, let's simplify the fraction part. We can start by splitting the numerator and denominator into prime factors. 15&=3* 5 100&=2* 2* 5* 5 The numbers share only one common factor, 5, which makes it their greatest common factor (GCF). We can simplify the fraction by dividing its numerator and denominator by 5.

If we add the integer part to the fraction part, we find that 715 % corresponds to the mixed number 7 320.

Second Percent: 69.2 %

The second percent is 69.2 %. Since it is less than 100 %, it cannot correspond to a mixed number or an improper fraction. This leaves only decimal numbers. We can rewrite the percent as a decimal number by dividing the it by 100. An easy way to divide by 100 is to move the decimal point two places to the left.

Therefore, 69.2 % is equivalent to the decimal number 0.692.

Third Percent: 83.1 %

Now let's consider 83.1 %. This number is also less than 100 %, so it looks like it might correspond to the remaining decimal number 0.831. Let's confirm this by converting 0.831 back to a percent. 0.831 → ? % First, we multiply the number by 100. We can do this easily by moving the decimal point two places to the right.

Do not forget to add a percent sign to the product.

We confirmed that 0.831 does indeed correspond to 83.1 %.

Fourth Percent: 212.5 %

Finally, let's consider 212.5 %. The only remaining number in the right column is the improper fraction 11956. Let's rewrite it as a percent to see if the numbers are, in fact, equivalent. 119/56 → ? % First, divide the numerator by the denominator. Let's use long division.

The quotient is 2.125. Now, we will rewrite this decimal as a percent by multiplying it by 100 %. To multiply by 100, move the decimal point two places to the right. 2.125* 100 %=212.5 % As we can see, 11956 does indeed correspond to 212.5 %. We have successfully matched all the percents!

Both Dylan and Emily are working with the mixed number 9 34. Let's analyze each of their solutions step by step.

Dylan's Solution

First, Dylan identifies that 34 is the fraction part of the mixed number. Step1 Fraction part: 3/4 ✓ Next, he rewrites the fraction as a decimal. Let's use long division to check whether his result is correct.

Dylan found the corresponding decimal correctly. Step 2 3/4=0.75 ✓ Finally, he adds the integer part 9 to the decimal part 0.75, getting the sum 9.75. This is the decimal corresponding to the mixed number. However, Dylan ended his process there by adding the percent sign. This is incorrect. Step 3 9+0.75=9.75 % * Instead, he needed to first multiply the decimal by 100 and only then add a percent sign. 9.75* 100=975 % ✓ Therefore, Dylan's solution is incorrect.

Emily's Solution

Let's now take a look at Emily's solution. She starts by applying the formula for rewriting a mixed number as an improper fraction. This step is not strictly necessary for converting a mixed number into a percent. However, we can solve math problems in different ways, so it does not immediately mean that the solution is incorrect. Step1 9 34=9* 4+3/4 ✓ Emily applied the formula for converting a mixed number to an improper fraction correctly. She moves on to evaluate the improper fraction by simplifying the numerator. Let's see how she did!

She simplified the fraction properly. Good job! Step2 9 34=39/4 ✓ Next, Emily calculates the quotient of 39 and 4 to rewrite the number as a decimal. Let's do this, too. We will divide using long division.

Once again, Emily's calculation is correct. The improper fraction 394 corresponds to 9.75. Step3 39/4=9.75 ✓ Finally, Emily multiplies the decimal by 100 to rewrite it as a percent. She gets 975 %, which is the correct result. Step4 9.75* 100=975 % ✓ Therefore, Emily's solution is correct even though she did not use the most common steps for the conversion.