Addition And Subtraction Of Fractions And Decimals
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Addition and subtraction of fractions and decimals
Questions and Answers
1.
7 4/5 + 2/3
A.
1 7/15
B.
8 7/15
C.
6
D.
3
Correct Answer
B. 8 7/15
Explanation To add the mixed numbers 7 4/5 and 2/3, we first convert them into improper fractions. 7 4/5 becomes 39/5, and 2/3 remains the same. Then, we find a common denominator, which in this case is 15. We multiply 39/5 by 3/3 to get 117/15, and 2/3 by 5/5 to get 10/15. Finally, we add the fractions together to get 127/15. This can be simplified to 8 7/15, which is the correct answer.
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2.
3/4 + 2/3
Correct Answer 1 5/12
Explanation The given expression involves adding two fractions, 3/4 and 2/3. To add fractions, we need to have a common denominator. In this case, the common denominator is 12. We convert 3/4 to an equivalent fraction with a denominator of 12 by multiplying the numerator and denominator by 3, resulting in 9/12. Similarly, we convert 2/3 to an equivalent fraction with a denominator of 12 by multiplying the numerator and denominator by 4, resulting in 8/12. Now, we can add the fractions by adding the numerators and keeping the common denominator of 12, giving us 17/12. This fraction can be simplified to the mixed number 1 5/12.
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3.
4 2/3 + 5 1/24 + 7 1/2
Correct Answer 17 5/24
Explanation The given problem involves adding mixed numbers. To solve it, we need to convert the mixed numbers into improper fractions. Then, we add the fractions together and simplify the result. In this case, 4 2/3 can be written as 14/3, 5 1/24 as 121/24, and 7 1/2 as 15/2. Adding these fractions gives us 14/3 + 121/24 + 15/2 = 408/24 + 121/24 + 180/24 = 709/24. Finally, we convert the improper fraction back into a mixed number, which is 17 5/24.
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4.
3/4 + 1/8 + 1/6
Correct Answer 1 1/24
Explanation The given expression represents the addition of three fractions: 3/4, 1/8, and 1/6. To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 24. So, we convert each fraction to have a denominator of 24: 3/4 becomes 18/24, 1/8 becomes 3/24, and 1/6 becomes 4/24. Adding these fractions gives us a sum of 25/24, which can be simplified to 1 1/24. Therefore, the answer is 1 1/24.
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5.
12 1/2 + 20 1/3
Correct Answer 32 5/6
Explanation The given expression represents the sum of two mixed numbers. To add mixed numbers, we first add the whole numbers together, which gives us 12 + 20 = 32. Then, we add the fractions together. The fractions have different denominators, so we need to find a common denominator. The least common multiple of 2 and 3 is 6. We convert 1/2 to 3/6 and 1/3 to 2/6. Adding 3/6 and 2/6 gives us 5/6. Therefore, the sum of the mixed numbers 12 1/2 and 20 1/3 is 32 5/6.
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6.
1/4 + 5 1/3
Correct Answer 5 7/12
Explanation The given expression is a sum of a fraction and a mixed number. To add them, we first convert the mixed number to an improper fraction. The mixed number 5 1/3 can be written as the improper fraction 16/3. Now, we have 1/4 + 16/3. To add these fractions, we need to find a common denominator, which is 12. Converting 1/4 to have a denominator of 12, we get 3/12. Now, we can add the fractions: 3/12 + 16/3 = (3*3)/(12*3) + 16/3 = 9/36 + 16/3 = (9+192)/36 = 201/36. Simplifying this fraction, we get 5 7/12. Therefore, the answer is 5 7/12.
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7.
12/17 + 5 2/7
Correct Answer 5 118/119
Explanation The given expression is a sum of a mixed number (12/17) and an improper fraction (5 2/7). To solve this, we need to convert the mixed number into an improper fraction. By multiplying the whole number (5) by the denominator (7) and adding the numerator (2), we get 37. So the mixed number becomes 37/7. Now we can add the two fractions together. To do this, we find a common denominator, which is 119. We multiply the numerator and denominator of the first fraction by 7, and the numerator and denominator of the second fraction by 17. This gives us 444/119 + 629/119 = 1073/119. Simplifying this fraction, we get 5 118/119.
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8.
1/4 + 5/33
Correct Answer 53/132
Explanation The given expression involves adding two fractions, 1/4 and 5/33. To add fractions, we need to find a common denominator. In this case, the common denominator is 132, which is the product of 4 and 33. We then convert both fractions to have the same denominator, which gives us 33/132 and 20/132. Adding these fractions together gives us 53/132 as the final answer.
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9.
34 1/2 + 8 1/2
Correct Answer 43
Explanation The given expression is a sum of two mixed numbers. To add mixed numbers, we first add the whole numbers together, which gives us 34 + 8 = 42. Then, we add the fractions together, which gives us 1/2 + 1/2 = 1. Finally, we combine the whole number and fraction parts, resulting in 42 1/2. However, the answer given is 43, which is incorrect. Therefore, the correct answer is 42 1/2, not 43.
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10.
3/4 - 1/4
Correct Answer 1/2
Explanation The given expression is subtracting 1/4 from 3/4. To subtract fractions, we need a common denominator, which in this case is 4. When we subtract 1/4 from 3/4, we get 2/4, which simplifies to 1/2. Therefore, the answer is 1/2.
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11.
8 1/12 - 3 1/4
Correct Answer 4 5/6
Explanation The given expression involves subtracting the mixed numbers 3 1/4 from 8 1/12. To subtract mixed numbers, we first need to convert them into improper fractions. 8 1/12 can be converted to 97/12 and 3 1/4 can be converted to 13/4. Then, we subtract the two fractions by finding a common denominator, which is 12 in this case. After subtracting, the result is 84/12, which simplifies to 7/1 or 7. Finally, we convert the improper fraction back into a mixed number, which is 4 5/6.
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12.
1/8 - 1/12
Correct Answer 1/24
Explanation The given expression represents the subtraction of 1/12 from 1/8. To subtract fractions, we need to have a common denominator. In this case, the common denominator is 24. So, we convert both fractions to have a denominator of 24. 1/8 is equivalent to 3/24, and 1/12 is equivalent to 2/24. Subtracting 2/24 from 3/24 gives us 1/24. Therefore, the correct answer is 1/24.
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13.
100 - 36 1/3
Correct Answer 63 2/3
Explanation The given expression 100 - 36 1/3 can be simplified by subtracting the whole numbers first, which gives us 63. Then, we subtract the fractions by finding a common denominator, which in this case is 3. Subtracting the fractions gives us 2/3. Therefore, the final result is 63 2/3.
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14.
355 1/5 - 55 2/5
Correct Answer 299 4/5
Explanation The given expression is a subtraction problem between two mixed numbers. To solve it, we need to convert both mixed numbers into improper fractions. The first mixed number, 355 1/5, can be written as an improper fraction: (355*5 + 1)/5 = 1776/5. The second mixed number, 55 2/5, can be written as (55*5 + 2)/5 = 277/5. Now, subtracting the two fractions gives us (1776/5) - (277/5) = (1776 - 277)/5 = 1499/5. Finally, we convert the improper fraction back into a mixed number: 1499/5 = 299 4/5.
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15.
2 3/5 - 1 1/5
Correct Answer 1 2/5
Explanation The given expression is a subtraction problem involving mixed numbers. To solve it, we need to convert the mixed numbers into improper fractions. The first mixed number, 2 3/5, can be written as 13/5, and the second mixed number, 1 1/5, can be written as 6/5. Subtracting these fractions gives us 13/5 - 6/5, which equals 7/5. Converting this improper fraction back to a mixed number gives us 1 2/5. Therefore, the answer to the expression 2 3/5 - 1 1/5 is 1 2/5.
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16.
25 - 17 7/9
Correct Answer 7 2/9
Explanation The given question is asking for the difference between 25 and 17 7/9. To find the difference, we subtract the second number from the first number. When we subtract 17 7/9 from 25, we get 7 2/9 as the answer.
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17.
4 7/10 - 3 9/20
Correct Answer 1 1/4
Explanation The given expression is a subtraction of two mixed numbers. To subtract mixed numbers, we need to convert them into improper fractions. Converting 4 7/10 to an improper fraction gives us 47/10, and converting 3 9/20 gives us 69/20. Subtracting the two fractions gives us (47/10) - (69/20). To subtract fractions, we need to find a common denominator, which in this case is 20. After finding the common denominator, we can subtract the numerators. The result is -22/20, which simplifies to -11/10. Converting -11/10 back to a mixed number gives us 1 1/4. Therefore, the answer is 1 1/4.
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18.
48 6/11 - 24
Correct Answer 24 6/11
Explanation The given expression represents the subtraction of 24 from 48 6/11. To subtract fractions, we need to have a common denominator. In this case, the common denominator is 11. Subtracting 24 from 48 leaves us with 24. The fraction 6/11 remains unchanged. Therefore, the answer is 24 6/11.
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19.
1 2/3 - 1 1/12
Correct Answer 7/12
Explanation The given expression is a subtraction of two mixed numbers. To subtract mixed numbers, we need to convert them into improper fractions. The first mixed number, 1 2/3, can be written as the improper fraction 5/3. The second mixed number, 1 1/12, can be written as the improper fraction 13/12. Now, subtracting these fractions gives us (5/3) - (13/12). To subtract fractions, we need a common denominator, which in this case is 12. After finding the common denominator, we can subtract the numerators and simplify the fraction. The result is 7/12.
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20.
A patient weighs 50 lbs. on admission and 48 lbs. on day 3 of his hospital stay. Write a fraction, reduce to lowest terms, to express the fraction of his original weight that he has lost.
Correct Answer 1/25
Explanation The fraction 1/25 represents the fraction of the patient's original weight that he has lost. This can be determined by subtracting the weight on day 3 (48 lbs) from the weight on admission (50 lbs), which gives a difference of 2 lbs. This difference is then expressed as a fraction of the original weight, which is 50 lbs. Simplifying 2/50 to its lowest terms gives 1/25.
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21.
A stock clerk finds that there are 34 1/2 pints of hydrogen peroxide on the shelf. If the fully stocked shelf held 56 pints of hydrogen peroxide, how many pints were used?
Correct Answer 21 1/2 pints
Explanation The stock clerk found that there were 34 1/2 pints of hydrogen peroxide on the shelf. The fully stocked shelf can hold 56 pints of hydrogen peroxide. To find out how many pints were used, we subtract the amount found from the fully stocked amount: 56 - 34 1/2 = 21 1/2 pints. Therefore, 21 1/2 pints were used.
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22.
Which fractions would be considered improper? (mark all that apply)
A.
2/3
B.
1 3/4
C.
6/6
D.
7/5
E.
16/17
Correct Answer(s)
C. 6/6 D. 7/5
Explanation An improper fraction is a fraction where the numerator is equal to or greater than the denominator. In the given options, the fractions 6/6 and 7/5 are considered improper. In 6/6, the numerator and denominator are equal, making it an improper fraction. In 7/5, the numerator (7) is greater than the denominator (5), also making it an improper fraction. The other fractions, 2/3, 1 3/4, and 16/17, are all proper fractions because the numerator is smaller than the denominator.
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23.
Which fractions would be considered proper? (mark all that apply)
A.
1/4
B.
144/14
C.
1/14
D.
14/14
E.
14/1
Correct Answer(s)
A. 1/4 C. 1/14
Explanation A proper fraction is a fraction where the numerator is smaller than the denominator. In this question, the fractions 1/4 and 1/14 satisfy this condition. The fraction 144/14 is an improper fraction because the numerator is larger than the denominator. The fraction 14/14 is also considered improper because the numerator is equal to the denominator. Lastly, the fraction 14/1 is not a proper fraction because the numerator is larger than the denominator.
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24.
Change the following mixed number into a improper fraction: 6 1/2
Correct Answer(s) 13/2
Explanation To change a mixed number into an improper fraction, we multiply the whole number by the denominator of the fraction and add the numerator. In this case, we have 6 multiplied by 2 (denominator) plus 1 (numerator), which gives us 13. The denominator remains the same, which is 2. Therefore, the improper fraction form of 6 1/2 is 13/2.
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25.
Change the following mixed number into a improper fraction: 10 2/3
Correct Answer(s) 32/3
Explanation To change a mixed number into an improper fraction, we multiply the whole number by the denominator of the fraction and add the numerator. Then, we place the result over the original denominator. In this case, we multiply 10 by 3, which equals 30, and add 2 to get 32. Therefore, the improper fraction form of 10 2/3 is 32/3.
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26.
Change the following mixed number into a improper fraction: 102 3/4
Correct Answer(s) 411/4
Explanation To change a mixed number into an improper fraction, we multiply the whole number by the denominator of the fraction and add the numerator. In this case, we multiply 102 by 4, which equals 408. Then we add the numerator 3 to get 411. The denominator remains the same, which is 4. Therefore, the mixed number 102 3/4 can be written as the improper fraction 411/4.
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27.
Change the following improper fraction to a whole number or mixed number and reduce to lowest terms: 24/12
Correct Answer(s) 2
Explanation The given fraction, 24/12, can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 12. This simplifies to 2/1, which can be written as a whole number, 2. Therefore, the correct answer is 2.
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28.
Change the following improper fraction to a whole number or mixed number and reduce to lowest terms: 44/16
Correct Answer(s) 2 3/4
Explanation The given improper fraction, 44/16, can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 4. This results in the fraction being reduced to 11/4. To express this as a mixed number, we divide the numerator (11) by the denominator (4), which gives us a quotient of 2 and a remainder of 3. Therefore, the improper fraction 44/16 can be written as the mixed number 2 3/4.
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29.
Change the following improper fraction to a whole number or mixed number and reduce to lowest terms: 8/8
Correct Answer(s) 1
Explanation The given improper fraction 8/8 can be simplified to 1 because both the numerator and denominator are the same. When the numerator and denominator are equal, the fraction represents a whole number. Therefore, 8/8 is equal to 1.
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30.
Change the following improper fraction to a whole number or mixed number and reduce to lowest terms: 100/75
Correct Answer(s) 1 1/3
Explanation To change the improper fraction 100/75 to a mixed number, we divide the numerator (100) by the denominator (75). The quotient is 1 with a remainder of 25. So, the whole number part is 1. Then, we write the remainder (25) as the numerator of the fraction, and the denominator remains the same (75). Finally, we simplify the fraction to lowest terms by dividing both the numerator and denominator by their greatest common divisor, which is 25. After simplifying, we get the mixed number 1 1/3.
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31.
Enlarge the following fraction to the nearest tenth: 2/5
Correct Answer(s) 4/10
Explanation The given fraction is 2/5. To enlarge the fraction to the nearest tenth, we need to find an equivalent fraction with a denominator of 10. To do this, we multiply both the numerator and denominator of the fraction by 2. This gives us 4/10, which is the enlarged fraction to the nearest tenth.
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32.
Enlarge the following fraction to the nearest twelfth: 2/3
Correct Answer(s) 8/12
Explanation To enlarge a fraction to the nearest twelfth, we need to find the equivalent fraction with a denominator of 12. To do this, we need to multiply both the numerator and denominator of the given fraction by a number that will result in a denominator of 12. In this case, we can multiply both 2 and 3 by 4, which gives us 8/12. Therefore, the correct answer is 8/12.
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33.
Which is smaller? 1/1,000 or 1/10,000
Correct Answer(s) 1/10,000
Explanation The fraction 1/10,000 is smaller than 1/1,000 because the denominator (10,000) is larger than the denominator of 1/1,000 (1,000). In fractions, when the denominators are different, the fraction with the larger denominator represents a smaller value. Therefore, 1/10,000 is a smaller fraction than 1/1,000.
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34.
Which is larger? 2/9 or 5/9
Correct Answer(s) 5/9
Explanation The fraction 5/9 is larger than 2/9 because the numerator (5) is greater than the numerator of 2/9 (2). Since the denominators are the same, the fraction with the larger numerator is always larger.
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35.
0.16 + 5.375 + 1.05 + 16=
Correct Answer(s) 22.585
Explanation The given expression involves adding four numbers: 0.16, 5.375, 1.05, and 16. When these numbers are added together, the sum is 22.585.
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36.
13.009 - 0.7=
Correct Answer(s) 12.309
Explanation The given question involves subtracting 0.7 from 13.009. When subtracting decimals, it is important to align the decimal points. Subtracting 0.7 from 13.009, we get 12.309.
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37.
700 - 325.65
Correct Answer(s) 374.35
Explanation The given question is asking for the result of subtracting 325.65 from 700. By performing the subtraction, we get the answer 374.35.
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38.
13.529 + 10.09=
Correct Answer(s) 23.619
Explanation The given question asks for the sum of 13.529 and 10.09. Adding these two numbers together gives us a total of 23.619.
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39.
A dietician calculates the sodium in a patient's breakfast: raisin bran cereal= 0.1 gram, 1 cup 2% milk= 0.125 gram, 6 ounces of orange juice= 0.001 gram, 1 corn muffin= 0.35 gram, and butter= 0.121 gram. How many grams of sodium did the patient consume?
Correct Answer(s) 0.697 grams
Explanation The patient consumed a total of 0.697 grams of sodium. This is calculated by adding up the sodium content of each item in the breakfast: 0.1 grams (raisin bran cereal) + 0.125 grams (2% milk) + 0.001 grams (orange juice) + 0.35 grams (corn muffin) + 0.121 grams (butter) = 0.697 grams.
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40.
A home health nurse accounts for her day at work. If she spent 3 hours and 20 mins at the office, 40 mins traveling, 3 1/2 hours caring for patients, 24 minutes for lunch, and 12 minutes on break, what is her total number of hours including all of her activities? Express your answer as a decimal
Correct Answer(s) 8.1 hours
Explanation The home health nurse spent 3 hours and 20 minutes at the office, which is equivalent to 3.33 hours. She spent 40 minutes traveling, which is equivalent to 0.67 hours. She spent 3 1/2 hours caring for patients, which is equivalent to 3.5 hours. She spent 24 minutes for lunch, which is equivalent to 0.4 hours. She spent 12 minutes on break, which is equivalent to 0.2 hours. Adding up all these amounts, we get a total of 8.1 hours.
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41.
Change the fraction 1/5 to a decimal
Correct Answer(s) 0.20 .20
Explanation The fraction 1/5 can be changed to a decimal by dividing 1 by 5, which equals 0.20 or .20.
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42.
Convert the decimal 1.05 to a fraction and reduce to lowest terms
Correct Answer(s) 1 1/20
Explanation To convert the decimal 1.05 to a fraction, we can first write it as a mixed number by separating the whole number part (1) and the decimal part (0.05). The decimal part can be written as 5/100, which can be simplified to 1/20. Therefore, the decimal 1.05 can be expressed as the fraction 1 1/20 in its lowest terms.
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43.
Convert 33 3/100 into a decimal
Correct Answer(s) 33.03
Explanation To convert a mixed number into a decimal, we first multiply the whole number by the denominator and then add the numerator. In this case, the whole number is 33, the denominator is 100, and the numerator is 3. So, multiplying 33 by 100 gives us 3300, and then adding 3 gives us a final result of 3303. However, since the numerator is out of 100, we need to move the decimal point two places to the left to get the correct decimal form. Therefore, the decimal representation of 33 3/100 is 33.03.
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44.
Convert the decimal 12.125 to a fraction in lowest terms
Correct Answer(s) 12 1/8
Explanation To convert the decimal 12.125 to a fraction in lowest terms, we first note that the whole number part, 12, remains the same in the fraction. Then, we convert the decimal part, 0.125, into a fraction. Since there are three decimal places, we put 125 over 1000. Simplifying this fraction gives 1/8. Therefore, the decimal 12.125 can be written as the fraction 12 1/8 in lowest terms.
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45.
Convert the fraction 1,000 1/200 to a decimal
Correct Answer(s) 1000.005
Explanation To convert the fraction 1,000 1/200 to a decimal, we divide the numerator (1,000) by the denominator (200). This gives us 5. We then add the whole number part (1,000) to the decimal part (0.005) to get the final answer of 1,000.005.
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46.
Write out the word form for : 12.125
Correct Answer(s) twelve and one hundred twenty five thousandths
Explanation The word form for the number 12.125 is "twelve and one hundred twenty five thousandths." This is because the number 12 represents the whole number part, and the decimal part 0.125 is expressed as "one hundred twenty five thousandths."
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