1.which of the following is not true for adding mixed numbers?
A.the denominators of the fractions must be the same in order to add them.
B.you can add mixed numbers by changing them into improper fractions or by using a number line.
C.the sum of the mixed numbers written as an improper fraction is in simplest form.
D.the sum of the mixed numbers must be written in simplest form.
2.joe was making mixed nuts.he used 2 1/4 pounds of pecans and 3 1/5 pounds of cashews.how many pounds of mixed nuts did joe make?
A.5 17/40
B.5 2/9
C.5 1/2
D.5 9/20
3.trent bought 3 3/4 pounds of strawberries and 2 1/6 pounds of raspberries at the farmers market.how many total pounds of fruit did trent buy?
A.5 1/12
B.2 2/5
C.5 11/12
D.5 1/6
4.Last week,mrs.hale worked 42 1/2hours,and this week,she worked 41 1/3hours.how many hours did she work in the last two weeks?
A.83 5/6
B.84 2/3
C.83 2/3
D.83 2/5
5.a chemist mixes 2 3/5g of an element and 16 4/9g of another element.when the two are mixed,what is the total mass in simplest form?
A.18 1/2 g
B.18 2/45g
C.19 2/45g
D.18 1/4g
1. The answer is D. The sum of the mixed numbers must be written in simplest form, but that's not a requirement for adding mixed numbers. It's just a good practice.
2. Joe made a total of B. 5 2/9 pounds of mixed nuts. That's quite a nutty combination!
3. Trent bought a total of C. 5 11/12 pounds of fruit. Looks like they'll have plenty of fruity goodness to enjoy!
4. Mrs. Hale worked a total of B. 84 2/3 hours over the past two weeks. That's a lot of hours, she must be exhausted!
5. When the two elements are mixed, the total mass is C. 19 2/45g. Keep mixing those elements, chemist!
1. The correct answer is C. The sum of the mixed numbers written as an improper fraction is in simplest form.
2. To find the total pounds of mixed nuts Joe made, we need to add the pounds of pecans (2 1/4) and the pounds of cashews (3 1/5). The answer is A. 5 17/40.
3. To find the total pounds of fruit Trent bought, we need to add the pounds of strawberries (3 3/4) and the pounds of raspberries (2 1/6). The answer is C. 5 11/12.
4. To find the total hours Mrs. Hale worked in the last two weeks, we need to add the hours she worked last week (42 1/2) and the hours she worked this week (41 1/3). The answer is B. 84 2/3.
5. To find the total mass when the two elements are mixed, we need to add the mass of the first element (2 3/5g) and the mass of the second element (16 4/9g). The answer is C. 19 2/45g.
1. To answer this question, we need to evaluate each statement and see which one is not true.
Statement A: The denominators of the fractions must be the same in order to add them. - This is true. When adding fractions, the denominators need to be the same.
Statement B: You can add mixed numbers by changing them into improper fractions or by using a number line. - This is true. Adding mixed numbers can be done by converting them into improper fractions or by using a number line.
Statement C: The sum of the mixed numbers written as an improper fraction is in simplest form. - This statement is not true. The sum of mixed numbers may not always be in simplest form. It may require further simplification.
Statement D: The sum of the mixed numbers must be written in simplest form. - This statement is true. When adding mixed numbers, it is generally preferable to write the sum in simplest form.
Therefore, the answer to question 1 is: C. the sum of the mixed numbers written as an improper fraction is in simplest form.
2. To find the answer to this question, we need to add the given mixed numbers:
2 1/4 + 3 1/5
To add mixed numbers, we first convert them into improper fractions:
2 1/4 = (2 * 4 + 1) / 4 = 9/4
3 1/5 = (3 * 5 + 1) / 5 = 16/5
Now, we add the improper fractions:
9/4 + 16/5 = (9 * 5 + 4 * 16) / (4 * 5) = 45/20 + 64/20 = 109/20
Since the answer is an improper fraction, we can simplify it:
109/20 = 5 9/20
Therefore, the answer to question 2 is: A. 5 9/20 pounds
3. To find the answer to this question, we need to add the given mixed numbers:
3 3/4 + 2 1/6
Again, we convert the mixed numbers into improper fractions:
3 3/4 = (3 * 4 + 3) / 4 = 15/4
2 1/6 = (2 * 6 + 1) / 6 = 13/6
Now, we add the improper fractions:
15/4 + 13/6 = (15 * 6 + 4 * 13) / (4 * 6) = 90/24 + 52/24 = 142/24
The answer is an improper fraction, so we can simplify it:
142/24 = 5 11/12
Therefore, the answer to question 3 is: C. 5 11/12 pounds
4. To find the answer to this question, we need to add the given mixed numbers:
42 1/2 + 41 1/3
Converting the mixed numbers to improper fractions:
42 1/2 = (42 * 2 + 1) / 2 = 85/2
41 1/3 = (41 * 3 + 1) / 3 = 124/3
Adding the improper fractions:
85/2 + 124/3 = (85 * 3 + 2 * 124) / (2 * 3) = 255/2 + 248/6 = 765/6 + 248/6 = 1013/6
Simplifying the answer:
1013/6 = 83 5/6
Therefore, the answer to question 4 is: A. 83 5/6 hours
5. To find the answer to this question, we need to add the given mixed numbers:
2 3/5 + 16 4/9
Convert the mixed numbers to improper fractions:
2 3/5 = (2 * 5 + 3) / 5 = 13/5
16 4/9 = (16 * 9 + 4) / 9 = 148/9
Adding the improper fractions:
13/5 + 148/9 = (13 * 9 + 5 * 148) / (5 * 9) = 117/5 + 740/45 = 117/5 + 740/45 = (117 * 9 + 5 * 740) / (5 * 9) = 1053/5 + 3700/45 = (1053 * 9 + 5 * 3700) / (5 * 9) = 9477/5 + 18500/45 = 35886/45
Simplifying the answer:
35886/45 = 796 26/45
Therefore, the answer to question 5 is: C. 796 26/45 g
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