Which of the following numbers should replace the missing denominator in order to add the fractions? 25/82 + 13/? (1 point)
Responses
13
28
25
82
7 answers
The missing denominator should be 82, because in order to add fractions, the denominators must be the same. So, the fractions 25/82 + 13/82 can be added together.
Find the least common multiple of 2 and 12.(1 point)
Responses
12
12
36
36
2
2
24
Responses
12
12
36
36
2
2
24
The least common multiple (LCM) of 2 and 12 is 12.
Jiani gets paid for a job every 9 weeks and Rosa gets paid for a job every 12 weeks. How many weeks will it take for them to get paid at the same time?
To find the number of weeks it will take for Jiani and Rosa to get paid at the same time, we need to find the least common multiple (LCM) of 9 and 12. The LCM is the smallest number that is divisible by both 9 and 12.
Prime factorizing 9: 9 = 3 * 3
Prime factorizing 12: 12 = 2 * 2 * 3
The LCM is found by taking the highest power of each prime factor that appears in either of the numbers. So, the LCM of 9 and 12 is 2 * 2 * 3 * 3 = 36.
Therefore, it will take 36 weeks for Jiani and Rosa to get paid at the same time.
Prime factorizing 9: 9 = 3 * 3
Prime factorizing 12: 12 = 2 * 2 * 3
The LCM is found by taking the highest power of each prime factor that appears in either of the numbers. So, the LCM of 9 and 12 is 2 * 2 * 3 * 3 = 36.
Therefore, it will take 36 weeks for Jiani and Rosa to get paid at the same time.
Vie wants to make friendship bracelets to sell. She has yellow, blue, and orange beads. She wants each bracelet to have a ratio of 3/10 blue and 1/10 yellow. What would be the remaining ratio of orange beads for each bracelet? Remember to simplify your ratio/fraction.
To find the ratio of orange beads for each bracelet, we need to subtract the ratios of blue and yellow beads from 1, as the sum of all the ratios should be 1.
Ratio of blue beads: 3/10
Ratio of yellow beads: 1/10
Adding these ratios together: 3/10 + 1/10 = 4/10
To find the remaining ratio of orange beads, we subtract 4/10 from 1:
1 - 4/10 = 10/10 - 4/10 = 6/10
The remaining ratio of orange beads for each bracelet is 6/10. We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:
6/10 = (6/2) / (10/2) = 3/5
Therefore, the simplified ratio of orange beads for each bracelet is 3/5.
Ratio of blue beads: 3/10
Ratio of yellow beads: 1/10
Adding these ratios together: 3/10 + 1/10 = 4/10
To find the remaining ratio of orange beads, we subtract 4/10 from 1:
1 - 4/10 = 10/10 - 4/10 = 6/10
The remaining ratio of orange beads for each bracelet is 6/10. We can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:
6/10 = (6/2) / (10/2) = 3/5
Therefore, the simplified ratio of orange beads for each bracelet is 3/5.