please explian this not sure about fractions thanks :)
1/3, 5/6 , and 3/8 =
add the fractions reduce to loewst terms
To start, all the fractions must have a common denominator (bottom number). That will be the lowest number by which all the denominators (3, 6, and 8) can be divided.
In this case, the common denominator is 24.
Now you need to see how to change all the fractions to have the common denominator.
Start with 1/3. By multiplying the top and bottom by 8, we can get 8/24. You just have to see what number you need to multiply by so that you can have 24 on bottom. Use a similar process for 5/6 and 3/8, and then add the numerators to get your final answer.
First, find a common denominator. What number is evenly divisible by 3, 6, and 8?
The common denominator for this fractions is 24.
Then, since 3 goes into 24 eight times, we multiply the numerator by 8.
1/3 = 8/24
Since 6 goes into 24 four times,
5/6 = 20/24
3/8 = 9/24
8/24 + 20/24 + 9/24
Now add the numerators
8/24 + 20/24 + 9/24 = 37/24
Divide 37 by 24 to get the lowest terms.
37/24 = 1 13/24
To add fractions, you need to have a common denominator. In this case, you can find the common denominator by finding the least common multiple (LCM) of the denominators 3, 6, and 8.
The LCM of 3, 6, and 8 is 24. Now, you need to convert each fraction so that they all have a denominator of 24.
For the fraction 1/3:
Multiply the numerator and denominator by 8 to get: (1/3) x (8/8) = 8/24
For the fraction 5/6:
Multiply the numerator and denominator by 4 to get: (5/6) x (4/4) = 20/24
For the fraction 3/8:
Multiply the numerator and denominator by 3 to get: (3/8) x (3/3) = 9/24
Now that all the fractions have the same denominator, you can simply add the numerators:
8/24 + 20/24 + 9/24 = (8 + 20 + 9)/24 = 37/24
To reduce the fraction to its lowest terms, you need to find the greatest common divisor (GCD) of the numerator and denominator, and then divide both by the GCD.
In this case, the GCD of 37 and 24 is 1. So, dividing both the numerator and denominator by 1:
37/24 รท 1/1 = 37/24
Therefore, the sum of the fractions 1/3, 5/6, and 3/8 is 37/24.
To add fractions, you need to have a common denominator. A common denominator is a number that can be divided evenly by the denominators of all the fractions involved.
In this case, the denominators of the fractions are 3, 6, and 8. To find the least common denominator, you can start by listing the multiples of each denominator:
- For 3: 3, 6, 9, 12, ...
- For 6: 6, 12, 18, 24, ...
- For 8: 8, 16, 24, 32, ...
From these lists, you can see that 24 is the least common denominator because it is the smallest number that appears in all three lists.
Now, you need to convert each fraction so it has a denominator of 24:
- For 1/3: Multiply the numerator and denominator by 8, which gives you 8/24.
- For 5/6: Multiply the numerator and denominator by 4, which gives you 20/24.
- For 3/8: Multiply the numerator and denominator by 3, which gives you 9/24.
Now that all three fractions have a common denominator of 24, you can add them together:
8/24 + 20/24 + 9/24 = 37/24.
However, it is always good to simplify the fraction to its lowest terms, if possible. In this case, the numerator and denominator have a common factor of 1, so the fraction cannot be simplified any further.
Therefore, the sum of 1/3, 5/6, and 3/8 is 37/24.