What is 2/7 - 1/4 + 9/14? What is the LCD? And how did you find it?
2/7 - 1/4 + 9/14
One way to find the LCD is to find the multiples of the largest denominator. It must be also divisible by the other denominators.
14, 28, 42
Ah -- 28 is also divisible by 7 and 2.
The LCD is 28.
To calculate the expression 2/7 - 1/4 + 9/14, we need to find the least common denominator (LCD). The LCD is the smallest multiple that two or more denominators have in common.
To find the LCD, we first need to identify the denominators in the expression: 7, 4, and 14.
To determine the LCD, we need to factorize these denominators.
The prime factors of 7 are 7 itself.
The prime factors of 4 are 2 and 2.
The prime factors of 14 are 2 and 7.
Next, we look for the highest exponent of each prime factor. In this case, the highest exponent of 2 is 2 (since it appears twice in the factorization of 4) and the highest exponent of 7 is 1.
Multiplying these highest exponents together, we get 2 * 1 = 2.
So the LCD is 2^2 * 7, which simplifies to 4 * 7 = 28.
Now that we have the LCD, we can proceed to find the solution. We need to rewrite each fraction with the new denominator of 28:
2/7 = (2/7) * (4/4) = 8/28
1/4 = (1/4) * (7/7) = 7/28
9/14 = (9/14) * (2/2) = 18/28
Now we can substitute these equivalent fractions into the original expression:
2/7 - 1/4 + 9/14 becomes (8/28) - (7/28) + (18/28).
Combining the numerators with the common denominator, we get:
= (8 - 7 + 18) / 28
= 19/28
Therefore, the solution to 2/7 - 1/4 + 9/14 is 19/28.
In summary, to find the LCD for the denominators, we factorize each denominator, identify the highest exponent for each prime factor, and multiply these highest exponents together.