What is 2(1x1/2)+2(1x1/4)+2(1/2x1/4)
2(1x1/2)+2(1x1/4)+2(1/2x1/4)
2*(1/2) + 2*(1/4) + 2 * (1/8)
1 + (1/2) + (1/4) = 1 3/4
To simplify the expression 2(1x1/2)+2(1x1/4)+2(1/2x1/4), we can first perform the operations inside the parentheses, then evaluate the multiplication and addition.
1 x 1/2 equals 1/2.
1 x 1/4 equals 1/4.
1/2 x 1/4 can be simplified by multiplying the numerators (1 x 1) and denominators (2 x 4), resulting in 1/8.
Now, let's substitute these values back into the original expression:
2(1/2) + 2(1/4) + 2(1/8)
Multiplying 2 by each fraction:
2/2 + 2/4 + 2/8
Simplifying each fraction:
2/2 is equal to 1,
2/4 can be simplified by dividing the numerator and denominator by their greatest common divisor (2), resulting in 1/2,
2/8 can be simplified by dividing the numerator and denominator by their greatest common divisor (2), resulting in 1/4.
Now, let's substitute the simplified fractions back into the expression:
1 + 1/2 + 1/4
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 4.
1 is equivalent to 4/4,
1/2 can be multiplied by 2/2 (which is the same as multiplying by 1) to get 2/4,
1/4 remains the same.
Substituting the equivalent fractions back into the expression:
4/4 + 2/4 + 1/4
Now, we can combine the numerators:
(4 + 2 + 1)/4 = 7/4
Therefore, the simplified form of the expression 2(1x1/2)+2(1x1/4)+2(1/2x1/4) is 7/4.