(47- 4/5) - (1/11-16
To simplify the expression (47 - 4/5) - (1/11 - 16), we need to first simplify the terms inside the parentheses and then perform the subtraction.
Starting with the first set of parentheses:
47 - 4/5 = 47 * 5/5 - 4/5 = 235/5 - 4/5 = (235 - 4)/5 = 231/5
Now let's simplify the second set of parentheses:
1/11 - 16 = 1/11 - 176/11 = (1 - 176)/11 = -175/11
Substituting the simplified expressions back into the original expression, we have:
(47 - 4/5) - (1/11 - 16) = 231/5 - (-175/11)
To subtract fractions, we need to have a common denominator. The least common multiple of 5 and 11 is 55, so we rewrite the fractions with a common denominator:
(231/5)*(11/11) - (-175/11)*(5/5)
= 231/55 + 875/55
= (231 + 875)/55
= 1106/55
= 22
Therefore, (47 - 4/5) - (1/11 - 16) simplifies to 22.
Let's break down the expression step-by-step:
1. Subtracting a fraction from a whole number:
47 - 4/5 = (47 * 5)/5 - 4/5
= (235/5) - 4/5
= (235 - 4)/5
= 231/5
2. Subtracting a fraction from another fraction:
1/11 - 16 = 1/11 - (16 * 11)/11
= 1/11 - 176/11
= (1 - 176)/11
= -175/11
3. Subtracting the results from step 1 and step 2:
(231/5) - (-175/11) = (231 * 11)/(5 * 11) - (-175 * 5)/(11 * 5)
= (2541/55) + (875/55)
= (2541 + 875)/55
= 3416/55
Therefore, (47 - 4/5) - (1/11 - 16) equals 3416/55.