Simplify, 12 divided by 1/4+2/5-2^3
1/4 + 2/5 -2^3 =1/4 + 2/5 -8
1/4 + 2/5 -2^3 =(1*5)/(4*5)+(2*4)/(5*4)-8*20/20=
5/20 + 8/20 - 160/20 =(5+8-160)/20= -147/20
12=(12*20)/20=240/20
12/(1/4+2/5-2^3)=(240/20)/(-147/20)=
(240*20)//-147*20)= -240/147
2/3-5/12+4/9 simplify
To simplify the expression, we follow the order of operations (PEMDAS), which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
First, let's simplify the exponent:
2^3 = 2 * 2 * 2 = 8
Now let's simplify the expression:
12 divided by 1/4 + 2/5 - 8
We need to find a common denominator for the fractions. The least common denominator (LCD) of 4 and 5 is 20. So we can convert both fractions to have 20 as the denominator:
1/4 multiplies numerator and denominator by 5: (1 * 5) / (4 * 5) = 5/20
2/5 multiplies numerator and denominator by 4: (2 * 4) / (5 * 4) = 8/20
Now the expression becomes:
12 / (5/20 + 8/20) - 8
Next, we can simplify the addition inside the parentheses:
5/20 + 8/20 = 13/20
Now the expression becomes:
12 / (13/20) - 8
To divide by a fraction, we can multiply by its reciprocal (flip the numerator and denominator):
12 * (20/13) - 8
Now we can calculate:
240/13 - 8
In order to subtract the whole number from a fraction, the whole number needs to be converted to a fraction with the same denominator:
240/13 - (8 * 13/13) = 240/13 - 104/13
Now we can subtract the fractions:
(240 - 104)/13 = 136/13
So, the simplified expression is 136/13.