minus 1 and 3 tenths plus left parenthesis minus 4 and 2 fifteenths right parenthesis
Using parentheses to clarify the computation, the expression "minus 1 and 3 tenths plus left parenthesis minus 4 and 2 fifteenths right parenthesis" can be written as:
-1.3 + (-4 + 2/15)
To simplify this expression, we need to start from the innermost parentheses and work our way out.
-4 + 2/15 can be simplified by finding a common denominator for the subtraction:
-4 + 2/15 = -4 * 15/15 + 2/15 = -60/15 + 2/15 = -58/15
Now, we can substitute this value back into the original expression:
-1.3 + (-58/15)
Next, we need to find a common denominator for addition:
-1.3 = -1 * 10/10 + 3/10 = -10/10 + 3/10 = -7/10
Now, we can substitute this value back into the overall expression:
-7/10 + (-58/15)
To add or subtract fractions, we need a common denominator. The least common multiple (LCM) of 10 and 15 is 30:
-7/10 = -7 * 3/3 * 10 = -21/30
-58/15 = -58 * 2/2 * 15 = -116/30
Substituting these values back into the expression:
-21/30 + (-116/30) = -137/30
Therefore, the simplified expression is -137/30.
To solve this expression:
Start by simplifying the operation inside the parentheses:
Minus 4 and 2 fifteenths can be written as -4 - 2/15.
Now add -1 and 3 tenths to this simplified expression:
(-4 - 2/15) + (-1 + 3/10)
Next, combine like terms:
-4 + (-1) = -5
-2/15 + 3/10 can be converted to a common denominator:
To find a common denominator, multiply 10 and 15:
10 × 15 = 150
(-2/15) becomes (-20/150) and (3/10) becomes (45/150).
Therefore, we can now rewrite the expression as:
-5 + (-20/150) + (45/150)
Adding the fractions:
-20/150 + 45/150 = 25/150
Simplifying:
25/150 can be reduced by dividing both the numerator and denominator by 25:
25 ÷ 25 = 1
150 ÷ 25 = 6
So, 25/150 can be simplified to 1/6.
Now substitute this value back into the expression:
-5 + (1/6)
Simplifying further:
To add fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 6.
So, -5 can be written as (-30/6) because -5 × 6 = -30.
Therefore, the final step is:
(-30/6) + (1/6) = -29/6.
Thus, the expression minus 1 and 3 tenths plus left parenthesis minus 4 and 2 fifteenths right parenthesis simplifies to -29/6.