How would you group the following expression to make it easier to add?
18−(9 4/9) +(7/9)−8
To make it easier to add the given expression, we can group the like terms together.
First, we can combine the whole numbers and fractions separately:
18 - 8 = 10
(9 4/9) + (7/9) = 9 (4/9 + 7/9) = 9 (11/9)
Now, we have:
10 - 9 (11/9)
To make the subtraction easier, we can convert 10 to a mixed number:
10 = 9 1/9
Now, we have:
9 1/9 - 9 (11/9)
We can further convert 9 to a fraction with a common denominator:
9 = 9/1
Now, we have:
9/1 1/9 - 9 (11/9)
To subtract fractions with different denominators, we need to find a common denominator. The least common multiple (LCM) of 1 and 9 is 9. So, we can rewrite the expression as:
(9/1)(9/9) + 1/9 - 9 (11/9)
Simplifying within the parentheses:
(81/9) + 1/9 - (99/9)
Combining like terms:
82/9 - 99/9
Now, we have:
(82 - 99)/9
Finally, we can subtract:
-17/9
Therefore, the grouped and simplified expression is -17/9.
To group the expression in a way that makes it easier to add, you can perform the following steps:
1. First, simplify the fraction 9 4/9.
This can be done by multiplying the whole number (9) by the denominator (9) and then adding the numerator (4):
9 * 9 + 4 = 81 + 4 = 85
So, the expression becomes: 18 - 85 + (7/9) - 8
2. Next, add the whole numbers together:
18 - 85 + (7/9) - 8 = -67 + (7/9) - 8
3. Finally, combine the remaining terms:
-67 + (7/9) - 8 = -67 - 8 + (7/9)
Now the expression is grouped in a way that makes it easier to add.