what is 4 over 21 − (−3 over 7) − 5 over 9
To simplify the expression, we need to find a common denominator for the fractions involved.
The denominators of the fractions are 21, 7, and 9.
To find the least common multiple (LCM) of these numbers, we can write out the multiples of each number until we find a common multiple.
For 21: 21, 42, 63, ...
For 7: 7, 14, 21, ...
For 9: 9, 18, 27, ...
We can see that the least common multiple (LCM) of 21, 7, and 9 is 63.
Now, we can rewrite the fractions using this common denominator.
The first fraction, 4/21, becomes (4/21) * (3/3) = 12/63.
The second fraction, -3/7, becomes (-3/7) * (9/9) = -27/63.
The third fraction, 5/9, remains as 5/9.
Now, we can substitute these values back into the expression:
12/63 - (-27/63) - 5/9
Next, we can simplify the expression by combining like terms.
12/63 + 27/63 - 5/9
The numerators of the fractions can be added since they have the same denominator.
(12+27)/63 - 5/9
The numerator becomes 39/63, and the denominator remains 63.
39/63 - 5/9
To combine these fractions, we need to find a common denominator again.
The denominators of the fractions are 63 and 9.
Again, we can find the LCM of these numbers.
For 63: 63, 126, 189, ...
For 9: 9, 18, 27, ...
The LCM of 63 and 9 is 63.
Now, we can rewrite the fractions using this common denominator.
(39/63) * (1/1) - (5/9) * (7/7)
This simplifies to:
39/63 - 35/63
Now, subtract the numerators:
(39-35)/63 = 4/63
Therefore, 4/21 − (-3/7) − 5/9 equals 4/63.
(10−6)^2 + 8 − 2^2.
To evaluate the expression (10−6)^2 + 8 − 2^2, we follow the order of operations:
First, we calculate the exponentiation within parentheses:
(10−6)^2 = 4^2 = 16.
Now, we substitute this value back into the expression:
16 + 8 − 2^2.
Next, we calculate the exponentiation of the remaining term:
2^2 = 2 * 2 = 4.
Now, we substitute this value back into the expression:
16 + 8 − 4.
Finally, we perform the addition and subtraction:
16 + 8 − 4 = 24 − 4 = 20.
Therefore, the expression (10−6)^2 + 8 − 2^2 equals 20.
1 over 4 − (−5 over 8)
To evaluate the expression 1 over 4 − (-5 over 8), we need to find a common denominator for the fractions involved.
The denominators of the fractions are 4 and 8.
To find a common denominator, we can observe that 8 is already a multiple of 4. Therefore, the common denominator is 8.
Now, we can rewrite the fractions using this common denominator.
1 over 4 becomes 2 over 8 because 1 multiplied by 2 equals 2.
-5 over 8 remains as -5 over 8.
Now, we can substitute these values back into the expression:
2 over 8 - (-5 over 8)
Next, since the denominators are the same, we can subtract the numerators directly.
(2 - (-5)) over 8
The double negative in front of -5 changes it to a positive number.
So, the expression simplifies to:
(2 + 5) over 8
The numerator now becomes 7.
Therefore, 1 over 4 − (-5 over 8) equals 7 over 8.
10.82 − 9.99
To subtract 9.99 from 10.82, you align the decimal points vertically and then perform the subtraction:
10.82
- 9.99
____________
0.83
Therefore, 10.82 − 9.99 equals 0.83.
260 − (−45) − 45
To evaluate the expression 260 − (-45) - 45, we start by simplifying the double negative (-45). A double negative becomes a positive number, so -(-45) is equal to 45.
Now we substitute the value back into the expression:
260 - 45 - 45
Next, we perform the subtraction from left to right:
260 - 45 = 215
215 - 45 = 170
Therefore, 260 - (-45) - 45 equals 170.