Use the additive inverse to find −1223−(−856). Write the answer as a mixed number
Use the additive inverse to find −12 2/3−(−8 5/6). Write the answer as a mixed number
To find the additive inverse of a number, we change its sign. Therefore, the additive inverse of −8 5/6 is 8 5/6.
Now, let's rewrite the expression as −12 2/3 + 8 5/6.
To add these two mixed numbers, we need to find a common denominator. The least common multiple of 3 and 6 is 6. Therefore, we convert both fractions to have a denominator of 6.
−12 2/3 can be converted to −12 * 6/3 + 2/3 = −72/3 + 2/3 = −70/3.
8 5/6 can be converted to 8 * 6/6 + 5/6 = 48/6 + 5/6 = 53/6.
Now, we can rewrite the expression as −70/3 + 53/6.
To add these fractions, we need to have a common denominator which is 6. So, we convert −70/3 to −70 * 2/3 * 2 = -140/6.
Now, −140/6 + 53/6 = -87/6.
As a mixed number, -87/6 can be written as -14 3/6.
Simplifying further, we can convert 3/6 to 1/2. Therefore, the final answer is -14 1/2.
What is the distance between −8 and 16 on a number line?
To find the distance between -8 and 16 on a number line, we need to subtract the smaller value from the larger value. In this case, 16 is the larger value, and -8 is the smaller value.
So, the distance is 16 - (-8).
To subtract a negative number, we can rewrite it as addition of the positive value. Therefore, -8 can be rewritten as +8.
Therefore, the expression becomes 16 + 8.
Adding these two numbers gives us 24.
So, the distance between -8 and 16 on a number line is 24.
What is the distance between 18.25 and −7.4 on the number line?
To find the distance between 18.25 and -7.4 on the number line, we need to subtract the smaller value from the larger value. In this case, 18.25 is the larger value, and -7.4 is the smaller value.
So, the distance is 18.25 - (-7.4).
To subtract a negative number, we can rewrite it as addition of the positive value. Therefore, -7.4 can be rewritten as +7.4.
Therefore, the expression becomes 18.25 + 7.4.
Adding these two numbers gives us 25.65.
So, the distance between 18.25 and -7.4 on the number line is 25.65.
Solve the mathematical problem involving absolute value.
7−(2+|5−3|)
First, we need to evaluate the expression inside the absolute value, which is |5 - 3|.
The absolute value of 5 - 3 is 2.
Now, we can rewrite the expression as 7 - (2 + 2).
Next, we must simplify the expression inside the parentheses, which is 2 + 2 = 4.
Substituting this value back into the original expression, we have 7 - 4.
Finally, we can subtract 4 from 7 to get the final answer: 3.
Therefore, 7 - (2 + |5 - 3|) equals 3.
To find the expression (-1223) - (-856), we can use the additive inverse property. The additive inverse of a number is the number that when added to the original number, the result is zero.
The additive inverse of -856 is 856. So, we can rewrite the expression as (-1223) + 856.
Now, we can simply add these two numbers: -1223 + 856.
To add them, arrange the numbers vertically ensuring that the place values line up correctly:
-1223
+ 856
_______
Start by adding the digits in the rightmost column, which are 3 and 6. The sum is 9.
-1223
+ 856
_______
...9
Next, add the digits in the next column to the left, which are 2 and 5. The sum is 7.
-1223
+ 856
______
...79
Now, add the digits in the next column to the left, which are 2 and 8. The sum is 10. Write down 0 in the sum column and carry over 1 to the next column.
-1223
+ 856
______
.079
Finally, add the digits in the leftmost column, which is 1 and the carried over 1. The sum is 2.
-1223
+ 856
______
2079
So, the answer to the expression (-1223) - (-856) is 2079.
To write the answer as a mixed number, we divide the answer (2079) by the denominator of the fraction part (100) to get the whole number part and the remainder:
2079 ÷ 100 = 20 remainder 79
So, the mixed number form of the answer is 20 79/100.
To find the additive inverse of a number, we need to change its sign. So, the additive inverse of -856 is 856.
Now, we can rewrite the expression as -1223 + 856.
To subtract these two numbers, we need to consider their signs. Since -1223 is negative and 856 is positive, we can subtract them by adding their absolute values and keeping the sign of the number with the larger absolute value.
So, |-1223 + 856| = |-367|
The absolute value of -367 is 367.
Since -367 is negative, the answer can be written as a mixed number as -367 = -367 + 0/1.
Therefore, the answer is -367.