Evaluate 4 1/2−2−5 2/3
Responses
A
–3 1/6
B
12 1/6
C 2 1/6
D-4 1/6
To evaluate the expression 4 1/2 - 2 - 5 2/3, we need to convert all the mixed numbers to improper fractions.
4 1/2 = 9/2
5 2/3 = 17/3
Now we can subtract:
9/2 - 2 - 17/3
To simplify this expression, we need a common denominator. The least common multiple of 2 and 3 is 6.
Converting all fractions to have a denominator of 6:
(9/2)*(3/3) - (2)*(3/3) - (17/3)*(2/2)
27/6 - 6/6 - 34/6
Now subtract the fractions:
27/6 - 6/6 - 34/6 = (27 - 6 - 34)/6 = -13/6
The final answer is -13/6, which can also be written as -2 1/6.
So the correct answer is C) -2 1/6.
Evaluate this expression.
32 + (−72.1)
To evaluate the expression 32 + (-72.1), simply add the two numbers together.
32 + (-72.1) = -40.1
Therefore, the answer is -40.1.
Evaluate this expression.
42.86 − 23.42
To evaluate the expression 42.86 - 23.42, simply subtract the two numbers.
42.86 - 23.42 = 19.44
Therefore, the answer is 19.44.
Determine the value of the expression –5.45 + 4.12 –8.66.
Responses
To determine the value of the expression –5.45 + 4.12 – 8.66, we need to add the three numbers together.
–5.45 + 4.12 – 8.66 = -5.45 + 4.12 - 8.66.
To add these numbers, combine the like terms:
-5.45 + 4.12 - 8.66 = (-5.45 + 4.12) - 8.66 = -1.33 - 8.66.
Now subtract:
-1.33 - 8.66 = -9.99.
Therefore, the value of the expression –5.45 + 4.12 – 8.66 is -9.99.
7 2/3+−5 1/4
To add the mixed numbers 7 2/3 and -5 1/4, we first need to convert them to improper fractions.
7 2/3 = (7 * 3 + 2)/3 = 23/3
-5 1/4 = (-5 * 4 + 1)/4 = -19/4
Now we can add the fractions:
23/3 + (-19/4)
To add fractions with different denominators, we need a common denominator. The least common multiple of 3 and 4 is 12.
Converting all fractions to have a denominator of 12:
(23/3)*(4/4) + (-19/4)*(3/3)
92/12 + (-57/12)
Now add the fractions:
92/12 + (-57/12) = (92 - 57)/12 = 35/12
The final answer is 35/12, which cannot be simplified any further.
To evaluate the expression 4 1/2 - 2 - 5 2/3, we need to follow the order of operations, which is parentheses, exponents, multiplication and division (left to right), and addition and subtraction (left to right).
First, let's simplify the subtraction of fractions. To do this, we need a common denominator. In this case, the denominator can be found by multiplying the two denominators together: 2 * 3 = 6.
Now let's convert the mixed numbers to improper fractions.
4 1/2 can be written as (4 * 2 + 1) / 2 = 9/2.
Similarly, 5 2/3 can be written as (5 * 3 + 2) / 3 = 17/3.
Our expression now becomes:
9/2 - 2 - 17/3.
Next, let's subtract the fractions. Since we have a mixed number, we need to convert it back to a mixed number once we have our answer.
To subtract the fractions, we need to find a common denominator, which is 6.
9/2 can be written as (9 * 3) / (2 * 3) = 27/6.
Now the expression becomes:
27/6 - 2 - 17/3.
Combining the fractions, we get:
(27 - 2 * 6 - 17 * 2) / 6 = (27 - 12 - 34) / 6 = (15 - 34) / 6 = -19/6.
So the answer is -19/6.
In mixed number form, -19/6 can be written as -3 1/6.
Therefore, the correct answer is option A: -3 1/6.