What is 4−1 1/4+1/2\
A.2 7/16
B. 2 3/4
C.2 1/4
D 3 1/4
To solve this problem, we need to follow the order of operations, which dictates that we perform any addition or subtraction before multiplication or division.
First, we simplify 4 - 1 1/4:
Since 1/4 can be written as 0.25, we have:
4 - 1 - 0.25
Next, we add 1/2 to the previous result:
4 - 1 - 0.25 + 0.5
Now, we solve from left to right:
4 - 1 = 3
3 - 0.25 + 0.5 = 2.75
Therefore, the answer is B. 2 3/4.
wrong
I apologize for the mistake. Let's solve the problem correctly.
To solve 4 - 1 1/4 + 1/2, we need to convert the mixed numbers to improper fractions.
4 can be written as 4/1.
1 1/4 can be written as (1 * 4 + 1)/4 = 5/4.
Now we can substitute these fractions into the expression:
4/1 - 5/4 + 1/2
To simplify this expression, we need to find a common denominator for the fractions. In this case, the common denominator is 4.
Multiplying the numerator and denominator of 4/1 by 4, we get 16/4.
So, the expression becomes:
16/4 - 5/4 + 1/2
Now we can subtract the fractions:
16/4 - 5/4 = (16 - 5)/4 = 11/4
Adding 11/4 and 1/2, we need to find a common denominator again. This time, it is 4.
Multiplying the numerator and denominator of 1/2 by 2, we get 2/4.
So, the expression becomes:
11/4 + 2/4
Now we can add the fractions:
11/4 + 2/4 = 13/4
To write this improper fraction as a mixed number, we divide the numerator (13) by the denominator (4):
13 ÷ 4 = 3 with a remainder of 1.
Therefore, the answer is:
3 1/4
So, the correct answer is D. 3 1/4.
To solve the expression 4 - 1 1/4 + 1/2, we need to follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
First, let's simplify the subtraction: 4 - 1 1/4.
To subtract mixed fractions, we need to make sure that the denominators are the same. The whole number 4 can be written as 4/1, so the expression becomes (4/1) - 1 1/4.
To get a common denominator, we multiply the denominator of the first fraction (1) by the denominator of the second fraction (4), and vice versa. This gives us:
(4/1) - (1/1) * (4/4) = 4/1 - 4/4 = 4/1 - 1/1 = 3/1 = 3.
Now, let's add 1/2 to the result we just obtained.
To add fractions, we need to have the same denominators. The whole number 3 can be written as 3/1, so the expression becomes 3/1 + 1/2.
To get a common denominator, we multiply the denominator of the first fraction (1) by the denominator of the second fraction (2), and vice versa. This gives us:
(3/1) * (2/2) + (1/2) = 6/2 + 1/2 = 7/2.
Finally, we need to simplify the mixed fraction 7/2.
7 divided by 2 equals 3 with a remainder of 1. So, the simplified mixed fraction 7/2 can be expressed as 3 1/2.
Therefore, the expression 4 - 1 1/4 + 1/2 equals 3 1/2.
The correct answer is B. 2 3/4.
To solve the equation 4 - 1 1/4 + 1/2, we can follow the order of operations, which is commonly known as PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).
Step 1: Simplify the subtraction 4 - 1 1/4.
4 - 1 1/4 can be rewritten as 4 - 5/4. To subtract these fractions, we need a common denominator, which in this case is 4. So we can rewrite the equation as:
4 - 5/4 = 16/4 - 5/4 = (16 - 5)/4 = 11/4.
Step 2: Add 11/4 + 1/2.
To add fractions, we also need a common denominator. In this case, the common denominator is 4. So we can rewrite the equation as:
11/4 + 1/2 = 11/4 + 2/4 = (11 + 2)/4 = 13/4.
Now, the equation is simplified to 13/4. We can convert this improper fraction to a mixed number to make it easier to understand.
To convert the fraction 13/4 to a mixed number, we divide 13 by 4. The quotient is 3 and the remainder is 1. So we can express 13/4 as the mixed number 3 1/4.
Therefore, the answer to the equation 4 - 1 1/4 + 1/2 is option D: 3 1/4.