6−14⋅28−2 1/4_______3/4+4⋅2−11
To solve this problem, follow the order of operations (PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) to simplify each expression separately and then perform the operations that are left.
First, simplify each expression separately:
6 − (14 ⋅ 28) − (2 1/4)
= 6 - (392) - (2 1/4)
= 6 - 392 - 2 1/4
= 6 - 392 - 9/4 (since 2 1/4 = 9/4 in improper fraction form)
Next, simplify the other expression:
3/4 + (4 ⋅ 2) - 11
= 3/4 + (8) - 11
= 3/4 + 8 - 11
Now, perform the remaining operations:
6 - 392 - 9/4 (separate expression)
= -386 - 9/4
3/4 + 8 - 11 (separate expression)
= -9 1/4 (since 3/4 + 8 = 8 3/4, and 8 3/4 - 11 = -9 1/4)
Therefore, the final answer is -386 - 9/4 = -386 9/4 or -9 1/4.
To simplify the given expression, let's break it down step by step.
Starting with the numerator:
6 − 14 × 28 − 2 1/4
First, we need to address the division, which is represented by the fraction 2 1/4. To convert it into a proper fraction, multiply the whole number, 2, by the denominator, 4, and add the numerator, 1. The result is 9/4.
Now, we can substitute the fraction back into the expression:
6 − 14 × 28 − 9/4
Next, multiply the numbers within the parentheses:
6 − 392 − 9/4
Now, let's simplify the denominator:
To add fractions, we need to have a common denominator. The denominator of the first fraction, 3/4, is 4, which is already a common denominator. So we can rewrite the expression as:
(3/4) + 4 × 2 − 11
Now, let's simplify the denominator further:
Multiply across:
(3/4) + 8 - 11
Combine these terms:
(3/4) - 3
To subtract fractions, we need a common denominator, which is already 4 in this case.
Rewrite the expression:
(3/4) - (12/4)
Subtract the numerators and maintain the common denominator:
-9/4
Therefore, the numerator simplifies to -9/4, and the denominator remains the same (which is 3/4) since we haven't altered it.
Hence, the final simplified expression is:
(-9/4) / (3/4) + 4 × 2 − 11
To solve the expression:
6 - 14 × 28 - 2 1/4 _______ 3/4 + 4 × 2 - 11
Let's break it down step-by-step:
Step 1: Perform multiplications and divisions from left to right
6 - (14 × 28) - 2 1/4 _______ (3/4 + (4 × 2)) - 11
6 - 392 - 2 1/4 _______ (3/4 + 8) - 11
Step 2: Simplify the mixed fraction
6 - 392 - 9/4 _______ (3/4 + 8) - 11
Step 3: Convert the mixed fraction to an improper fraction by finding a common denominator
6 - 392 - (9/4 × 4/4) _______ (3/4 + 8) - 11
6 - 392 - (36/16) _______ (3/4 + 8) - 11
Step 4: Simplify the expression inside the parentheses
6 - 392 - (9/2) _______ (3/4 + 8) - 11
Step 5: Simplify the addition and subtraction from left to right
6 - 392 - (9/2) _______ (24/4 + 32/4) - 11
6 - 392 - (9/2) _______ (56/4) - 11
6 - 392 - (9/2) _______ 14 - 11
Step 6: Simplify the expression further
6 - 392 - (9/2) _______ 3
-392 - (9/2) _______ 3
Step 7: Calculate the expression
-392 - (9/2)
To subtract a fraction from a whole number, we need to find a common denominator.
-392 = -392/1 and (9/2) = (18/2)
Therefore, the expression becomes:
-392/1 - 18/2
To subtract fractions, the denominators should be the same.
-392/1 - 18/2 = -392/1 - 9/1
Now, we can simply subtract the numerators:
-392 - 9 = -401
So, the expression becomes:
-401 _______ 3
Step 8: Calculate the final answer
-401 ÷ 3 = -133.67 (rounded to two decimal places)