Consider this expression:
1/4− 0.5 + 1/2− 0.25 + 3/5+ 0.4
To simplify the expression 1/4 - 0.5 + 1/2 - 0.25 + 3/5 + 0.4, follow these steps:
Step 1: Combine the like terms.
1/4 - 0.5 = -0.25 + 1/2 - 0.25 = 1/2 - 0.5 = -0.5
3/5 + 0.4 = 3/5 + 2/5 = 5/5 = 1
Step 2: Add all the combined terms together.
-0.5 + 1 = 0.5
Therefore, the simplified form of the expression is 0.5.
To simplify this expression, we can combine like terms.
First, let's consider the fractions:
1/4 + 1/2 + 3/5
To add fractions, we need to find a common denominator. The least common multiple of 4, 2, and 5 is 20.
1/4 is equivalent to 5/20 (since we multiply the numerator and denominator by 5)
1/2 is equivalent to 10/20 (since we multiply the numerator and denominator by 10)
3/5 remains the same
Thus, the sum of these fractions is:
5/20 + 10/20 + 3/5 = 18/20 + 3/5
To add these fractions, we need a common denominator of 20.
18/20 + 3/5 = (18 * 1)/(20 * 1) + (3 * 4)/(5 * 4) = 18/20 + 12/20 = 30/20 = 3/2
Now, let's consider the decimal numbers:
0.5 - 0.25 + 0.4
We can simply add these decimal numbers:
0.5 + (-0.25) + 0.4 = 0.65
Finally, we add the sum of the fractions (3/2) and the sum of the decimal numbers (0.65):
3/2 + 0.65 = 1.5 + 0.65 = 2.15
Therefore, the simplified value of the expression 1/4 − 0.5 + 1/2 − 0.25 + 3/5 + 0.4 is 2.15.
To simplify the given expression, we need to perform addition and subtraction operations according to the order of operations (also known as PEMDAS or BODMAS).
Let's break down the expression step by step:
1/4 - 0.5 + 1/2 - 0.25 + 3/5 + 0.4
First, let's combine the two fractions:
1/4 - 0.5 + 1/2 - 0.25 + 3/5 + 0.4 = (1/4 + 1/2) - 0.5 - 0.25 + 3/5 + 0.4
Next, let's find the common denominator for the fractions:
The common denominator for 1/4 and 1/2 is 4, so we can rewrite them as:
1/4 = 1/4 * 2/2 = 2/8
1/2 = 1/2 * 4/4 = 4/8
Now, let's substitute these fractions back into the expression:
(2/8 + 4/8) - 0.5 - 0.25 + 3/5 + 0.4
Now, let's add the fractions with the same denominator:
(6/8) - 0.5 - 0.25 + 3/5 + 0.4
Next, let's find the least common denominator (LCD) between 8 and 5, which is 40.
Now, we need to adjust all the fractions in the expression to have the same denominator of 40:
(6/8 * 5/5) - 0.5 * 40/40 - 0.25 * 40/40 + 3/5 * 8/8 + 0.4 * 8/8
Simplifying further:
(30/40) - 20/40 - 10/40 + 24/40 + 3.2/8
Finally, let's add and subtract the values:
30/40 - 20/40 - 10/40 + 24/40 + 3.2/8 = 27/40 + 3.2/8
Now, let's find the common denominator for 40 and 8, which is 320:
27/40 + 40/320 + 3.2/320
To add these fractions, we need to have the same denominator:
(27/40 * 8/8) + 40/320 + 3.2/320
Simplifying:
216/320 + 40/320 + 3.2/320
Now, let's add the fractions:
(216 + 40 + 3.2)/320
Finally:
259.2/320
Now, let's simplify the fraction (reduce it to its simplest form) by dividing the numerator and the denominator by their greatest common divisor, which is 16:
259.2/320 = (259.2/16) / (320/16) = 16.2/20
So, the simplified expression is 16.2/20.