Consider this expression:
1/4 − 0.5 + 1/2 − 0.25 + 3/5 + 0.4
To simplify the expression, we can start by combining like terms:
1/4 - 0.5 = -0.25
1/2 - 0.25 = 0.25
Now the expression becomes:
-0.25 + 0.25 + 3/5 + 0.4
Next, we can add the fractions:
3/5 can be converted to the same denominator as 1/5 by multiplying the numerator and denominator by 2.
(3/5) * (2/2) = 6/10
Now the expression becomes:
-0.25 + 0.25 + 6/10 + 0.4
We can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor (which is 2 in this case):
6/10 = (6 ÷ 2) / (10 ÷ 2) = 3/5
Finally, the expression becomes:
-0.25 + 0.25 + 3/5 + 0.4 = 0 + 3/5 + 0.4
Now we can add the remaining terms:
0 + 3/5 + 0.4 = 0.6 + 0.4 = 1
So, the simplified expression is 1.
To simplify the expression, we need to perform the addition and subtraction in the given sequence.
First, we can add the fractions together:
1/4 + 1/2 + 3/5
To add fractions, we need to find a common denominator. In this case, we can use 20 as the least common denominator (LCD).
1/4 × 5/5 = 5/20
1/2 × 10/10 = 10/20
3/5 × 4/4 = 12/20
Now we can combine the fractions:
5/20 + 10/20 + 12/20 = (5 + 10 + 12) / 20 = 27/20
Next, we can add the decimal numbers:
-0.5 - 0.25 + 0.4
We can simply add these numbers:
-0.5 - 0.25 + 0.4 = -1.25 + 0.4 = -0.85
Finally, we can add the fractions and decimal number together:
27/20 + (-0.85)
To add fractions and a decimal number together, we need to convert the decimal number into a fraction. Since -0.85 is equivalent to -85/100, we can write it as -85/100.
Now we can combine the fractions:
27/20 + (-85/100)
To add fractions, we need to find a common denominator. In this case, we can use 100 as the least common denominator (LCD).
27/20 × 5/5 = 135/100
Now we can combine the fractions and decimal number:
135/100 + (-85/100) = (135 - 85) / 100 = 50/100 = 1/2
Therefore, the simplified expression is 1/2.
To simplify the given expression, you need to perform the following operations in order: addition and subtraction. The general rule to remember is to perform the operations from left to right.
Let's break down the expression step by step:
Step 1: Addition and Subtraction
1/4 − 0.5 + 1/2 − 0.25 + 3/5 + 0.4
First, let's add and subtract the numbers on the left side:
1/4 − 0.5 = -0.25 (subtracting 0.5 from 1/4)
-0.25 + 1/2 = 0.25 (adding 1/2 to -0.25)
0.25 − 0.25 = 0 (subtracting 0.25 from 0.25)
Now, let's move to the right side:
0 + 3/5 = 3/5 (adding 3/5 to 0)
3/5 + 0.4 = 2/10 + 4/10 = 6/10 = 3/5 (adding 0.4 to 3/5)
Step 2: Final Result
The final simplified expression is 3/5.
In summary, to simplify the expression, you performed the addition and subtraction operations from left to right, combining the terms and fractions as you went along.