Let's try it with Rational Numbers!
Answer the following problems in the space below. Label your answers 1-4.
1) 2.5 + 4.75=
2) −7.20 − 9.80=
3) −3
1
2 − −5=
4) −8 + 3
2
3=
1) 2.5 + 4.75 = 7.25
2) -7.20 - 9.80 = -17.00
3) -3 1/2 - (-5) = -1 1/2
4) -8 + 3 2/3 = -4 1/3
To solve these problems involving rational numbers, we will follow the steps below:
1) Addition or Subtraction of Rational Numbers:
To add or subtract rational numbers, we need to have a common denominator.
For example:
1) To solve 2.5 + 4.75:
First, convert both numbers to fractions.
2.5 is equivalent to 2.5/1 = 5/2
4.75 is equivalent to 4.75/1 = 19/4
Now, we need to find a common denominator for 2 and 4. The least common multiple (LCM) of 2 and 4 is 4.
Multiply the numerator and denominator of 5/2 by 2 to get a common denominator of 4:
5/2 * 2/2 = 10/4
Now, we can add the fractions:
10/4 + 19/4 = (10 + 19)/4 = 29/4
So, the answer to 2.5 + 4.75 is 29/4.
2) To solve -7.20 - 9.80:
First, convert both numbers to fractions.
-7.20 is equivalent to -7.20/1 = -720/100 = -36/5
-9.80 is equivalent to -9.80/1 = -980/100 = -49/5
Since both fractions already have a common denominator of 5, we can subtract the fractions directly:
-36/5 - 49/5 = (-36 - 49)/5 = -85/5 = -17
So, the answer to -7.20 - 9.80 is -17.
3) To solve -3 1/2 - (-5):
First, convert mixed number -3 1/2 to an improper fraction.
-3 1/2 is equivalent to -3 - 1/2 = -6/2 - 1/2 = -7/2
Now we can simplify the subtraction:
-7/2 - (-5) = -7/2 + 5 = -7/2 + 10/2 = (-7 + 10)/2 = 3/2
So, the answer to -3 1/2 - (-5) is 3/2.
4) To solve -8 + 3 2/3:
First, convert mixed number 3 2/3 to an improper fraction.
3 2/3 is equivalent to 3 + 2/3 = 9/3 + 2/3 = 11/3
Now we can simplify the addition:
-8 + 11/3 = -8/1 + 11/3
To find the common denominator, we multiply the denominator of the second fraction by the denominator of the first fraction:
-8 + 11/3 = -8/1 + (11/3 * 1/1) = -8/1 + 11/3 = -24/3 + 11/3 = (-24 + 11)/3 = -13/3
So, the answer to -8 + 3 2/3 is -13/3.
Now you can solve the problems and write the solutions labeled 1-4.
1) To add 2.5 and 4.75, we align the decimal points and add the numbers:
2.5
+ 4.75
-------
7.25
So, 2.5 + 4.75 = 7.25.
Answer 1: 7.25
2) To subtract -7.20 from -9.80, we align the decimal points and subtract the numbers:
-9.80
- (-7.20)
----------
-9.80 + 7.20 = -2.60
So, -7.20 - 9.80 = -2.60.
Answer 2: -2.60
3) To subtract -3 1/2 from -5, we first convert -3 1/2 to an improper fraction:
-3 1/2 = -7/2
Then we subtract the fractions:
-5
- (-7/2)
-----------
-5 + 7/2
To add the whole number and fraction, we need to find a common denominator. The common denominator here is 2, so we have:
-5 + 7/2 = -5 + 7/2
Next, we convert -5 to an improper fraction:
-5 = -10/2
Now we can rewrite the expression:
-10/2 + 7/2 = (-10 + 7)/2 = -3/2
So, -3 1/2 - (-5) = -3/2.
Answer 3: -3/2
4) To add -8 and 3 2/3, we first convert 3 2/3 to an improper fraction:
3 2/3 = 11/3
Then, we add the fractions:
-8 + 11/3
To add a whole number and fraction, we need to find a common denominator. The common denominator here is 3, so we have:
-8 + 11/3 = -8 + 11/3
Next, we convert -8 to an improper fraction:
-8 = -24/3
Now we can rewrite the expression:
-24/3 + 11/3 = (-24 + 11)/3 = -13/3
So, -8 + 3 2/3 = -13/3.
Answer 4: -13/3