How do you solve problems like -1/2+1/3 or -3 1/5+-6 1/2 without a number line?
Thank to everyone who helps!
I posted this question at 10ish but noone helped so I'm posting it again.
When we add or subtract fractions, they must have the same denominator.
Example:
-1/2 = -3/6
1/3 = 2/6
Because the negative number is smaller than the positive number, our answer will be negative.
2/6 - 3/6 = -1/6
thanks
To solve problems involving addition or subtraction of fractions or mixed numbers without using a number line, you can follow these steps:
Step 1: Convert mixed numbers to improper fractions (if necessary).
If you have mixed numbers (such as -3 1/5 or -6 1/2), convert them into improper fractions. To do this, multiply the whole number by the denominator, then add the numerator. Write the result over the original denominator.
For example:
-3 1/5 = (-3 * 5 + 1) / 5 = (-15 + 1) / 5 = -14/5
-6 1/2 = (-6 * 2 + 1) / 2 = (-12 + 1) / 2 = -11/2
Step 2: Find a common denominator.
To add or subtract fractions, you need to have a common denominator. Find the least common multiple (LCM) of the denominators. Once you have the common denominator, convert each fraction to have the same denominator.
For example:
-1/2 + 1/3
The LCM of 2 and 3 is 6.
-1/2 becomes -3/6 (multiplying the numerator and denominator by 3)
1/3 becomes 2/6 (multiplying the numerator and denominator by 2)
Step 3: Perform the addition/subtraction.
Now that you have fractions with the same denominator, you can simply add or subtract the numerators while keeping the denominator the same.
For example:
-3/6 + 2/6 = (-3 + 2) / 6 = -1/6
Step 4: Convert your answer back to a whole number or mixed number (if desired).
If you want your answer in a mixed number or whole number format, you can convert the improper fraction back into a mixed number. Divide the numerator by the denominator, and write the remainder as the numerator of the new fraction.
For example:
-1/6 as a mixed number = -1 divided by 6, which gives -1 remainder 5
So, the final answer is -1 5/6.
In summary, to solve problems like -1/2 + 1/3 or -3 1/5 + -6 1/2 without a number line:
1. Convert mixed numbers to improper fractions.
2. Find a common denominator.
3. Perform the addition or subtraction using the common denominator.
4. Convert the result back to a whole number or mixed number (if desired).