I have this fraction:
6 2/9 + 1 3/4 - 3 5/6=
Okay First I changed the mixed numbers into improper fractions. I got this:
56/9 + 7/4 + 23/6
Then I thought you have to find the least common denominator, which for 9,4, and 6 would be 36.
Then I muliplied the fractions by 4, 9, and 6 repectively, and got this equation:
224/36 + 161/36 - 138/36=
The answer I got was 23/36, but I know this is wrong. Looking at the steps I have taken, could someone tell me where I went wrong. I DO NOT WANT THE ANSWER. Just HOW to GET the right answer.
Thank you
7/4 = 63/36
There is your error.
I hope this helps. Thanksfor asking.
The 224/36 is correct.
The 138/36 is correct.
The 161/36 is not correct.
The LCD is 36, 36/4 = 9 and 9 x 7 = ?? and ??/36 is the fraction.
Thanks for showing your work. It helps us find the error much easier.
To get the correct answer, let's go through the steps you took and find the mistake.
Step 1: Changing mixed numbers to improper fractions
You correctly changed the mixed numbers into improper fractions:
6 2/9 = (6 * 9 + 2) / 9 = 56/9
1 3/4 = (1 * 4 + 3) / 4 = 7/4
3 5/6 = (3 * 6 + 5) / 6 = 23/6
So far, so good!
Step 2: Finding the least common denominator (LCD)
You correctly identified the LCD for 9, 4, and 6 as 36.
Step 3: Multiplying fractions by the LCD
Here is where the mistake occurred. Instead of multiplying each fraction by the LCD separately, you multiplied by each denominator individually (4, 9, and 6). This will not give you the correct equivalent fractions.
To fix this, multiply each fraction by the appropriate factor to create an equivalent fraction with a denominator of 36.
For 56/9, multiply numerator (56) and denominator (9) by 4 to get [56*4]/[9*4] = 224/36.
For 7/4, multiply numerator (7) and denominator (4) by 9 to get [7*9]/[4*9] = 63/36.
For 23/6, multiply numerator (23) and denominator (6) by 6 to get [23*6]/[6*6] = 138/36.
Now, the equation becomes:
224/36 + 63/36 - 138/36
Step 4: Adding and Subtracting
Now that all the fractions have the same denominator, you can add and subtract them:
224/36 + 63/36 - 138/36 = (224 + 63 - 138) / 36 = 149/36
So, the simplified fraction is 149/36.
Remember, it is always important to double-check your work, especially when dealing with fractions and complex calculations.