SOLUTION: How do you solve 2/3+5/6+2/9= and 11/12- 5/12= and 3 4/7+ 2 3/5= and 4 3/4x 1 5/19=

Algebra ->  Numeric Fractions Calculators, Lesson and Practice -> SOLUTION: How do you solve 2/3+5/6+2/9= and 11/12- 5/12= and 3 4/7+ 2 3/5= and 4 3/4x 1 5/19=      Log On


   

Question 980066: How do you solve 2/3+5/6+2/9=
and 11/12- 5/12=
and 3 4/7+ 2 3/5=
and 4 3/4x 1 5/19=
Answer by josh_jordan(263) About Me  (Show Source):
You can put this solution on YOUR website!
1. 2/3 + 5/6 + 2/9

To solve, all your denominators must be the same. You have to find the LCM for the fractions (i.e., the first number that all 3 numbers in the denominator can go into). The LCM is 18.

Next, multiply the numerators and denominators of each fraction by the number the denominator needs to be multiplied by to get 18:

%282%2A6%29%2F%283%2A6%29%2B%285%2A3%29%2F%286%2A3%29%2B%282%2A2%29%2F%289%2A2%29 -----> %2812%2F18%29%2B%2815%2F18%29%2B%284%2F18%29

Now add the numerators together and put that sum in the numerator and 18 in the denominator:

31%2F18

Convert this to a mixed number, since it is an improper fraction, by dividing 31 by 18:

31 / 18 = 1 with a remainder of 13, so 1 13/18

2. 11/12 - 5/12

Since the denominators are the same, just subtract the numerator of the second fraction from the numerator of the first fraction, and place that result in the numerator and place 12 in the denominator:

6/12

Reduce this fraction to lowest terms by dividing the numerator and denominator by 6:

1/2

3. 3 4/7 + 2 3/5

First, only look at the fractional portion of each mixed number and follow the instructions presented for question 1 above.

You will get 1 6/35

Add 1 (from the 1 6/35) to the 2 numbers in front of the original mixed numbers and tack on the 6/35 to the result:

1 + 3 + 2 -----> 6 and tack on 6/35 to that: 6 6/35 is your answer

4. 4 3/4 x 1 5/19

Convert each mixed number to an improper fraction by multiplying the whole number in front of each fraction by each denominator and then adding that result to the number in each numerator and keeping the denominator what is originally is:

4 3/4 = %284%2A4%2B3%29%2F4 = 19%2F4

1 5/19 = %281%2A19%2B5%29%2F19 = 24%2F19

Now, we can multiply: %2819%2F4%29%2A%2824%2F19%29

But, if you look closely, you'll see the numerator in the first fraction is the same as the denominator in the second fraction, so you can cancel them out and put 1's in their places:

%281%2F4%29%2A%2824%2F1%29

Look closer and you see that the numerator in the second fraction is a multiple of the denominator in the first fraction, so you can replace the 4 in the first fraction with 1 and replace the numerator in the second fraction with 6:

%281%2F1%29%2A%286%2F1%29

You're now left with 1 x 6, which equals 6, so 6 is the answer.