Question

PLEASE HELP ME I AM SOOO DESPERATE

Answer 1

Answer:

13) 71/84

14) 25/24

Step-by-step explanation:

13) 3/7 + 5/12

36/84 + 35/84 --- you need to have a common denominator

71/84

14) 3/8+4/6

9/24+16/24 -- common denominator by LCM

25/24

Answer 2

To add these two fractions together, 3/7 + 5/12, we need a common denominator. The common denominator is simply the least common multiple for the 2 denominators. So here, our first step is to find the least common multiple for 7 and 12.

7 doesn't factor but 12 factors as 2 x 6 and 6 factors as 2 x 3.

When finding the least common multiple, we're looking for factors that match up and here we have no factors that match up so our least common multiple or lcm is 7 · 12 or 84. So our least common denominator for these two fractions is 84.

In order to get a denominator of 84 in the first fraction, we must multiply our denominator of 7 by 12. The problem is we can't just multiply the denominator of a fraction by 12 because that changes its value.

However, if we also multiply the numerator of the fraction by 12, we're actually multiplying the fraction by 12/12 which is 1 and when we multiply anything by 1, it doesn't change its value.

So our first fraction becomes 36/84. Notice that 35/84 has the same value as 3/7.

For our second fraction we have a 12 in the denominator and we want a common denominator of 84 so we must multiply this 12 by 7 and when we multiply the denominator of a fraction by 7, we must also multiply the numerator by 7. When we do this, we get the fraction 35/84.

Now adding across the numerators, we get 71/84.

My explanation for why this fraction is less than 1 is provided in the image that is attached below.

To add unlike fractions such as 3/8 + 4/6, first find a common denominator. The common denominator will be the least common multiple for 8 and 6 which is 24.

To get a 24 in the denominator of 3/8, we multiply top and bottom by 3 to get 9/24 and we multiply top and bottom of 4/6 by 4 to get 16/24.

So we have 9/24 + 16/24 which is 25/24 or 1 and 1/4.

To write an improper fraction as a mixed number, simply divide the denominator into the numerator.

Ask me in the comments if you need help understanding that.

My work for these 2 problems is attached below.