Question

5/6*9/15-5/12*4/15=? 7/18*9/14+1/3*6/7=? 9/20*2/3+5/14*7/25=?

Answer 1

5/6*9/15-5/12*4/15=1/2*3/3-1/3*1/3=1/2-1/9=9/18-2/18=7/18
7/18*9/14+1/3*6/7=1/2*1/2+1/1*2/7=1/4+2/7=7/28+8/28=15/28
9/20*2/3+5/14*7/25=3/10*1/1+1/2*1/5=3/10+1/10=4/10=2/5

Answer 2

To solve these problems, we need to perform arithmetic operations using fractions. Here are the step-by-step solutions to each problem:

1. 5/6 * 9/15 - 5/12 * 4/15

First, we can simplify each fraction by canceling out common factors:

= 5/6 * 3/5 - 5/12 * 2/5 = 1/2 - 1/6 = 1/3

Therefore, 5/6 * 9/15 - 5/12 * 4/15 = 1/3.

2. 7/18 * 9/14 + 1/3 * 6/7

We can simplify each fraction first:

= 1/6 * 9/2 + 2/6 * 6/7 = 9/12 + 12/42

To add these fractions, we need to find a common denominator, which is the least common multiple of 12 and 42, which is 84:

= 63/84 + 32/84 = 95/84

Therefore, 7/18 * 9/14 + 1/3 * 6/7 = 95/84.

3. 9/20 * 2/3 + 5/14 * 7/25

We can simplify each fraction:

= 3/20 * 2/1 + 5/14 * 7/25

To add these fractions, we need to find a common denominator, which is the least common multiple of 20, 1, 14, and 25, which is 700:

= 105/700 + 100/700 = 205/700

Therefore, 9/20 * 2/3 + 5/14 * 7/25 = 205/700.