Find the value of this expression. 2/7 times 42/45 plus 2/5 times 11/3
2/7 * 42/45 = 84/315
2/5 * 11/3 = 22/15, Multiply both numerator and denominator by 21 to get common denominator and add the two terms. Reduce, if possible.
22/45
To find the value of this expression, we need to evaluate two multiplication operations and one addition operation.
Step 1: Multiply 2/7 by 42/45.
To multiply fractions, we multiply the numerators together and the denominators together. So, (2/7) * (42/45) equals (2 * 42) / (7 * 45).
Calculating the numerator: 2 * 42 = 84.
Calculating the denominator: 7 * 45 = 315.
So, (2/7) * (42/45) equals 84/315.
Step 2: Multiply 2/5 by 11/3.
Again, we multiply the numerators and the denominators. So, (2/5) * (11/3) equals (2 * 11) / (5 * 3).
Calculating the numerator: 2 * 11 = 22.
Calculating the denominator: 5 * 3 = 15.
Therefore, (2/5) * (11/3) equals 22/15.
Step 3: Add the two results from Step 1 and Step 2.
To add fractions, the denominators must be the same. We can achieve this by finding a common denominator.
The least common multiple of 315 and 15 is 315, so we need to convert 22/15 to have a denominator of 315. To do this, we multiply both the numerator and the denominator of 22/15 by 21.
22/15 * 21/21 = (22 * 21) / (15 * 21) = 462/315.
Now we can add 84/315 and 462/315: (84/315) + (462/315) = (84 + 462) / 315 = 546/315.
So, the value of the expression 2/7 times 42/45 plus 2/5 times 11/3 is 546/315.