Please show work.
9 1/10 + 7 2/5
11 5/10
9 1/10 + 7 2/5
you have to find the common denominators of 1/10 and 2/5 which is 10 so you leave 1/10 the same and multiply 2/5 with 2 each to get 4/10 then you add 1/10 + 4/10 which is equal to 5/10. now that you got that just add the 9+7 you get 11 so your answer is 11 5/10
Reduce 5/10 to 1/2 so your answer is 11 1/2
To solve the expression 9 1/10 + 7 2/5, you need to convert the mixed numbers into improper fractions and then add them together.
Step 1: Convert the mixed numbers into improper fractions.
To convert 9 1/10 into an improper fraction, you can multiply the whole number (9) by the denominator (10) and add the numerator (1). So, the improper fraction is (9 * 10 + 1) / 10 = 91/10.
Similarly, to convert 7 2/5 into an improper fraction, you can multiply the whole number (7) by the denominator (5) and add the numerator (2). So, the improper fraction is (7 * 5 + 2) / 5 = 37/5.
Step 2: Add the improper fractions.
To add the fractions, you need to find a common denominator. In this case, the common denominator is 10.
(91/10) + (37/5)
Now, to have a common denominator of 10, we need to multiply the numerator and the denominator of the second fraction by 2.
(91/10) + (37/5 * 2/2)
This becomes:
(91/10) + (74/10)
Now, we can add the two fractions, keeping the denominator the same.
(91/10) + (74/10) = (91 + 74) / 10 = 165/10
So, the result of 9 1/10 + 7 2/5 is 165/10.
If you need to simplify the fraction further, you can divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, the GCD of 165 and 10 is 5.
(165/10) ÷ 5/5 = (165/10) * (1/5) = 33/2
Therefore, the simplified result is 33/2, or as a mixed number, it is 16 1/2.