Can someone explain how to do this problem
8 9/10 + 5 3/4 - 5
When you add (i.e. never need to borrow), you can calculate the integer and fractional parts separately, and carry if necessary.
Integer part:
8+5-5=8
Fractional part:
9/10 + 3/4
find common denominator (=20)
18/20 + 15/20
=33/20
= 1 13/20
Carry the 1 to give
9 13/20
You need to express the whole thing in terms of a common denominator (the denominator is the bottom of a fraction). You've got two fractions in the calculation: (9/10) and (3/4), so the best common denominator is probably 20, because 9/10 = 18/20, and 3/4 = 15/20. Now, 8 + (9/10) = 89/10 = 178/20, and 5 + (3/4) - 5 is just (3/4) = 15/20 (because the two fives cancel out). So you've got 178/20 + 15/20, which is just 193/20. You can't simplify that fraction any more, so that's the answer. (If you actually work that fraction out you'll get 9.65.)
An alternative way to do it is to notice that both 9/10 and 3/4 are very easily expressed as decimals: 9/10 = 0.9, and 3/4 = 0.75. So you've actually got 8.9 + 5.75 - 5 = 8.9 + 0.75 = 9.65 as before. (But the form of the question suggests to me that you're supposed to do this by the first method, not the second.)
To solve this problem, you need to add and subtract mixed numbers. Here's a step-by-step explanation:
Step 1: Convert all the mixed numbers to improper fractions.
The first mixed number, 8 9/10, can be converted to an improper fraction by multiplying the whole number (8) by the denominator (10) and adding the numerator (9), then writing the sum over the denominator. In this case, it becomes (8 * 10 + 9) / 10 = 89/10.
The second mixed number, 5 3/4, can be converted to an improper fraction in a similar way: (5 * 4 + 3) / 4 = 23/4.
Step 2: Perform the addition and subtraction.
To add or subtract fractions, they need to have a common denominator. Find the least common multiple (LCM) of the denominators, which in this case is 20. Multiply both the numerators and denominators of the fractions by the necessary factors to make the denominators equal to 20.
The expression becomes:
(89/10 + 23/4 - 5)
Step 3: Add and subtract the fractions.
To add fractions, add the numerators together and keep the denominator the same. In this case, the numerators are 89 and 23, so the sum is 112.
The expression becomes:
(112/10 - 5)
Divide the numerator (112) by the denominator (10) to simplify the fraction:
112/10 = 11 2/10 = 11 1/5.
Step 4: Perform the subtraction.
Subtract 5 from the fraction 11 1/5:
11 1/5 - 5 = (11 1/5) - (5 0/1) = (11 1/5) - (25/5) = (11 - 25 + 1)/5 = -13/5.
The final simplified answer to the problem 8 9/10 + 5 3/4 - 5 is -13/5.