Mixed Rationals:
Solve these question in two or three steps:
879 + 47/22
4591 - 133/61
-1 + 17/13
-68 - 18/7
-1297 + 763/512
Thank you!
in each case, multiply by the denominator, then add the numerators. For example
-1 + 17/13 = (-13+17)/13 = 4/13
Sure, here are the solutions to the mixed rationals:
1. 879 + 47/22 = 879.090909090909... (approximately)
2. 4591 - 133/61 = 4590.18 (approximately)
3. -1 + 17/13 = 0.3076923076923077... (approximately)
4. -68 - 18/7 = -69.57142857142857... (approximately)
5. -1297 + 763/512 = -1296.5048828125 (approximately)
Remember, I'm a clown bot, so take these answers with a grain of salt and remember to have fun with math!
Step 1: Simplify the fraction in each question.
879 + 47/22 = 879 + (2*22 + 3)/22 = 879 + 2 + 3/22 = 881 + 3/22
4591 - 133/61 = 4591 - (2*61 + 11)/61 = 4591 - 2 - 11/61 = 4589 - 11/61
-1 + 17/13 = -1 + (1*13 + 4)/13 = -1 + 1 + 4/13 = 4/13
-68 - 18/7 = -68 - (2*7 + 4)/7 = -68 - 2 - 4/7 = -70 - 4/7
-1297 + 763/512 = -1297 + (1*512 + 251)/512 = -1297 + 1 + 251/512 = -1296 + 251/512
Step 2: Add or subtract the whole number and the fraction in each question.
879 + 47/22 = 881 + 3/22
4591 - 133/61 = 4589 - 11/61
-1 + 17/13 = 4/13
-68 - 18/7 = -70 - 4/7
-1297 + 763/512 = -1296 + 251/512
Note: The final answers may need further simplification depending on the requirements of the problem.
To solve these mixed rational addition and subtraction problems, you need to find a common denominator and then perform the operation. Here are the step-by-step solutions for each problem:
1. 879 + 47/22:
To add a whole number and a fraction, you need to convert the whole number into a fraction with the same denominator as the fraction. In this case, the denominator is already 22, so you can rewrite 879 as 879/1. Now, you can add the fractions by adding the numerators: (879/1) + (47/22) = (879*22 + 47)/(1*22) = 19375/22.
2. 4591 - 133/61:
Similarly, we need to convert the whole number 4591 into a fraction with the same denominator as the fraction 133/61. The denominator is already 61, so we can rewrite 4591 as 4591/1. Then, subtract the fractions by subtracting the numerators: (4591/1) - (133/61) = (4591*61 - 133)/(1*61) = 279397/61.
3. -1 + 17/13:
The procedure is the same. Rewrite -1 as (-1/1) and add the fractions: (-1/1) + (17/13) = (-1*13 + 17)/(1*13) = 4/13.
4. -68 - 18/7:
To subtract a fraction from a negative whole number, rewrite -68 as (-68/1) and subtract the fractions: (-68/1) - (18/7) = (-68*7 - 18)/(1*7) = -482/7.
5. -1297 + 763/512:
Again, rewrite -1297 as (-1297/1) and add the fractions: (-1297/1) + (763/512) = (-1297*512 + 763)/(1*512) = -648807/512.
So, the solutions are:
879 + 47/22 = 19375/22
4591 - 133/61 = 279397/61
-1 + 17/13 = 4/13
-68 - 18/7 = -482/7
-1297 + 763/512 = -648807/512