-5 7/12+3, 9/12-2 5/12
To add -5 7/12 and 3 9/12, we need to first find a common denominator. The common denominator for 12 and 12 is 12.
So, -5 7/12 + 3 9/12 can be rewritten as (-5 + 3) + (7/12 + 9/12).
Working out the addition inside the parentheses, we get (-2) + (16/12).
Now, we need to simplify this addition. The fraction 16/12 can be simplified by dividing the numerator and denominator by their greatest common divisor, which in this case is 4.
So (-2) + (16/12) equals -2 + (4/3).
Since the -2 and 4/3 do not have like terms, we cannot further simplify the expression.
Therefore, -5 7/12 + 3 9/12 = -2 + 4/3.
To solve the expression -5 7/12 + 3 9/12, we need to add the whole numbers separately from the fractions. Here's the step-by-step breakdown:
1. Add the whole numbers: -5 + 3 = -2
2. Add the fractions: 7/12 + 9/12 = (7 + 9)/12 = 16/12
3. Simplify the fraction: 16/12 can be reduced to 4/3 by dividing both the numerator and denominator by 4.
4. Add the whole number result from step 1 with the fraction result from step 3:
-2 + 4/3
To add a fraction to a whole number, we need to find a common denominator. In this case, the common denominator is 3.
5. Convert the whole number (-2) into a fraction with a denominator of 3:
-2 = -2/1 * 3/3 = -6/3
6. Add the fraction result from step 4 with the converted whole number result from step 5:
-6/3 + 4/3 = (-6 + 4)/3 = -2/3
Therefore, -5 7/12 + 3 9/12 equals -2/3.
Now, let's solve the expression 9/12 - 2 5/12:
1. Subtract the whole numbers: 9 - 2 = 7
2. Subtract the fractions: 5/12 - 5/12 = (5 - 5)/12 = 0/12
3. Simplify the fraction: Since the numerator is 0, the result will be 0.
Therefore, 9/12 - 2 5/12 equals 7.
To add or subtract mixed fractions, you can follow these steps:
1. Convert the mixed fractions into improper fractions: To do this, multiply the whole number by the denominator, and then add the result to the numerator. Keep the same denominator. For example:
-5 7/12 = (-5 * 12 + 7)/12 = -63/12
3, 9/12 = (3 * 12 + 9)/12 = 45/12
2 5/12 = (2 * 12 + 5)/12 = 29/12
2. Add or subtract the numerators: For addition, simply add the numerators together; for subtraction, subtract the second numerator from the first. Keep the same denominator. For example:
-63/12 + 45/12 = -18/12
29/12 - 45/12 = -16/12
3. Simplify the resulting fraction, if necessary: Reduce the fraction to its simplest form by finding the greatest common divisor (GCD) of the numerator and denominator, and then divide both by the GCD. For example:
-18/12 = (-18 ÷ 6) / (12 ÷ 6) = -3/2
-16/12 = (-16 ÷ 4) / (12 ÷ 4) = -4/3
Therefore, -5 7/12 + 3, 9/12 = -3/2 and 2 5/12 - 2 5/12 = -4/3