simplify
7 2/3 + -5 1/4
-2
2 5/12
2 11/12
12 11/12
To simplify 7 2/3 + -5 1/4, we first need to convert the mixed numbers to improper fractions. 7 2/3 is equivalent to (7*3 + 2)/3 = 23/3, and -5 1/4 is equivalent to (-5*4 + 1)/4 = -19/4.
Now we can add the fractions: 23/3 + (-19/4). To do this, we need to find a common denominator for the fractions, which in this case is 12.
Multiplying the numerator and denominator of 23/3 by 4, we get (23*4)/ (3*4) = 92/12.
Multiplying the numerator and denominator of -19/4 by 3, we get (-19*3)/ (4*3) = -57/12.
Now we can add the fractions: 92/12 + (-57/12) = (92 - 57)/12 = 35/12.
Therefore, the simplified answer is 2 11/12.
To simplify 7 2/3 + -5 1/4, we first need to convert the mixed numbers to improper fractions.
7 2/3 can be converted to an improper fraction by multiplying the whole number (7) by the denominator (3) and adding the numerator (2). This gives us (7 * 3) + 2 = 21 + 2 = 23. So, 7 2/3 is equivalent to 23/3.
-5 1/4 can be converted to an improper fraction by multiplying the whole number (-5) by the denominator (4) and adding the numerator (1), then multiplying the result by -1 to account for the negative sign. This gives us (-5 * 4) + 1 = -20 + 1 = -19. So, -5 1/4 is equivalent to -19/4.
Now, we can add the two fractions: 23/3 + (-19/4).
To add fractions, we need to have a common denominator. The common denominator for 3 and 4 is 12.
To convert 23/3 to a fraction with a denominator of 12, we can multiply the numerator and denominator by 4: (23 * 4) / (3 * 4) = 92/12.
To convert -19/4 to a fraction with a denominator of 12, we can multiply the numerator and denominator by 3: (-19 * 3) / (4 * 3) = -57/12.
Now, we can add the fractions with the common denominator of 12: 92/12 + (-57/12).
To add the fractions, we add the numerators and keep the common denominator: (92 - 57) / 12 = 35/12.
Therefore, 7 2/3 + -5 1/4 simplifies to 2 11/12.
To simplify the expression 7 2/3 + -5 1/4, you need to perform the addition operation between the whole numbers and the fractions separately. Here's how:
Step 1: Add the whole numbers:
7 + (-5) = 2
Step 2: Add the fractions:
To add fractions, you need to have a common denominator. In this case, the common denominator for 3 and 4 is 12.
Converting 2/3 to twelfths:
Multiply the numerator and denominator of 2/3 by 4:
2/3 = (2 * 4) / (3 * 4) = 8/12
Converting 1/4 to twelfths:
Multiply the numerator and denominator of 1/4 by 3:
1/4 = (1 * 3) / (4 * 3) = 3/12
Now, you can add the fractions:
8/12 + 3/12 = 11/12
Step 3: Combine the results:
The sum of the whole numbers is 2, and the sum of the fractions is 11/12. Therefore, the simplified answer is 2 11/12.
So, the correct answer is 2 11/12.