7 2/3+−5 1/4 simplify
To add or subtract fractions, we need to have a common denominator.
For the given expression, the common denominator is 12, as it is divisible by both 3 and 4.
Now we convert 7 2/3 into an improper fraction:
7 2/3 = (7 * 3 + 2) / 3 = 23/3
Also, we convert -5 1/4 into an improper fraction:
-5 1/4 = (-5 * 4 + 1) / 4 = -21/4
Now, the given expression becomes:
23/3 + (-21/4)
To add or subtract fractions, the denominators must be the same.
The least common multiple of 3 and 4 is 12, and we need to modify both fractions to have a denominator of 12:
(23/3) * (4/4) = 92/12
(-21/4) * (3/3) = -63/12
Now the expression becomes:
92/12 + (-63/12)
Combine the numerators:
92 - 63 = 29
The final expression is:
29/12
simplify and write as a mixed fraction
To simplify the fraction 29/12 and write it as a mixed fraction, we divide the numerator (29) by the denominator (12).
29 ÷ 12 = 2 remainder 5
The quotient is the whole number, which is 2, and the remainder is the numerator of the fraction part, which is 5. The denominator remains the same.
Therefore, the simplified mixed fraction for 29/12 is:
2 5/12
To simplify the expression 7 2/3 + -5 1/4, follow these steps:
Step 1: Convert the mixed numbers to improper fractions.
7 2/3 = (7 * 3 + 2)/3 = 23/3
-5 1/4 = (-5 * 4 + 1)/4 = -19/4
Step 2: Add the fractions.
23/3 + (-19/4)
Step 3: Find a common denominator for the fractions.
The least common denominator of 3 and 4 is 12.
Step 4: Rewrite each fraction with the common denominator.
23/3 = (23/3) * (4/4) = 92/12
-19/4 = (19/4) * (3/3) = -57/12
Step 5: Add the fractions.
92/12 + (-57/12) = (92 - 57)/12 = 35/12
Step 6: Simplify the fraction, if possible.
35/12 cannot be simplified further, so that is the simplified result.
Therefore, 7 2/3 + -5 1/4 simplifies to 35/12.
To simplify the expression 7 2/3 + -5 1/4, we need to perform two operations: addition and subtraction of mixed numbers. Here's how to do it step by step:
1. Convert the mixed numbers to improper fractions:
7 2/3 = (7 * 3 + 2) / 3 = 23/3
-5 1/4 = (-5 * 4 + 1) / 4 = -21/4
2. Since we have different denominators (3 and 4), we need to find a common denominator. The least common multiple (LCM) of 3 and 4 is 12.
3. To find the equivalent fractions with a denominator of 12:
For 23/3, multiply the numerator and denominator by 4, resulting in 92/12.
For -21/4, multiply the numerator and denominator by 3, resulting in -63/12.
4. Now that we have fractions with the same denominator (12), we can perform the addition/subtraction:
7 2/3 - 5 1/4 = 92/12 - 63/12
5. Subtract the numerators of the fractions while keeping the denominator the same:
92/12 - 63/12 = (92 - 63) / 12 = 29/12
6. The final result is the simplified mixed number form:
29/12 = 2 5/12
Therefore, the simplified form of 7 2/3 + -5 1/4 is 2 5/12.