Simplify 7 2/3 + - 5 1/4
We can simplify the addition of mixed numbers by converting them into improper fractions.
To convert 7 2/3 to an improper fraction, we multiply the whole number (7) by the denominator of the fraction (3), and then add the numerator (2). This gives us (7 * 3 + 2) / 3 = 23/3.
Similarly, to convert -5 1/4 to an improper fraction, we multiply the whole number (-5) by the denominator of the fraction (4), and then add the numerator (1). This gives us (-5 * 4 + 1) / 4 = (-20 + 1) / 4 = -19/4.
Now, we can add the two improper fractions:
23/3 + (-19/4)
To add these fractions, we need a common denominator. The least common multiple (LCM) of 3 and 4 is 12.
To make the denominators 12, we multiply the numerator and denominator of the first fraction by 4, and the numerator and denominator of the second fraction by 3:
(23/3) * (4/4) = 92/12
(-19/4) * (3/3) = -57/12
Now that we have a common denominator, we can add the fractions:
92/12 + (-57/12)
To add these fractions, we simply add the numerators while keeping the denominator the same:
(92 - 57) / 12 = 35/12
Therefore, 7 2/3 + - 5 1/4 simplifies to 35/12.
7 2/3 + -5 1/4 in mixed number
To simplify 7 2/3 + -5 1/4 as a mixed number, we need to first find the sum as an improper fraction.
We already found that 7 2/3 can be expressed as the improper fraction 23/3, and -5 1/4 can be expressed as the improper fraction -19/4.
To add these improper fractions, we need a common denominator. The least common multiple (LCM) of 3 and 4 is 12.
To convert 23/3 to have a denominator of 12, we multiply the numerator and denominator by 4:
(23/3) × (4/4) = 92/12
To convert -19/4 to have a denominator of 12, we multiply the numerator and denominator by 3:
(-19/4) × (3/3) = -57/12
Now, we can add the fractions:
92/12 + (-57/12) = 35/12
To express 35/12 as a mixed number, we divide the numerator (35) by the denominator (12). The quotient will be the whole number, and the remainder will be the numerator of the fraction.
35 ÷ 12 = 2 remainder 11
Therefore, the simplified form of 7 2/3 + -5 1/4 as a mixed number is 2 11/12.
Evaluate 32 + (-73.1)
To evaluate 32 + (-73.1), we simply add the two numbers together:
32 + (-73.1) = -41.1
Therefore, 32 + (-73.1) equals -41.1.
To simplify the expression 7 2/3 + - 5 1/4, we first need to convert both mixed numbers to improper fractions. Here's how we can do that:
First, let's convert the fraction part of each mixed number to improper fractions:
For 2/3:
Since the denominator is 3, we multiply the whole number (2) by the denominator (3), which gives us 6. We then add the numerator (2) to get the new numerator, which is 8. Therefore, 2/3 as an improper fraction is 8/3.
For 1/4:
Again, since the denominator is 4, we multiply the whole number (1) by the denominator (4), which gives us 4. We then add the numerator (1) to get the new numerator, which is 5. Therefore, 1/4 as an improper fraction is 5/4.
Now that we have converted both mixed numbers to improper fractions, we can rewrite the expression:
7 2/3 + -5 1/4 becomes 7 + 8/3 + -5 + 5/4
To simplify further, we can add the whole numbers and fractions separately:
7 + -5 = 2
Now let's add the fractions:
8/3 + 5/4
To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 3 and 4 is 12. So, we can write both fractions with a denominator of 12:
(8/3) x (4/4) = 32/12
(5/4) x (3/3) = 15/12
Now, adding the fractions:
32/12 + 15/12 = 47/12
Therefore, the final simplified expression is 2 + 47/12.
To simplify the expression 7 2/3 + (-5 1/4), you can follow these steps:
Step 1: Convert the mixed numbers into improper fractions.
7 2/3 = (7 * 3 + 2)/3 = 23/3
-5 1/4 = (-5 * 4 + 1)/4 = -21/4
Step 2: Find the common denominator.
The common denominator for 3 and 4 is 12.
Step 3: Convert the fractions to have a common denominator.
23/3 = (23/3) * (4/4) = 92/12
-21/4 = (-21/4) * (3/3) = -63/12
Step 4: Perform the addition.
92/12 + (-63/12) = (92 - 63)/12 = 29/12
Step 5: Simplify the resulting fraction (if necessary).
29/12 is already in its simplest form.
Therefore, the simplified form of 7 2/3 + (-5 1/4) is 29/12.