4 5/8 + 9 3/5 =
rename or simplify as needed
LCD = 40
14 9/40
To add the mixed numbers 4 5/8 and 9 3/5, we need to find a common denominator.
The denominators are 8 and 5, which have a common multiple of 40. So, we'll convert both fractions to have a denominator of 40.
For 4 5/8:
Step 1: Multiply the whole number (4) by the denominator (8), which equals 32.
Step 2: Add the result (32) to the numerator (5), which equals 37.
Step 3: Write the sum (37) over the denominator (8) to get 37/8.
Step 4: Multiply both the numerator and denominator of 37/8 by 5 to get a common denominator of 40. This gives us (37 * 5) / (8 * 5) = 185/40.
For 9 3/5:
Step 1: Multiply the whole number (9) by the denominator (5), which equals 45.
Step 2: Add the result (45) to the numerator (3), which equals 48.
Step 3: Write the sum (48) over the denominator (5) to get 48/5.
Step 4: Multiply both the numerator and denominator of 48/5 by 8 to get a common denominator of 40. This gives us (48 * 8) / (5 * 8) = 384/40.
Now, we can add the fractions:
185/40 + 384/40 = (185 + 384) / 40 = 569/40.
Therefore, 4 5/8 + 9 3/5 can be simplified as 569/40.
To simplify the calculation, you can convert the mixed numbers into improper fractions.
First, let's convert 4 5/8 to an improper fraction:
4 is the whole number, and we need to add it to the fraction. So, we multiply the denominator (8) by the whole number (4) and add the numerator (5). The result becomes the new numerator, while the denominator remains the same.
4 x 8 + 5 = 32 + 5 = 37
So, 4 5/8 can be written as the improper fraction 37/8.
Now, let's convert 9 3/5 to an improper fraction:
9 x 5 + 3 = 45 + 3 = 48
So, 9 3/5 can be written as the improper fraction 48/5.
Now that we have both numbers as improper fractions, we can add them together:
37/8 + 48/5
To add fractions, we need a common denominator. In this case, the least common multiple (LCM) of 8 and 5 is 40. So, we can rewrite the fractions with the common denominator of 40:
(37/8) x (5/5) = 185/40
(48/5) x (8/8) = 384/40
Now, we can add the fractions together:
185/40 + 384/40 = (185 + 384)/40 = 569/40
Therefore, 4 5/8 + 9 3/5 equals 569/40.