I need to solve this problem in two diferent ways showing work. I have one way but I don't know what the other way could be the problem is
3 3/4 +5 1/3
is it 3 * 3/4 + 5 * 1/3?
which way have you done?
the way u did
ok well maybe changing them to decimals then adding will count as another way
To solve the addition problem 3 3/4 + 5 1/3, you can use two different approaches:
Method 1: Converting mixed numbers to improper fractions
Step 1: Convert the mixed numbers to improper fractions.
3 3/4 can be written as (4 * 3 + 3)/4 = 15/4.
5 1/3 can be written as (3 * 5 + 1)/3 = 16/3.
Step 2: Find a common denominator for the two fractions. The common denominator in this case is 12 (the product of 3 and 4).
Step 3: Convert each fraction so it has the common denominator of 12.
To convert 15/4 to have a denominator of 12, multiply both the numerator and denominator by 3: (15 * 3)/(4 * 3) = 45/12.
To convert 16/3 to have a denominator of 12, multiply both the numerator and denominator by 4: (16 * 4)/(3 * 4) = 64/12.
Step 4: Add the fractions.
45/12 + 64/12 = (45 + 64)/12 = 109/12.
Step 5: Simplify the fraction, if necessary.
109/12 cannot be simplified further, so this is the final answer.
Method 2: Using the algorithm for addition of mixed numbers directly
Step 1: Add the whole numbers.
3 + 5 = 8.
Step 2: Add the fractions.
3/4 + 1/3.
To add fractions with different denominators, find a common denominator. In this case, the common denominator is 12 (the product of 4 and 3).
Step 3: Convert each fraction so it has a denominator of 12.
To convert 3/4 to have a denominator of 12, multiply both the numerator and denominator by 3: (3 * 3)/(4 * 3) = 9/12.
To convert 1/3 to have a denominator of 12, multiply both the numerator and denominator by 4: (1 * 4)/(3 * 4) = 4/12.
Step 4: Add the fractions.
9/12 + 4/12 = (9 + 4)/12 = 13/12.
Step 5: Check if the result can be simplified.
13/12 cannot be simplified further, so this is the final answer.
Therefore, the solutions to the problem 3 3/4 + 5 1/3 are:
Method 1: 109/12
Method 2: 13/12.