how do you do this problem using distributive property and not using it:
6(1/2+2/3+3/4)
same as with any other distributive property problem:
with:
6(1/2+2/3+3/4)
6(1/2) + 6(2/3) + 6(3/4)
3 + 4 + 4 1/2
11 1/2
without:
6(1/2+2/3+3/4)
6(6/12 + 8/12 + 9/12)
6(21/12)
21/2
11 1/2
Steve is right
Steve is correct
To solve the given problem using the distributive property, we can distribute the number 6 to each term inside the parentheses and then simplify the resulting expression. Here's how you can do it step by step:
Step 1: Distribute 6 to each term inside the parentheses
6(1/2 + 2/3 + 3/4) becomes (6 * 1/2) + (6 * 2/3) + (6 * 3/4)
Step 2: Simplify each term
(6 * 1/2) = 6/2 = 3
(6 * 2/3) = 12/3 = 4
(6 * 3/4) = 18/4 = 4.5
Step 3: Add the simplified terms
3 + 4 + 4.5 = 11.5
Therefore, using the distributive property, the result of 6(1/2 + 2/3 + 3/4) is 11.5.
If you want to solve the problem without using the distributive property, you can find a common denominator for the fractions inside the parentheses and then add them together. Here's how:
Step 1: Find a common denominator
To find a common denominator for 2, 3, and 4, we need to find the least common multiple (LCM) of these numbers, which is 12.
Step 2: Rewrite each fraction with the common denominator
1/2 becomes 6/12
2/3 becomes 8/12
3/4 becomes 9/12
Step 3: Add the fractions with the common denominator
6/12 + 8/12 + 9/12 = (6 + 8 + 9) / 12 = 23/12
Therefore, without using the distributive property, the result of 6(1/2 + 2/3 + 3/4) is 23/12.