Which expression is equivalent to 1/3
+ (3/4
+ 2/
3
)?
The expression equivalent to 1/3 + (3/4 + 2/3) is (1/3) + (9/12 + 8/12).
To simplify the expression 1/3 + (3/4 + 2/3), we can use the common denominator method.
Step 1: Find the common denominator for the fractions involved, which is 12.
Step 2: Rewrite each fraction with the common denominator:
1/3 = 4/12
3/4 = 9/12
2/3 = 8/12
Step 3: Add the fractions together:
4/12 + (9/12 + 8/12)
Step 4: Reduce the fractions:
4/12 + (17/12)
Step 5: Add the fractions:
4/12 + 17/12 = 21/12
Step 6: Simplify the fraction:
21/12 can be reduced by dividing both the numerator and denominator by the greatest common divisor (GCD), which is 3.
21 ÷ 3 / 12 ÷ 3 = 7/4
So, the expression 1/3 + (3/4 + 2/3) is equivalent to 7/4.