simplify 5+ 1/3x1/3x1/3-(1/9+1/9)
5 +(1/3*1/3*1/3)-(1/9+1/9)
5+1/27-2/9
5+1/27-6/27
5-5/27
130/27
4 22/27
thanks so much!
To simplify the expression "5 + 1/3 × 1/3 × 1/3 - (1/9 + 1/9)," let's break it down step by step.
Step 1: Simplify the expressions within parentheses:
1/9 + 1/9 = 2/9
Now the expression becomes:
5 + 1/3 × 1/3 × 1/3 - 2/9
Step 2: Simplify the multiplication:
1/3 × 1/3 × 1/3
To multiply fractions, we multiply the numerators and multiply the denominators:
(1 × 1 × 1) / (3 × 3 × 3) = (1) / (27)
Now the expression becomes:
5 + 1/27 - 2/9
Step 3: Find a common denominator (LCD) between the fractions:
The least common denominator (LCD) between 9 and 27 is 27.
Step 4: Convert the fractions so that they have the same denominator:
For 1/27, we multiply both numerator and denominator by 27:
(1 × 27) / (27 × 1) = 27 / 27 = 1
For 2/9, we multiply both numerator and denominator by 3:
(2 × 3) / (9 × 3) = 6 / 27
Now the expression becomes:
5 + 1 - 6/27
Step 5: Add or subtract the fractions:
Now that the fractions have the same denominator, we can add or subtract their numerators directly.
5 + 1 = 6
Now the expression becomes:
6 - 6/27
Step 6: Simplify the subtraction:
To subtract fractions, we need to have a common denominator. Since 6/27 already have a denominator of 27, we can subtract the numerators directly:
6 - 6 = 0
Therefore, the simplified form of the expression "5 + 1/3 × 1/3 × 1/3 - (1/9 + 1/9)" is 0.