Simplify 1/5 + (5/9 ÷ 6/9)
Show workings
1/5 + (5/9 ÷ 6/9)
1/5 + (5/9 x 9/6) (dividing by a fraction is the same as multiplying by its reciprocal)
1/5 + (5/6)
6/30 + 25/30 (finding a common denominator of 30)
31/30
To simplify the expression 1/5 + (5/9 ÷ 6/9), follow these steps:
Step 1: Simplify the division inside the parentheses.
5/9 ÷ 6/9 = 5/9 × 9/6 (flipping the second fraction to change division to multiplication)
= (5 × 9) / (9 × 6) (multiply the numerators and denominators respectively)
= 45/54 (simplify)
Step 2: Now, add 1/5 and 45/54.
To add fractions with different denominators, we need to achieve a common denominator.
The least common multiple (LCM) of 5 and 54 is 270, so let's use that as the common denominator.
1/5 = (1 × 54) / (5 × 54) = 54/270
45/54 remains as it is.
Step 3: Add the fractions.
54/270 + 45/54 = (54 + 45) / 270 (add the numerators)
= 99/270
Step 4: Simplify the fraction if needed.
The greatest common divisor (GCD) of 99 and 270 is 9.
Dividing both numerator and denominator by 9, we get:
99/270 = (99 ÷ 9) / (270 ÷ 9) = 11/30
Therefore, the simplified form of 1/5 + (5/9 ÷ 6/9) is 11/30.