Evaluate 7.7 x 0.18 divided by 1.16.

Step-by-step solution

1. 1

   Work left to right, since multiplication and division have equal precedence. First the product:

   $7.7\times 0.18=1.386$

   Count the decimal places to check: $77\times 18=1386$, and one place plus two places gives three, so $1.386\;\checkmark$.

2. 2

   Set up the division.

   $1.386\div 1.16=\frac{1.386}{1.16}$

3. 3

   Clear the decimals by scaling both parts. Multiplying numerator and denominator by $1000$:

   $\frac{1.386}{1.16}=\frac{1386}{1160}$

   Scaling both parts by the same factor never changes a fraction’s value, and it removes decimal-point bookkeeping from the rest of the work.

4. 4

   Reduce the fraction. Both are even, and $\gcd(1386,1160)=2$:

   $\frac{1386}{1160}=\frac{693}{580}$

   It reduces no further: $693=3^2\cdot 7\cdot 11$ while $580=2^2\cdot 5\cdot 29$, sharing no prime factor.

5. 5

   Convert to a decimal and check.

   $\frac{693}{580}\approx 1.194828$

   Because $580$ carries the prime factor $29$, the decimal does not terminate — it repeats with a long period, so the fraction is the exact answer. Multiplying back: $1.194828\times 1.16=1.386\;\checkmark$.