Solve ((34)(.64)div48.60)<52<((34)(.64)div21.66)

$$( ( 34 ) ( .64 ) \div 48.60 ) < 52 < ( ( 34 ) ( .64 ) \div 21.66 )$$

Verify

Solution Steps

Multiply 34 and 0.64 to get 21.76.

$$\frac{21.76}{48.6}<52\text{ and }52<\frac{34\times 0.64}{21.66}$$

Expand \frac{21.76}{48.6} by multiplying both numerator and the denominator by 100.

$$\frac{2176}{4860}<52\text{ and }52<\frac{34\times 0.64}{21.66}$$

Reduce the fraction \frac{2176}{4860} to lowest terms by extracting and canceling out 4.

$$\frac{544}{1215}<52\text{ and }52<\frac{34\times 0.64}{21.66}$$

Convert 52 to fraction \frac{63180}{1215}.

$$\frac{544}{1215}<\frac{63180}{1215}\text{ and }52<\frac{34\times 0.64}{21.66}$$

Compare \frac{544}{1215} and \frac{63180}{1215}.

$$\text{true}\text{ and }52<\frac{34\times 0.64}{21.66}$$

Multiply 34 and 0.64 to get 21.76.

$$\text{true}\text{ and }52<\frac{21.76}{21.66}$$

Expand \frac{21.76}{21.66} by multiplying both numerator and the denominator by 100.

$$\text{true}\text{ and }52<\frac{2176}{2166}$$

Reduce the fraction \frac{2176}{2166} to lowest terms by extracting and canceling out 2.

$$\text{true}\text{ and }52<\frac{1088}{1083}$$

Convert 52 to fraction \frac{56316}{1083}.

$$\text{true}\text{ and }\frac{56316}{1083}<\frac{1088}{1083}$$

Compare \frac{56316}{1083} and \frac{1088}{1083}.

$$\text{true}\text{ and }\text{false}$$

The conjunction of \text{true} and \text{false} is \text{false}.

$$\text{false}$$