Three quantities are given as 0.\overline{6}, \frac{12}{25}, and 1.4. What is the exact ra… — State PSC Exam

Three quantities are given as $0.\overline{6}$ , $\frac{12}{25}$ , and $1.4$ . What is the exact ratio of the Least Common Multiple (LCM) of these three quantities to their Highest Common Factor (HCF)?

6300Cevap
B
$\frac{1}{6300}$
C
420
D
84

Cevap

6300

Converting the given values yields the reduced fractions

\frac{2}{3}

\frac{12}{25}

, and

\frac{7}{5}

. Applying standard fraction formulas,

\text{LCM} = \frac{\text{LCM}(2,12,7)}{\text{HCF}(3,25,5)} = \frac{84}{1} = 84

and

\text{HCF} = \frac{\text{HCF}(2,12,7)}{\text{LCM}(3,25,5)} = \frac{1}{75}

. Taking the ratio

\frac{\text{LCM}}{\text{HCF}}

gives

84 \div \frac{1}{75} = 6300

Adım Adım Çözüm

Convert all terms to irreducible fractions

0.\overline{6} = \frac{6}{9} = \frac{2}{3}

\frac{12}{25} = \frac{12}{25}

, and

1.4 = \frac{14}{10} = \frac{7}{5}

All numbers must be expressed as simplified fractions

\frac{a}{b}

in lowest terms before applying fraction HCF and LCM formulas.

Calculate the Least Common Multiple (LCM) of the fractions

\text{LCM}\left(\frac{2}{3}, \frac{12}{25}, \frac{7}{5}\right) = \frac{\text{LCM}(2, 12, 7)}{\text{HCF}(3, 25, 5)} = \frac{84}{1} = 84

The LCM of a set of fractions is given by

\frac{\text{LCM of numerators}}{\text{HCF of denominators}}

Calculate the Highest Common Factor (HCF) of the fractions

\text{HCF}\left(\frac{2}{3}, \frac{12}{25}, \frac{7}{5}\right) = \frac{\text{HCF}(2, 12, 7)}{\text{LCM}(3, 25, 5)} = \frac{1}{75}

The HCF of a set of fractions is given by

\frac{\text{HCF of numerators}}{\text{LCM of denominators}}

Find the ratio of the LCM to the HCF

\text{Ratio} = \frac{84}{\frac{1}{75}} = 84 \times 75 = 6300

Dividing the computed LCM by the computed HCF yields the required ratio.

Anahtar Kavram

HCF and LCM of Fractions and Recurring Decimals

Soru

Cevap

Adım Adım Çözüm

Anahtar Kavram

Sık Yapılan Hatalar

Konular

Bu konudan daha fazla soru