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question 29
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solve the following \\(\frac{6}{7} \times \frac{21}{12} = a \frac{x}{y}\\)
a =
\\(x = \\)
\\(y = \\)
question 30
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solve the following \\(\frac{8}{15} \times \frac{21}{32} = \frac{x}{y}\\)
\\(x = \\)
\\(y = \\)
question 31
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solve the following \\(\frac{3}{5} \times \frac{10}{15} \times \frac{25}{30} = \frac{x}{y}\\)
\\(x = \\)
\\(y = \\)

Explanation:

Question 29

Step1: Multiply numerators and denominators

Multiply the numerators \(6\times21 = 126\) and denominators \(7\times12 = 84\). So we have \(\frac{6}{7}\times\frac{21}{12}=\frac{126}{84}\).

Step2: Simplify the fraction

Simplify \(\frac{126}{84}\). Divide numerator and denominator by 42: \(\frac{126\div42}{84\div42}=\frac{3}{2}\). Now, \(\frac{3}{2}=1\frac{1}{2}\), so \(A = 1\), \(x = 1\), \(y = 2\).

Step1: Multiply numerators and denominators

Multiply numerators \(8\times21 = 168\) and denominators \(15\times32 = 480\). So \(\frac{8}{15}\times\frac{21}{32}=\frac{168}{480}\).

Step2: Simplify the fraction

Simplify \(\frac{168}{480}\). Divide numerator and denominator by 24: \(\frac{168\div24}{480\div24}=\frac{7}{20}\). So \(x = 7\), \(y = 20\).

Step1: Multiply the first two fractions

First, multiply \(\frac{3}{5}\times\frac{10}{15}\). Numerators: \(3\times10 = 30\), denominators: \(5\times15 = 75\). So \(\frac{3}{5}\times\frac{10}{15}=\frac{30}{75}=\frac{2}{5}\) (after simplifying by dividing numerator and denominator by 15).

Step2: Multiply the result with the third fraction

Now multiply \(\frac{2}{5}\times\frac{25}{30}\). Numerators: \(2\times25 = 50\), denominators: \(5\times30 = 150\). So \(\frac{2}{5}\times\frac{25}{30}=\frac{50}{150}\).

Step3: Simplify the final fraction

Simplify \(\frac{50}{150}\) by dividing numerator and denominator by 50: \(\frac{50\div50}{150\div50}=\frac{1}{3}\). So \(x = 1\), \(y = 3\).

Answer:

\(A = 1\), \(x = 1\), \(y = 2\)

Question 30