Question

insert < or > to form a true statement.
\frac{4}{5} \frac{7}{15}
\bigcirc <
\bigcirc >
question 10
write the fraction as an equivalent fraction with the given denominator.
\frac{3}{10} = \frac{}{50}
\bigcirc \frac{3}{50}
\bigcirc \frac{15}{50}
\bigcirc \frac{5}{50}
\bigcirc \frac{30}{50}

Explanation:

First problem: Comparing \(\frac{4}{5}\) and \(\frac{7}{15}\)

Step1: Find a common denominator

The common denominator of \(5\) and \(15\) is \(15\).

Step2: Rewrite \(\frac{4}{5}\) with denominator \(15\)

Multiply numerator and denominator of \(\frac{4}{5}\) by \(3\): \(\frac{4\times3}{5\times3}=\frac{12}{15}\)

Step3: Compare the two fractions

Since \(\frac{12}{15}\) and \(\frac{7}{15}\) have the same denominator, compare numerators. \(12>7\), so \(\frac{12}{15}>\frac{7}{15}\), which means \(\frac{4}{5}>\frac{7}{15}\)

Step1: Determine the multiplier

To get from \(10\) (denominator of \(\frac{3}{10}\)) to \(50\), we multiply by \(5\) (\(50\div10 = 5\))

Step2: Multiply numerator and denominator by the multiplier

Multiply numerator \(3\) and denominator \(10\) of \(\frac{3}{10}\) by \(5\): \(\frac{3\times5}{10\times5}=\frac{15}{50}\)

Answer:

\(>\)

Second problem: Finding an equivalent fraction for \(\frac{3}{10}\) with denominator \(50\)