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On Sunday, $1/6$ of the dogs seen in the park were on leashes. On Wednesday, $3/7$ of the dogs in the same park were on leashes. Which day had a greater fraction of dogs on leashes? $\newline$ A)Sunday $\newline$ B)Wednesday $\newline$

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Multiply fractions: word problems

Full solution

Q. On Sunday,

1/6

of the dogs seen in the park were on leashes. On Wednesday,

3/7

of the dogs in the same park were on leashes. Which day had a greater fraction of dogs on leashes?

\newline

A)Sunday

\newline

B)Wednesday

\newline

Understand fractions given: Understand the fractions given for each day. $\newline$ On Sunday, the fraction of dogs on leashes is $(1)/(6)$ . $\newline$ On Wednesday, the fraction of dogs on leashes is $(3)/(7)$ . $\newline$ We need to compare these two fractions to determine which is greater.
Compare fractions directly: Compare the two fractions directly. $\newline$ Since the denominators are different $6$ and $7$ , we cannot directly compare the fractions by looking at the numerators. We need to find a common denominator or use another method to compare the fractions.
Use cross-multiplication: Use cross-multiplication to compare the fractions. $\newline$ Cross-multiply the fractions to compare their sizes without finding a common denominator. Multiply the numerator of the first fraction by the denominator of the second fraction and vice versa. $\newline$ $(1)/(6)$ compared to $(3)/(7)$ becomes: $\newline$ $1 \times 7 = 7$ (for Sunday) $\newline$ $3 \times 6 = 18$ (for Wednesday)
Determine greater product: Determine which product is greater. $\newline$ The product for Sunday is $7$ , and the product for Wednesday is $18$ . Since $18$ is greater than $7$ , the fraction $(3)/(7)$ is greater than $(1)/(6)$ .
Conclude greater fraction day: Conclude which day had a greater fraction of dogs on leashes. Since $(3)/(7)$ is greater than $(1)/(6)$ , Wednesday had a greater fraction of dogs on leashes than Sunday.

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