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$Which statement below best explains how to subtract (14)/(15)-(2)/(3) ? A. Subtract the numerators first then subtract the denominators. B. Write an equivalent fraction for (14)/(15) with 3 as the new denominator. Then subtract only the numerators. C. Write equivalent fractions for both fractions with 45 as the denominator. Then subtract the numerators and denominators separately. D. Write an equivalent fraction for (2)/(3) with 15 as the new denominator. Then subtract only the numerators.$

$7$ . Which statement below best explains how to subtract $\frac{14}{15}-\frac{2}{3}$ ? $\newline$ A. Subtract the numerators first then subtract the denominators. $\newline$ B. Write an equivalent fraction for $\frac{14}{15}$ with $3$ as the new denominator. Then subtract only the numerators. $\newline$ C. Write equivalent fractions for both fractions with $45$ as the denominator. Then subtract the numerators and denominators separately. $\newline$ D. Write an equivalent fraction for $\frac{2}{3}$ with $15$ as the new denominator. Then subtract only the numerators.

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Full solution

7

. Which statement below best explains how to subtract

\frac{14}{15}-\frac{2}{3}

\newline

A. Subtract the numerators first then subtract the denominators.

\newline

B. Write an equivalent fraction for

\frac{14}{15}

with

3

as the new denominator. Then subtract only the numerators.

\newline

C. Write equivalent fractions for both fractions with

45

as the denominator. Then subtract the numerators and denominators separately.

\newline

D. Write an equivalent fraction for

\frac{2}{3}

with

15

as the new denominator. Then subtract only the numerators.

Find Common Denominator: Find a common denominator for both fractions to subtract them properly.
Calculate LCD: The least common denominator (LCD) for $15$ and $3$ is $45$ .
Convert $\frac{14}{15}$ to $45$ : Convert $\left(\frac{14}{15}\right)$ to a fraction with a denominator of $45$ . Multiply both the numerator and denominator by $3$ to get $\left(\frac{42}{45}\right)$ .
Convert $\frac{2}{3}$ to $45$ : Convert $\left(\frac{2}{3}\right)$ to a fraction with a denominator of $45$ . Multiply both the numerator and denominator by $15$ to get $\left(\frac{30}{45}\right)$ .
Subtract Numerators: Subtract the numerators of the equivalent fractions: $42 - 30 = 12$ .
Write Result as Fraction: Write the result as a fraction over the common denominator: $\frac{12}{45}.$
Simplify Fraction: Simplify the fraction if possible. In this case, $\frac{12}{45}$ can be simplified by dividing both the numerator and denominator by $3$ to get $\frac{4}{15}$ .