Question

which number is a common denominator for $3\frac{2}{3}$ and $1\frac{4}{5}$? 15
write equivalent fractions for $3\frac{2}{3}$ and $1\frac{4}{5}$ using 15 as the common denominator.
$3\frac{2}{3}-1\frac{4}{5}=3\frac{?}{15}-1\frac{?}{15}$

Explanation:

Step1: Convert \( 3\frac{2}{3} \) to improper fraction

First, convert the mixed number \( 3\frac{2}{3} \) to an improper fraction. The formula for converting a mixed number \( a\frac{b}{c} \) to an improper fraction is \( \frac{a\times c + b}{c} \). So for \( 3\frac{2}{3} \), we have \( a = 3 \), \( b = 2 \), \( c = 3 \). Then \( 3\times3 + 2 = 11 \), so \( 3\frac{2}{3}=\frac{11}{3} \). Now we need to find an equivalent fraction with denominator 15. To do this, we multiply the numerator and denominator by 5 (since \( 15\div3 = 5 \)). So \( \frac{11\times5}{3\times5}=\frac{55}{15} \), and \( 3\frac{2}{3}=3\frac{10}{15} \) (because \( 55\div15 = 3\frac{10}{15} \)).

Step2: Convert \( 1\frac{4}{5} \) to improper fraction

Next, convert the mixed number \( 1\frac{4}{5} \) to an improper fraction. Using the same formula, \( a = 1 \), \( b = 4 \), \( c = 5 \). Then \( 1\times5 + 4 = 9 \), so \( 1\frac{4}{5}=\frac{9}{5} \). Now we need to find an equivalent fraction with denominator 15. We multiply the numerator and denominator by 3 (since \( 15\div5 = 3 \)). So \( \frac{9\times3}{5\times3}=\frac{27}{15} \), and \( 1\frac{4}{5}=1\frac{12}{15} \) (because \( 27\div15 = 1\frac{12}{15} \)).

Step3: Identify the numerators

Now, looking at the equation \( 3\frac{2}{3}-1\frac{4}{5}=3\frac{?}{15}-1\frac{?}{15} \), from the conversion above, \( 3\frac{2}{3}=3\frac{10}{15} \) and \( 1\frac{4}{5}=1\frac{12}{15} \). So the first blank (numerator of the first fraction) is 10 and the second blank (numerator of the second fraction) is 12.

Answer:

The first blank is 10 and the second blank is 12. So the completed equation is \( 3\frac{2}{3}-1\frac{4}{5}=3\frac{10}{15}-1\frac{12}{15} \)