Question

b. write 1 multiplication and 1 division sentence to show what fraction represented on the number line is equivalent to \\(\frac{2}{3}\\).\\(\frac{2}{3}=\frac{2\times2}{3\times2}=\frac{4}{6}\\)\\(\frac{4}{6}=\frac{4\div2}{6\div2}=\frac{2}{3}\\)

Explanation:

Step1: Multiplication Sentence

To find an equivalent fraction using multiplication, we multiply the numerator and denominator of \(\frac{2}{3}\) by the same non - zero number. Let's choose 3.
\(\frac{2}{3}=\frac{2\times3}{3\times3}=\frac{6}{9}\)
The multiplication sentence is \(\frac{2}{3}=\frac{2\times3}{3\times3}=\frac{6}{9}\)

Step2: Division Sentence

To find an equivalent fraction using division, we divide the numerator and denominator of a fraction equivalent to \(\frac{2}{3}\) (for example, \(\frac{8}{12}\)) by the same non - zero number. Let's take the fraction \(\frac{8}{12}\) and divide numerator and denominator by 4.
\(\frac{8}{12}=\frac{8\div4}{12\div4}=\frac{2}{3}\)
The division sentence is \(\frac{8}{12}=\frac{8\div4}{12\div4}=\frac{2}{3}\)

Answer:

Multiplication sentence: \(\frac{2}{3}=\frac{2\times3}{3\times3}=\frac{6}{9}\)
Division sentence: \(\frac{8}{12}=\frac{8\div4}{12\div4}=\frac{2}{3}\) (answers can vary as long as we multiply or divide numerator and denominator by the same non - zero number)