Question

1. determine which of the following are true number sentences. correct those that are false by changing the right - hand side of the number sentence.

a. \\(\frac{2}{3}=\frac{4}{9}\\)
b. \\(\frac{5}{6}=\frac{10}{12}\\)
c. \\(\frac{3}{5}=\frac{6}{15}\\)
d. \\(\frac{7}{4}=\frac{21}{12}\\)

Explanation:

Part a

Step1: Cross - multiply to check equality

To check if $\frac{2}{3}=\frac{4}{9}$, we cross - multiply. The cross - product of $\frac{a}{b}$ and $\frac{c}{d}$ is $a\times d$ and $b\times c$. So, for $\frac{2}{3}$ and $\frac{4}{9}$, we have $2\times9 = 18$ and $3\times4=12$. Since $18
eq12$, the equation is false.

Step2: Find the correct fraction

To make the right - hand side equal to $\frac{2}{3}$, we can multiply the numerator and denominator of $\frac{2}{3}$ by 2. $\frac{2\times2}{3\times2}=\frac{4}{6}$. So the correct number sentence is $\frac{2}{3}=\frac{4}{6}$.

Part b

Step1: Cross - multiply to check equality

For $\frac{5}{6}$ and $\frac{10}{12}$, cross - multiply: $5\times12 = 60$ and $6\times10 = 60$.

Step2: Conclusion

Since the cross - products are equal, $\frac{5}{6}=\frac{10}{12}$ is a true number sentence.

Part c

Step1: Cross - multiply to check equality

For $\frac{3}{5}$ and $\frac{6}{15}$, cross - multiply: $3\times15=45$ and $5\times6 = 30$. Since $45
eq30$, the equation is false.

Step2: Find the correct fraction

Multiply the numerator and denominator of $\frac{3}{5}$ by 3: $\frac{3\times3}{5\times3}=\frac{9}{15}$. So the correct number sentence is $\frac{3}{5}=\frac{9}{15}$.

Part d

Answer:

s:
a. False, correct: $\frac{2}{3}=\frac{4}{6}$
b. True
c. False, correct: $\frac{3}{5}=\frac{9}{15}$
d. True