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Answer :
Let's check each pair of ratios step by step.
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Problem 20: Compare
$$\frac{3}{5} \quad \text{and} \quad \frac{4}{7}.$$
One method is to cross-multiply to see if the fractions are equivalent. We check if
$$3 \times 7 \stackrel{?}{=} 5 \times 4.$$
Calculating each side:
$$3 \times 7 = 21,$$
$$5 \times 4 = 20.$$
Since $21 \neq 20$, we conclude that
$$\frac{3}{5} \neq \frac{4}{7}.$$
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Problem 21: Compare
$$\frac{18}{20} \quad \text{and} \quad \frac{9}{10}.$$
We can simplify $\frac{18}{20}$ by dividing the numerator and denominator by $2$:
$$\frac{18 \div 2}{20 \div 2} = \frac{9}{10}.$$
Since $\frac{18}{20}$ simplifies exactly to $\frac{9}{10}$, we have
$$\frac{18}{20} = \frac{9}{10}.$$
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Problem 22: Compare the ratios
$$5:25 \quad \text{and} \quad 4:16.$$
Interpreting the ratios as fractions, we have:
$$\frac{5}{25} \quad \text{and} \quad \frac{4}{16}.$$
Simplify each fraction:
- For the first ratio:
$$\frac{5}{25} = \frac{1}{5} = 0.2.$$
- For the second ratio:
$$\frac{4}{16} = \frac{1}{4} = 0.25.$$
Since $0.2 \neq 0.25$, the ratios are not equivalent. Thus,
$$5:25 \neq 4:16.$$
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Problem 23: Compare the ratios
$$7:9 \quad \text{and} \quad 21:27.$$
Express these ratios as fractions:
$$\frac{7}{9} \quad \text{and} \quad \frac{21}{27}.$$
Notice that $21 = 3 \times 7$ and $27 = 3 \times 9$. We can factor out the common multiple in the second fraction:
$$\frac{21}{27} = \frac{3 \times 7}{3 \times 9} = \frac{7}{9}.$$
Since both fractions are the same, we have
$$7:9 = 21:27.$$
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Summary of Answers:
20) $$\frac{3}{5} \neq \frac{4}{7}.$$
21) $$\frac{18}{20} = \frac{9}{10}.$$
22) $$5:25 \neq 4:16.$$
23) $$7:9 = 21:27.$$
------------------------------------------------------------
Problem 20: Compare
$$\frac{3}{5} \quad \text{and} \quad \frac{4}{7}.$$
One method is to cross-multiply to see if the fractions are equivalent. We check if
$$3 \times 7 \stackrel{?}{=} 5 \times 4.$$
Calculating each side:
$$3 \times 7 = 21,$$
$$5 \times 4 = 20.$$
Since $21 \neq 20$, we conclude that
$$\frac{3}{5} \neq \frac{4}{7}.$$
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Problem 21: Compare
$$\frac{18}{20} \quad \text{and} \quad \frac{9}{10}.$$
We can simplify $\frac{18}{20}$ by dividing the numerator and denominator by $2$:
$$\frac{18 \div 2}{20 \div 2} = \frac{9}{10}.$$
Since $\frac{18}{20}$ simplifies exactly to $\frac{9}{10}$, we have
$$\frac{18}{20} = \frac{9}{10}.$$
------------------------------------------------------------
Problem 22: Compare the ratios
$$5:25 \quad \text{and} \quad 4:16.$$
Interpreting the ratios as fractions, we have:
$$\frac{5}{25} \quad \text{and} \quad \frac{4}{16}.$$
Simplify each fraction:
- For the first ratio:
$$\frac{5}{25} = \frac{1}{5} = 0.2.$$
- For the second ratio:
$$\frac{4}{16} = \frac{1}{4} = 0.25.$$
Since $0.2 \neq 0.25$, the ratios are not equivalent. Thus,
$$5:25 \neq 4:16.$$
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Problem 23: Compare the ratios
$$7:9 \quad \text{and} \quad 21:27.$$
Express these ratios as fractions:
$$\frac{7}{9} \quad \text{and} \quad \frac{21}{27}.$$
Notice that $21 = 3 \times 7$ and $27 = 3 \times 9$. We can factor out the common multiple in the second fraction:
$$\frac{21}{27} = \frac{3 \times 7}{3 \times 9} = \frac{7}{9}.$$
Since both fractions are the same, we have
$$7:9 = 21:27.$$
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Summary of Answers:
20) $$\frac{3}{5} \neq \frac{4}{7}.$$
21) $$\frac{18}{20} = \frac{9}{10}.$$
22) $$5:25 \neq 4:16.$$
23) $$7:9 = 21:27.$$
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