1. Replace the * with the correct relationship sign $$ $$ or $$ = $$ $$ \begin{array}{ll} ext { a) } \frac{1}{2}=\frac{3}{4} & ext { b) } \frac{1}{3}=\frac{1}{4} \ ext { c) } \frac{1}{10}=\frac{1}{100} & ext { d) } \frac{10}{100}=\frac{100}{1000} \ ext { e) } \frac{2}{10}+\frac{20}{1000} & ext { f) } 2=\frac{7}{3} \ ext { g) } \frac{2}{5}+\frac{6}{10} & ext { h) } \frac{1}{7}+\frac{8}{17} \ ext { i) } \frac{21}{100}+\frac{11}{50} & ext { j) } \frac{3}{2}=\frac{5}{3}\end{array} $$

Question

1. Replace the * with the correct relationship sign $$ <,> $$ or $$ = $$ $$ \begin{array}{ll}	ext { a) } \frac{1}{2}=\frac{3}{4} & 	ext { b) } \frac{1}{3}=\frac{1}{4} \ 	ext { c) } \frac{1}{10}=\frac{1}{100} & 	ext { d) } \frac{10}{100}=\frac{100}{1000} \ 	ext { e) } \frac{2}{10}+\frac{20}{1000} & 	ext { f) } 2=\frac{7}{3} \ 	ext { g) } \frac{2}{5}+\frac{6}{10} & 	ext { h) } \frac{1}{7}+\frac{8}{17} \ 	ext { i) } \frac{21}{100}+\frac{11}{50} & 	ext { j) } \frac{3}{2}=\frac{5}{3}\end{array} $$

UpStudy AI · Accepted Answer

Alright, I need to determine the correct relationship signs (<, >, or =) for each of the given fractions. Let's tackle them one by one. **a) $$\frac{1}{2} = \frac{3}{4}$$** - To compare these fractions, I'll convert them to decimals. - $$\frac{1}{2} = 0.5$$ - $$\frac{3}{4} = 0.75$$ - Since 0.5 < 0.75, the correct sign is <. **b) $$\frac{1}{3} = \frac{1}{4}$$** - Converting to decimals: - $$\frac{1}{3} \approx 0.333$$ - $$\frac{1}{4} = 0.25$$ - 0.333 > 0.25, so the correct sign is >. **c) $$\frac{1}{10} = \frac{1}{100}$$** - Converting to decimals: - $$\frac{1}{10} = 0.1$$ - $$\frac{1}{100} = 0.01$$ - 0.1 > 0.01, so the correct sign is >. **d) $$\frac{10}{100} = \frac{100}{1000}$$** - Simplifying both fractions: - $$\frac{10}{100} = \frac{1}{10} = 0.1$$ - $$\frac{100}{1000} = \frac{1}{10} = 0.1$$ - Both are equal, so the correct sign is =. **e) $$\frac{2}{10} + \frac{20}{1000}$$** - Simplifying each fraction: - $$\frac{2}{10} = \frac{1}{5} = 0.2$$ - $$\frac{20}{1000} = \frac{1}{50} = 0.02$$ - Adding them: 0.2 + 0.02 = 0.22 - Since 0.22 is greater than 0.2, the correct sign is >. **f) $$2 = \frac{7}{3}$$** - Converting $$\frac{7}{3}$$ to a decimal: - $$\frac{7}{3} \approx 2.333$$ - 2 < 2.333, so the correct sign is <. **g) $$\frac{2}{5} + \frac{6}{10}$$** - Simplifying each fraction: - $$\frac{2}{5} = 0.4$$ - $$\frac{6}{10} = 0.6$$ - Adding them: 0.4 + 0.6 = 1.0 - Since 1.0 is equal to 1, the correct sign is =. **h) $$\frac{1}{7} + \frac{8}{17}$$** - Converting to decimals: - $$\frac{1}{7} \approx 0.142857$$ - $$\frac{8}{17} \approx 0.470588$$ - Adding them: 0.142857 + 0.470588 ≈ 0.613445 - Since 0.613445 is greater than 0.6, the correct sign is >. **i) $$\frac{21}{100} + \frac{11}{50}$$** - Simplifying each fraction: - $$\frac{21}{100} = 0.21$$ - $$\frac{11}{50} = 0.22$$ - Adding them: 0.21 + 0.22 = 0.43 - Since 0.43 is greater than 0.4, the correct sign is >. **j) $$\frac{3}{2} = \frac{5}{3}$$** - Converting to decimals: - $$\frac{3}{2} = 1.5$$ - $$\frac{5}{3} \approx 1.666$$ - 1.5 < 1.666, so the correct sign is <. a) < b) > c) > d) = e) > f) < g) = h) > i) > j) <

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