write \\ , \=\ or \

Question

write \>\ , \=\ or \<\ to compare the fractions.
1. $\frac{8}{20}$ $\underline{}$ $\frac{3}{6}$
2. $\frac{1}{10}$ $\underline{}$ $\frac{1}{4}$
3. $\frac{1}{5}$ $\underline{}$ $\frac{5}{10}$
4. $\frac{5}{15}$ $\underline{}$ $\frac{7}{12}$
5. $\frac{2}{4}$ $\underline{}$ $\frac{10}{40}$
6. $\frac{2}{6}$ $\underline{}$ $\frac{20}{50}$
7. $\frac{4}{5}$ $\underline{}$ $\frac{7}{10}$
8. $\frac{5}{12}$ $\underline{}$ $\frac{1}{2}$
9. $\frac{4}{6}$ $\underline{}$ $\frac{42}{48}$
10. $\frac{3}{6}$ $\underline{}$ $\frac{2}{4}$
11. $\frac{3}{9}$ $\underline{}$ $\frac{10}{50}$
12. $\frac{10}{20}$ $\underline{}$ $\frac{4}{8}$
13. $\frac{5}{8}$ $\underline{}$ $\frac{2}{6}$
14. $\frac{5}{60}$ $\underline{}$ $\frac{16}{20}$
15. $\frac{6}{24}$ $\underline{}$ $\frac{2}{10}$
16. $\frac{20}{24}$ $\underline{}$ $\frac{3}{9}$
17. $\frac{18}{48}$ $\underline{}$ $\frac{10}{30}$
18. $\frac{2}{10}$ $\underline{}$ $\frac{1}{2}$

Accepted Answer

### 1. Compare $\boldsymbol{\frac{8}{20}}$ and $\boldsymbol{\frac{3}{6}}$ # Explanation: ## Step1: Simplify fractions Simplify $\frac{8}{20}$: $\frac{8\div4}{20\div4}=\frac{2}{5}$; Simplify $\frac{3}{6}$: $\frac{3\div3}{6\div3}=\frac{1}{2}$. ## Step2: Find common denominator Common denominator of 5 and 2 is 10. $\frac{2}{5}=\frac{4}{10}$, $\frac{1}{2}=\frac{5}{10}$. ## Step3: Compare numerators Since $4 < 5$, $\frac{4}{10}<\frac{5}{10}$, so $\frac{8}{20}<\frac{3}{6}$? Wait, no, wait: Wait, $\frac{8}{20}=0.4$, $\frac{3}{6}=0.5$, so $0.4 < 0.5$? Wait, I made a mistake. Wait, $\frac{8}{20}=0.4$, $\frac{3}{6}=0.5$, so $\frac{8}{20}<\frac{3}{6}$? But the original mark is $>$, maybe I miscalculated. Wait, no, let's do it again. $\frac{8}{20}=\frac{2}{5}=0.4$, $\frac{3}{6}=0.5$, so $0.4 < 0.5$, so the correct symbol is $<$. Wait, maybe the original mark is wrong, but let's solve it properly. Wait, maybe I messed up. Let's use cross - multiplication. For $\frac{a}{b}$ and $\frac{c}{d}$, if $ad>bc$, then $\frac{a}{b}>\frac{c}{d}$. So for $\frac{8}{20}$ and $\frac{3}{6}$, $8 imes6 = 48$, $3 imes20 = 60$. Since $48<60$, so $\frac{8}{20}<\frac{3}{6}$. ### 2. Compare $\boldsymbol{\frac{1}{10}}$ and $\boldsymbol{\frac{1}{4}}$ # Explanation: ## Step1: Analyze numerators and denominators When numerators are the same, the fraction with the larger denominator is smaller. ## Step2: Compare denominators Since $10 > 4$, so $\frac{1}{10}<\frac{1}{4}$. ### 3. Compare $\boldsymbol{\frac{1}{5}}$ and $\boldsymbol{\frac{5}{10}}$ # Explanation: ## Step1: Simplify $\frac{5}{10}$ $\frac{5}{10}=\frac{1}{2}$. ## Step2: Compare $\frac{1}{5}$ and $\frac{1}{2}$ When numerators are the same, the fraction with the larger denominator is smaller. Since $5 > 2$, so $\frac{1}{5}<\frac{1}{2}$, that is $\frac{1}{5}<\frac{5}{10}$. ### 4. Compare $\boldsymbol{\frac{5}{15}}$ and $\boldsymbol{\frac{7}{12}}$ # Explanation: ## Step1: Simplify $\frac{5}{15}$ $\frac{5}{15}=\frac{1}{3}\approx0.333$. ## Step2: Simplify $\frac{7}{12}\approx0.583$ ## Step3: Compare decimals Since $0.333<0.583$, so $\frac{5}{15}<\frac{7}{12}$. ### 5. Compare $\boldsymbol{\frac{2}{4}}$ and $\boldsymbol{\frac{10}{40}}$ # Explanation: ## Step1: Simplify fractions $\frac{2}{4}=\frac{1}{2}=0.5$, $\frac{10}{40}=\frac{1}{4}=0.25$. ## Step2: Compare decimals Since $0.5 > 0.25$, so $\frac{2}{4}>\frac{10}{40}$. ### 6. Compare $\boldsymbol{\frac{2}{6}}$ and $\boldsymbol{\frac{20}{50}}$ # Explanation: ## Step1: Simplify fractions $\frac{2}{6}=\frac{1}{3}\approx0.333$, $\frac{20}{50}=\frac{2}{5}=0.4$. ## Step2: Compare decimals Since $0.333<0.4$, so $\frac{2}{6}<\frac{20}{50}$. ### 7. Compare $\boldsymbol{\frac{4}{5}}$ and $\boldsymbol{\frac{7}{10}}$ # Explanation: ## Step1: Find common denominator Common denominator of 5 and 10 is 10. $\frac{4}{5}=\frac{8}{10}$. ## Step2: Compare numerators Since $8 > 7$, so $\frac{8}{10}>\frac{7}{10}$, that is $\frac{4}{5}>\frac{7}{10}$. ### 8. Compare $\boldsymbol{\frac{5}{12}}$ and $\boldsymbol{\frac{1}{2}}$ # Explanation: ## Step1: Convert $\frac{1}{2}$ to twelfths $\frac{1}{2}=\frac{6}{12}$. ## Step2: Compare numerators Since $5 < 6$, so $\frac{5}{12}<\frac{1}{2}$. ### 9. Compare $\boldsymbol{\frac{4}{6}}$ and $\boldsymbol{\frac{42}{48}}$ # Explanation: ## Step1: Simplify fractions $\frac{4}{6}=\frac{2}{3}\approx0.666$, $\frac{42}{48}=\frac{7}{8}=0.875$. ## Step2: Compare decimals Since $0.666<0.875$, so $\frac{4}{6}<\frac{42}{48}$. ### 10. Compare $\boldsymbol{\frac{3}{6}}$ and $\boldsymbol{\frac{2}{4}}$ # Explanation: ## Step1: Simplify fractions $\frac{3}{6}=\frac{1}{2}$, $\frac{2}{4}=\frac{1}{2}$. ## Step2: Compare Since both are equal to $\frac{1}{2}$, so $\frac{3}{6}=\frac{2}{4}$. ### 11. Compare $\boldsymbol{\frac{3}{9}}$ and $\boldsymbol{\frac{10}{50}}$ # Explanation: ## Step1: Simplify fractions $\frac{3}{9}=\frac{1}{3}\approx0.333$, $\frac{10}{50}=\frac{1}{5}=0.2$. ## Step2: Compare decimals Since $0.333>0.2$, so $\frac{3}{9}>\frac{10}{50}$. ### 12. Compare $\boldsymbol{\frac{10}{20}}$ and $\boldsymbol{\frac{4}{8}}$ # Explanation: ## Step1: Simplify fractions $\frac{10}{20}=\frac{1}{2}$, $\frac{4}{8}=\frac{1}{2}$. ## Step2: Compare Since both are equal to $\frac{1}{2}$, so $\frac{10}{20}=\frac{4}{8}$. ### 13. Compare $\boldsymbol{\frac{5}{8}}$ and $\boldsymbol{\frac{2}{6}}$ # Explanation: ## Step1: Simplify $\frac{2}{6}$ $\frac{2}{6}=\frac{1}{3}\approx0.333$, $\frac{5}{8}=0.625$. ## Step2: Compare decimals Since $0.625>0.333$, so $\frac{5}{8}>\frac{2}{6}$. ### 14. Compare $\boldsymbol{\frac{5}{60}}$ and $\boldsymbol{\frac{16}{20}}$ # Explanation: ## Step1: Simplify fractions $\frac{5}{60}=\frac{1}{12}\approx0.083$, $\frac{16}{20}=\frac{4}{5}=0.8$. ## Step2: Compare decimals Since $0.083<0.8$, so $\frac{5}{60}<\frac{16}{20}$. ### 15. Compare $\boldsymbol{\frac{6}{24}}$ and $\boldsymbol{\frac{2}{10}}$ # Explanation: ## Step1: Simplify fractions $\frac{6}{24}=\frac{1}{4}=0.25$, $\frac{2}{10}=\frac{1}{5}=0.2$. ## Step2: Compare decimals Since $0.25>0.2$, so $\frac{6}{24}>\frac{2}{10}$. ### 16. Compare $\boldsymbol{\frac{20}{24}}$ and $\boldsymbol{\frac{3}{9}}$ # Explanation: ## Step1: Simplify fractions $\frac{20}{24}=\frac{5}{6}\approx0.833$, $\frac{3}{9}=\frac{1}{3}\approx0.333$. ## Step2: Compare decimals Since $0.833>0.333$, so $\frac{20}{24}>\frac{3}{9}$. ### 17. Compare $\boldsymbol{\frac{18}{48}}$ and $\boldsymbol{\frac{10}{30}}$ # Explanation: ## Step1: Simplify fractions $\frac{18}{48}=\frac{3}{8}=0.375$, $\frac{10}{30}=\frac{1}{3}\approx0.333$. ## Step2: Compare decimals Since $0.375>0.333$, so $\frac{18}{48}>\frac{10}{30}$. ### 18. Compare $\boldsymbol{\frac{2}{10}}$ and $\boldsymbol{\frac{1}{2}}$ # Explanation: ## Step1: Simplify $\frac{2}{10}$ $\frac{2}{10}=\frac{1}{5}=0.2$, $\frac{1}{2}=0.5$. ## Step2: Compare decimals Since $0.2<0.5$, so $\frac{2}{10}<\frac{1}{2}$. # Answers: 1. $\frac{8}{20}<\frac{3}{6}$ 2. $\frac{1}{10}<\frac{1}{4}$ 3. $\frac{1}{5}<\frac{5}{10}$ 4. $\frac{5}{15}<\frac{7}{12}$ 5. $\frac{2}{4}>\frac{10}{40}$ 6. $\frac{2}{6}<\frac{20}{50}$ 7. $\frac{4}{5}>\frac{7}{10}$ 8. $\frac{5}{12}<\frac{1}{2}$ 9. $\frac{4}{6}<\frac{42}{48}$ 10. $\frac{3}{6}=\frac{2}{4}$ 11. $\frac{3}{9}>\frac{10}{50}$ 12. $\frac{10}{20}=\frac{4}{8}$ 13. $\frac{5}{8}>\frac{2}{6}$ 14. $\frac{5}{60}<\frac{16}{20}$ 15. $\frac{6}{24}>\frac{2}{10}$ 16. $\frac{20}{24}>\frac{3}{9}$ 17. $\frac{18}{48}>\frac{10}{30}$ 18. $\frac{2}{10}<\frac{1}{2}$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

1. Compare $\boldsymbol{\frac{8}{20}}$ and $\boldsymbol{\frac{3}{6}}$

Step1: Simplify fractions

Step2: Find common denominator

Step3: Compare numerators

2. Compare $\boldsymbol{\frac{1}{10}}$ and $\boldsymbol{\frac{1}{4}}$

Step1: Analyze numerators and denominators

Step2: Compare denominators

3. Compare $\boldsymbol{\frac{1}{5}}$ and $\boldsymbol{\frac{5}{10}}$

Step1: Simplify $\frac{5}{10}$

Step2: Compare $\frac{1}{5}$ and $\frac{1}{2}$

4. Compare $\boldsymbol{\frac{5}{15}}$ and $\boldsymbol{\frac{7}{12}}$

Answer: