Complete the following equivalent fractions: $$ \begin{array}{lllll} ext { a) } \frac{3}{5}=\frac{\square}{10}=\frac{\square}{100} & ext { b) } \frac{2}{9}=\frac{\square}{27}=\frac{\square}{54} & ext { c) } \frac{6}{7}=\frac{42}{\square}=\frac{\square}{21} \ \begin{array}{llll} ext { d) } \frac{10}{100}=\frac{1}{\square}=\frac{\square}{10000} & ext { e) } \frac{7}{3}=\frac{14}{\square}=\frac{\square}{30} & ext { f) } \frac{300}{2000}=\frac{150}{\square}=\frac{900}{\square} \ ext { Give three equivalent fractions for each of the following fractions: } \ \begin{array}{lllll} ext { a) } \frac{1}{4} & ext { b) } \frac{2}{5} & ext { c) } \frac{3}{15} & ext { d) } \frac{19}{31} & ext { e) } \frac{200}{10000}\end{array} & ext { f) } \frac{24}{9}\end{array}\end{array} $$.

Question

Complete the following equivalent fractions: $$ \begin{array}{lllll}	ext { a) } \frac{3}{5}=\frac{\square}{10}=\frac{\square}{100} & 	ext { b) } \frac{2}{9}=\frac{\square}{27}=\frac{\square}{54} & 	ext { c) } \frac{6}{7}=\frac{42}{\square}=\frac{\square}{21} \ \begin{array}{llll}	ext { d) } \frac{10}{100}=\frac{1}{\square}=\frac{\square}{10000} & 	ext { e) } \frac{7}{3}=\frac{14}{\square}=\frac{\square}{30} & 	ext { f) } \frac{300}{2000}=\frac{150}{\square}=\frac{900}{\square} \ 	ext { Give three equivalent fractions for each of the following fractions: } \ \begin{array}{lllll}	ext { a) } \frac{1}{4} & 	ext { b) } \frac{2}{5} & 	ext { c) } \frac{3}{15} & 	ext { d) } \frac{19}{31} & 	ext { e) } \frac{200}{10000}\end{array} & 	ext { f) } \frac{24}{9}\end{array}\end{array} $$.

UpStudy AI · Accepted Answer

Sure! Let's go through each part step by step.

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### **Complete the Equivalent Fractions**

#### **a) $$\frac{3}{5} = \frac{\square}{10} = \frac{\square}{100}$$**
- To find the fraction with denominator **10**:
  $$
  \frac{3}{5} = \frac{3 \times 2}{5 \times 2} = \frac{6}{10}
  $$
- To find the fraction with denominator **100**:
  $$
  \frac{3}{5} = \frac{3 \times 20}{5 \times 20} = \frac{60}{100}
  $$
  
**Completed Fractions:**
$$
\frac{3}{5} = \frac{6}{10} = \frac{60}{100}
$$

---

#### **b) $$\frac{2}{9} = \frac{\square}{27} = \frac{\square}{54}$$**
- To find the fraction with denominator **27**:
  $$
  \frac{2}{9} = \frac{2 \times 3}{9 \times 3} = \frac{6}{27}
  $$
- To find the fraction with denominator **54**:
  $$
  \frac{2}{9} = \frac{2 \times 6}{9 \times 6} = \frac{12}{54}
  $$
  
**Completed Fractions:**
$$
\frac{2}{9} = \frac{6}{27} = \frac{12}{54}
$$

---

#### **c) $$\frac{6}{7} = \frac{42}{\square} = \frac{\square}{21}$$**
- To find the missing denominator when numerator is **42**:
  $$
  \frac{6}{7} = \frac{42}{x} \Rightarrow 6x = 7 \times 42 \Rightarrow x = 49
  $$
- To find the missing numerator when denominator is **21**:
  $$
  \frac{6}{7} = \frac{y}{21} \Rightarrow 7y = 6 \times 21 \Rightarrow y = 18
  $$
  
**Completed Fractions:**
$$
\frac{6}{7} = \frac{42}{49} = \frac{18}{21}
$$

---

#### **d) $$\frac{10}{100} = \frac{1}{\square} = \frac{\square}{10000}$$**
- Simplify $$\frac{10}{100}$$:
  $$
  \frac{10}{100} = \frac{1}{10}
  $$
- To find the fraction with denominator **10,000**:
  $$
  \frac{10}{100} = \frac{10 \times 100}{100 \times 100} = \frac{1000}{10000}
  $$
  
**Completed Fractions:**
$$
\frac{10}{100} = \frac{1}{10} = \frac{1000}{10000}
$$

---

#### **e) $$\frac{7}{3} = \frac{14}{\square} = \frac{\square}{30}$$**
- To find the missing denominator when numerator is **14**:
  $$
  \frac{7}{3} = \frac{14}{x} \Rightarrow 7x = 3 \times 14 \Rightarrow x = 6
  $$
- To find the missing numerator when denominator is **30**:
  $$
  \frac{7}{3} = \frac{y}{30} \Rightarrow 3y = 7 \times 30 \Rightarrow y = 70
  $$
  
**Completed Fractions:**
$$
\frac{7}{3} = \frac{14}{6} = \frac{70}{30}
$$

---

#### **f) $$\frac{300}{2000} = \frac{150}{\square} = \frac{900}{\square}$$**
- To find the missing denominator when numerator is **150**:
  $$
  \frac{300}{2000} = \frac{150}{x} \Rightarrow 300x = 2000 \times 150 \Rightarrow x = 1000
  $$
- To find the missing denominator when numerator is **900**:
  $$
  \frac{300}{2000} = \frac{900}{x} \Rightarrow 300x = 2000 \times 900 \Rightarrow x = 6000
  $$
  
**Completed Fractions:**
$$
\frac{300}{2000} = \frac{150}{1000} = \frac{900}{6000}
$$

---

### **Give Three Equivalent Fractions for Each**

#### **a) $$\frac{1}{4}$$**
1. $$\frac{2}{8}$$ (multiply numerator and denominator by 2)
2. $$\frac{3}{12}$$ (multiply by 3)
3. $$\frac{4}{16}$$ (multiply by 4)

#### **b) $$\frac{2}{5}$$**
1. $$\frac{4}{10}$$ (multiply by 2)
2. $$\frac{6}{15}$$ (multiply by 3)
3. $$\frac{8}{20}$$ (multiply by 4)

#### **c) $$\frac{3}{15}$$**
1. $$\frac{6}{30}$$ (multiply by 2)
2. $$\frac{9}{45}$$ (multiply by 3)
3. $$\frac{12}{60}$$ (multiply by 4)

*Note:* $$\frac{3}{15}$$ simplifies to $$\frac{1}{5}$$, but equivalent fractions maintain the same ratio.

#### **d) $$\frac{19}{31}$$**
1. $$\frac{38}{62}$$ (multiply by 2)
2. $$\frac{57}{93}$$ (multiply by 3)
3. $$\frac{76}{124}$$ (multiply by 4)

#### **e) $$\frac{200}{10000}$$**
1. $$\frac{400}{20000}$$ (multiply by 2)
2. $$\frac{600}{30000}$$ (multiply by 3)
3. $$\frac{800}{40000}$$ (multiply by 4)

*Alternatively, since $$\frac{200}{10000}$$ simplifies to $$\frac{1}{50}$$, any multiples maintaining the ratio are correct.*

#### **f) $$\frac{24}{9}$$**
1. $$\frac{48}{18}$$ (multiply by 2)
2. $$\frac{72}{27}$$ (multiply by 3)
3. $$\frac{96}{36}$$ (multiply by 4)

*Note:* This fraction can also be simplified to $$\frac{8}{3}$$, but equivalent fractions preserve the original ratio.

---

Feel free to ask if you need further explanations or assistance!
Here are the completed equivalent fractions: **a)** $$ \frac{3}{5} = \frac{6}{10} = \frac{60}{100} $$ **b)** $$ \frac{2}{9} = \frac{6}{27} = \frac{12}{54} $$ **c)** $$ \frac{6}{7} = \frac{42}{49} = \frac{18}{21} $$ **d)** $$ \frac{10}{100} = \frac{1}{10} = \frac{1000}{10000} $$ **e)** $$ \frac{7}{3} = \frac{14}{6} = \frac{70}{30} $$ **f)** $$ \frac{300}{2000} = \frac{150}{1000} = \frac{900}{6000} $$ **Equivalent Fractions:** **a) $$\frac{1}{4}$$** 1. $$\frac{2}{8}$$ 2. $$\frac{3}{12}$$ 3. $$\frac{4}{16}$$ **b) $$\frac{2}{5}$$** 1. $$\frac{4}{10}$$ 2. $$\frac{6}{15}$$ 3. $$\frac{8}{20}$$ **c) $$\frac{3}{15}$$** 1. $$\frac{6}{30}$$ 2. $$\frac{9}{45}$$ 3. $$\frac{12}{60}$$ **d) $$\frac{19}{31}$$** 1. $$\frac{38}{62}$$ 2. $$\frac{57}{93}$$ 3. $$\frac{76}{124}$$ **e) $$\frac{200}{10000}$$** 1. $$\frac{400}{20000}$$ 2. $$\frac{600}{30000}$$ 3. $$\frac{800}{40000}$$ **f) $$\frac{24}{9}$$** 1. $$\frac{48}{18}$$ 2. $$\frac{72}{27}$$ 3. $$\frac{96}{36}$$

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