Fraction comparison worksheet using cross multiplication to determine equivalence.

Problem Overview:

The task involves comparing pairs of fractions using cross multiplication to determine if they are equivalent. Two fractions are equivalent if their cross products are equal. The general steps for cross multiplication are:

1. Multiply the numerator of the first fraction by the denominator of the second fraction.
2. Multiply the numerator of the second fraction by the denominator of the first fraction.
3. Compare the two products:
- If the products are equal, the fractions are equivalent.
- If the products are not equal, the fractions are not equivalent.

Solution:

We will solve each pair of fractions step by step using cross multiplication.

---

#### 1) $\frac{2}{4}$ and $\frac{10}{7}$
- Cross multiply:
$$
2 \times 7 = 14 \quad \text{and} \quad 4 \times 10 = 40
$$
- Compare: $14 \neq 40$
- Answer: No

---

#### 2) $\frac{1}{3}$ and $\frac{5}{15}$
- Cross multiply:
$$
1 \times 15 = 15 \quad \text{and} \quad 3 \times 5 = 15
$$
- Compare: $15 = 15$
- Answer: Yes

---

#### 3) $\frac{2}{3}$ and $\frac{4}{5}$
- Cross multiply:
$$
2 \times 5 = 10 \quad \text{and} \quad 3 \times 4 = 12
$$
- Compare: $10 \neq 12$
- Answer: No

---

#### 4) $\frac{2}{5}$ and $\frac{12}{30}$
- Cross multiply:
$$
2 \times 30 = 60 \quad \text{and} \quad 5 \times 12 = 60
$$
- Compare: $60 = 60$
- Answer: Yes

---

#### 5) $\frac{2}{3}$ and $\frac{3}{7}$
- Cross multiply:
$$
2 \times 7 = 14 \quad \text{and} \quad 3 \times 3 = 9
$$
- Compare: $14 \neq 9$
- Answer: No

---

#### 6) $\frac{15}{36}$ and $\frac{5}{12}$
- Cross multiply:
$$
15 \times 12 = 180 \quad \text{and} \quad 36 \times 5 = 180
$$
- Compare: $180 = 180$
- Answer: Yes

---

#### 7) $\frac{8}{12}$ and $\frac{40}{60}$
- Cross multiply:
$$
8 \times 60 = 480 \quad \text{and} \quad 12 \times 40 = 480
$$
- Compare: $480 = 480$
- Answer: Yes

---

#### 8) $\frac{3}{9}$ and $\frac{12}{36}$
- Cross multiply:
$$
3 \times 36 = 108 \quad \text{and} \quad 9 \times 12 = 108
$$
- Compare: $108 = 108$
- Answer: Yes

---

#### 9) $\frac{3}{5}$ and $\frac{4}{7}$
- Cross multiply:
$$
3 \times 7 = 21 \quad \text{and} \quad 5 \times 4 = 20
$$
- Compare: $21 \neq 20$
- Answer: No

---

#### 10) $\frac{10}{15}$ and $\frac{20}{30}$
- Cross multiply:
$$
10 \times 30 = 300 \quad \text{and} \quad 15 \times 20 = 300
$$
- Compare: $300 = 300$
- Answer: Yes

---

#### 11) $\frac{7}{3}$ and $\frac{10}{7}$
- Cross multiply:
$$
7 \times 7 = 49 \quad \text{and} \quad 3 \times 10 = 30
$$
- Compare: $49 \neq 30$
- Answer: No

---

#### 12) $\frac{45}{75}$ and $\frac{15}{25}$
- Cross multiply:
$$
45 \times 25 = 1125 \quad \text{and} \quad 75 \times 15 = 1125
$$
- Compare: $1125 = 1125$
- Answer: Yes

---

#### 13) $\frac{5}{15}$ and $\frac{4}{20}$
- Cross multiply:
$$
5 \times 20 = 100 \quad \text{and} \quad 15 \times 4 = 60
$$
- Compare: $100 \neq 60$
- Answer: No

---

#### 14) $\frac{32}{60}$ and $\frac{8}{15}$
- Cross multiply:
$$
32 \times 15 = 480 \quad \text{and} \quad 60 \times 8 = 480
$$
- Compare: $480 = 480$
- Answer: Yes

---

#### 15) $\frac{20}{35}$ and $\frac{5}{7}$
- Cross multiply:
$$
20 \times 7 = 140 \quad \text{and} \quad 35 \times 5 = 175
$$
- Compare: $140 \neq 175$
- Answer: No

---

#### 16) $\frac{4}{5}$ and $\frac{2}{7}$
- Cross multiply:
$$
4 \times 7 = 28 \quad \text{and} \quad 5 \times 2 = 10
$$
- Compare: $28 \neq 10$
- Answer: No

---

Final Answers:

$$
\boxed{
\begin{array}{ll}
1) \text{No} & 2) \text{Yes} \\
3) \text{No} & 4) \text{Yes} \\
5) \text{No} & 6) \text{Yes} \\
7) \text{Yes} & 8) \text{Yes} \\
9) \text{No} & 10) \text{Yes} \\
11) \text{No} & 12) \text{Yes} \\
13) \text{No} & 14) \text{Yes} \\
15) \text{No} & 16) \text{No} \\
\end{array}
}
$$