Question

j. \\(\frac{25}{40}\\) \\(\underline{\hspace{5cm}}\\) k. \\(\frac{8}{12}\\) \\(\underline{\hspace{5cm}}\\) find three equivalent fractions for each fraction show m. \\(\frac{2}{4}\\) \\(\underline{\hspace{8cm}}\\) o. \\(\frac{4}{12}\\) \\(\underline{\hspace{8cm}}\\) q. anthony baked two pizzas that were the same si one to his sister, keyarra. anthony ate \\(\frac{1}{4}\\) of his pi use multiplication or division to show that they b

Explanation:

Part j: $\boldsymbol{\frac{25}{40}}$

To find equivalent fractions, we multiply or divide the numerator and denominator by the same non - zero number.

Step 1: Simplify by dividing by 5

We know that to simplify a fraction, we can divide both the numerator and the denominator by their greatest common divisor. The GCD of 25 and 40 is 5. So, $\frac{25\div5}{40\div5}=\frac{5}{8}$.

Step 2: Multiply by 2

Multiply the numerator and denominator of $\frac{5}{8}$ by 2. We get $\frac{5\times2}{8\times2}=\frac{10}{16}$.

Step 3: Multiply by 3

Multiply the numerator and denominator of $\frac{5}{8}$ by 3. We have $\frac{5\times3}{8\times3}=\frac{15}{24}$.

Part m: $\boldsymbol{\frac{2}{4}}$

We use the property of equivalent fractions (multiplying numerator and denominator by the same non - zero number).

Step 1: Simplify by dividing by 2

The GCD of 2 and 4 is 2. So, $\frac{2\div2}{4\div2}=\frac{1}{2}$.

Step 2: Multiply by 2

Multiply the numerator and denominator of $\frac{1}{2}$ by 2. We obtain $\frac{1\times2}{2\times2}=\frac{2}{4}$ (original, but we can also get a new one: multiply by 3, $\frac{1\times3}{2\times3}=\frac{3}{6}$). Wait, let's do it properly. Start with $\frac{2}{4}$, divide numerator and denominator by 2 to get $\frac{1}{2}$. Then multiply $\frac{1}{2}$ by 2: $\frac{1\times2}{2\times2}=\frac{2}{4}$ (not new), multiply by 3: $\frac{1\times3}{2\times3}=\frac{3}{6}$, multiply by 4: $\frac{1\times4}{2\times4}=\frac{4}{8}$. So three equivalent fractions: $\frac{1}{2}$, $\frac{3}{6}$, $\frac{4}{8}$.

Part o: $\boldsymbol{\frac{4}{12}}$

We use the method of multiplying or dividing numerator and denominator by the same non - zero number.

Step 1: Simplify by dividing by 4

The GCD of 4 and 12 is 4. So, $\frac{4\div4}{12\div4}=\frac{1}{3}$.

Step 2: Multiply by 2

Multiply the numerator and denominator of $\frac{1}{3}$ by 2. We get $\frac{1\times2}{3\times2}=\frac{2}{6}$.

Step 3: Multiply by 3

Multiply the numerator and denominator of $\frac{1}{3}$ by 3. We have $\frac{1\times3}{3\times3}=\frac{3}{9}$.

Part q: (Incomplete question, but assuming we need to find something about the pizza consumption)

Since the question is incomplete, we can't provide a full solution. But if we assume the question is about comparing the amount Anthony and Keyarra ate (assuming Keyarra's pizza and Anthony's pizza are the same size), and Anthony ate $\frac{1}{4}$ of his pizza. If we want to find equivalent fractions for $\frac{1}{4}$, we can do the following:

Step 1: Multiply by 2

$\frac{1\times2}{4\times2}=\frac{2}{8}$

Step 2: Multiply by 3

$\frac{1\times3}{4\times3}=\frac{3}{12}$

Step 3: Multiply by 4

$\frac{1\times4}{4\times4}=\frac{4}{16}$

Answer:

s:

• j: $\frac{5}{8}$, $\frac{10}{16}$, $\frac{15}{24}$ (and more are possible)
• m: $\frac{1}{2}$, $\frac{3}{6}$, $\frac{4}{8}$ (and more are possible)
• o: $\frac{1}{3}$, $\frac{2}{6}$, $\frac{3}{9}$ (and more are possible)
• q: (Depends on the complete question, but equivalent fractions for $\frac{1}{4}$ could be $\frac{2}{8}$, $\frac{3}{12}$, $\frac{4}{16}$)