Chapter 7: Q14. (page 243)

. $x = 12, y = 10, a n d z = 24$ Write each ratio in simplest form.
$x : (x + y) : (y + z)$

Short Answer

Expert verified

The simplest form is $x : (x + y) : (y + z) = 12 : 22 : 34$

Step by step solution

Step 1. Given information.

According to the given values,

$\begin{array}{l} x = 12 \\ y = 10 \\ z = 24 \end{array}$

Thus,

$\begin{array}{l} \frac{x}{x + y} = \frac{12}{12 + 10} \\ = \frac{12}{22} \\ and \\ \frac{x + y}{y + z} = \frac{12 + 10}{10 + 24} \\ = \frac{22}{34} \end{array}$

Step 2. Concept Used.

To write the fraction in simplest form, divide the numerator and denominator with the GCF (Greatest Common Factor).

Step 3. Now find the GCF.

Write the prime factors of numerator and denominator.

$\begin{array}{l} 12 = 2 \times 2 \times 3 \\ 22 = 2 \times 11 \\ 34 = 2 \times 17 \end{array}$

Here GCF is2.

Step 4. Let’s divide the numerator and denominator with the GCF.

Here we will divide the numerator and denominator by.2

$\begin{array}{l} \frac{x}{x + y} = \frac{12 / 2}{22 / 2} \\ = \frac{6}{11} \end{array}$

And

Here we will divide the numerator and denominator by2.

$\begin{matrix} \frac{x + y}{y + z} = \frac{22 / 2}{34 / 2} \\ = \frac{11}{17} \end{matrix}$

Therefore, the simplest form of the given ratio is $z : (x + y) : (y + z) = 6 : 11 : 17$ .

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. $x = 12, y = 10, a n d z = 24$ Write each ratio in simplest form.
$x : (x + y) : (y + z)$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept Used.

Step 3. Now find the GCF.

Step 4. Let’s divide the numerator and denominator with the GCF.

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.x=12,y=10,andz=24Write each ratio in simplest form.x:(x+y):(y+z)

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Concept Used.

Step 3. Now find the GCF.

Step 4. Let’s divide the numerator and denominator with the GCF.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Calculus

Applied Mathematics

Discrete Mathematics

Pure Maths

Decision Maths

Study anywhere. Anytime. Across all devices.

. $x = 12, y = 10, a n d z = 24$ Write each ratio in simplest form.
$x : (x + y) : (y + z)$