64 = 64
D
Learning Task 1: Solve and determine whether each is a proportion or not.
Write YES or NO on your notebook.
1.) 2/3 and 4/6
2.) 6/7 and 24/28
3) 2/5 and 4/12
4.) 28/42 and 2/3
5.) 15/20 and 5/6

In math, proportion means to say that two or more fractions are equal or equivalent or the same. So, for example, let's take [tex]\frac{1}{2}[/tex], we know that [tex]\frac{1}{2}[/tex] is proportional to these fractions [tex]\frac{5}{10}[/tex], [tex]\frac{2}{4}[/tex], [tex]\frac{3}{6}[/tex], [tex]\frac{50}{100}[/tex] and etc.

Techniques in Finding the Proportion Fraction

Reduce the fractions to their lowest terms
Find the greatest common factor of both the numerator and denominator.
If you can't find the greatest common factor other than 1, this means to say that the fraction is irreducible.

Solution

1. Notice that [tex]\frac{2}{3}[/tex] is not irreducible. So, let's take a look at the second fraction which is [tex]\frac{4}{6}[/tex]. We can factor the greatest common factor of both numerator and denominator, in this case, it's 2. Reduce the fraction by dividing both the numerator and the denominator by 2.

[tex]\begin{aligned}\frac{4}{6}&=\frac{4\div 2}{6\div 2}\\&=\frac{2}{3}\end{aligned}[/tex]

This means that [tex]\frac{2}{3}[/tex] and [tex]\frac{4}{6}[/tex] are proportions.

2. Similar to number 1, we cannot reduce [tex]\frac{6}{7}[/tex] since its greatest common factor for both numerator and denominator is 1. So, let's work on [tex]\frac{24}{28}[/tex]. e can factor the greatest common factor of both numerator and denominator, in this case, it's 4. Reduce the fraction by dividing both the numerator and the denominator by 4.

[tex]\begin{aligned}\frac{24}{28}&=\frac{24\div 4}{28\div 4}\\&=\frac{6}{7}\end{aligned}[/tex]

This means that [tex]\frac{6}{7}[/tex] and [tex]\frac{24}{28}[/tex] are proportions.

3. [tex]\frac{2}{5}[/tex] is not reducible, since the greatest common factor of both the numerator and the denominator is 1. Now, for [tex]\frac{4}{12}[/tex], we can find the greatest common factor for both numerator and denominator, in this case, it's 4. Reduce the fraction by dividing both the numerator and the denominator by 4.

[tex]\begin{aligned}\frac{4}{12}&=\frac{4\div 4}{12\div 4}\\&=\frac{1}{3}\end{aligned}[/tex]

Since [tex]\frac{2}{5}[/tex] is different from [tex]\frac{1}{3}[/tex], then the fractions [tex]\frac{2}{5}[/tex] and [tex]\frac{4}{12}[/tex] are NOT proportions.

4. [tex]\frac{2}{3}[/tex] is not reducible. [tex]\frac{28}{42}[/tex] has a greatest common factor of 14 for both the numerator and the denominator. Reduce the fraction by dividing both the numerator and the denominator by 14.

[tex]\begin{aligned}\frac{28}{42}&=\frac{28\div 14}{42\div 14}\\&=\frac{2}{3}\end{aligned}[/tex]

This means that [tex]\frac{28}{42}[/tex] and [tex]\frac{2}{3}[/tex] are proportions.

5. [tex]\frac{5}{6}[/tex] is not reducible. [tex]\frac{15}{20}[/tex] has a greatest common factor of 5 for both the numerator and the denominator. Reduce the fraction by dividing both the numerator and the denominator by 5.

[tex]\begin{aligned}\frac{15}{20}&=\frac{15\div 5}{20\div 5}\\&=\frac{3}{4}\end{aligned}[/tex]

Since [tex]\frac{3}{4}[/tex] is different from [tex]\frac{5}{6}[/tex], then the fractions [tex]\frac{15}{20}[/tex] and [tex]\frac{5}{6}[/tex] are NOT proportions.

To learn more about fractions, click the links below

Types of Fractions: https://brainly.ph/question/7009887

Adding and reducing fractions: https://brainly.ph/question/653140

Fractions in lowest terms: https://brainly.ph/question/1842154

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