Answer :
Sure! Let's go through each part of the question step by step:
### a.) Reduce to the lowest fraction.
i.) [tex]\(\frac{36}{72}\)[/tex]
To reduce this fraction, find the greatest common divisor (GCD) of 36 and 72, which is 36.
Then, divide both the numerator and the denominator by 36:
[tex]\[
\frac{36 \div 36}{72 \div 36} = \frac{1}{2}
\][/tex]
ii.) [tex]\(\frac{18}{20}\)[/tex]
Find the GCD of 18 and 20, which is 2.
Divide both the numerator and the denominator by 2:
[tex]\[
\frac{18 \div 2}{20 \div 2} = \frac{9}{10}
\][/tex]
iii.) [tex]\(\frac{144}{156}\)[/tex]
Find the GCD of 144 and 156, which is 12.
Divide both the numerator and the denominator by 12:
[tex]\[
\frac{144 \div 12}{156 \div 12} = \frac{12}{13}
\][/tex]
iv.) [tex]\(\frac{288}{512}\)[/tex]
Find the GCD of 288 and 512, which is 32.
Divide both the numerator and the denominator by 32:
[tex]\[
\frac{288 \div 32}{512 \div 32} = \frac{9}{16}
\][/tex]
### b.) What should be added to [tex]\(\frac{1}{5}\)[/tex] to get 15?
First, convert [tex]\(\frac{1}{5}\)[/tex] to a decimal, which is 0.2.
To find the number to add, subtract 0.2 from 15:
[tex]\[
15 - 0.2 = 14.8
\][/tex]
So, you need to add 14.8 to [tex]\(\frac{1}{5}\)[/tex] to get 15.
### c.) Check if the following are in proportion.
i.) [tex]\(5: 25\)[/tex] and [tex]\(15: 45\)[/tex]
Calculate the ratios:
- Ratio of [tex]\(5: 25\)[/tex] is [tex]\(\frac{5}{25} = 0.2\)[/tex]
- Ratio of [tex]\(15: 45\)[/tex] is [tex]\(\frac{15}{45} = 0.333...\)[/tex]
Since [tex]\(0.2\)[/tex] is not equal to [tex]\(0.333...\)[/tex], they are not in proportion.
ii.) Check if [tex]\(5: 25\)[/tex] is the same as [tex]\(1.5\)[/tex].
As calculated above, the ratio of [tex]\(5: 25\)[/tex] is [tex]\(0.2\)[/tex].
Since [tex]\(0.2\)[/tex] is not equal to [tex]\(1.5\)[/tex], they are not in proportion.
I hope this helps you understand how to approach these problems! If you have any more questions, feel free to ask.
### a.) Reduce to the lowest fraction.
i.) [tex]\(\frac{36}{72}\)[/tex]
To reduce this fraction, find the greatest common divisor (GCD) of 36 and 72, which is 36.
Then, divide both the numerator and the denominator by 36:
[tex]\[
\frac{36 \div 36}{72 \div 36} = \frac{1}{2}
\][/tex]
ii.) [tex]\(\frac{18}{20}\)[/tex]
Find the GCD of 18 and 20, which is 2.
Divide both the numerator and the denominator by 2:
[tex]\[
\frac{18 \div 2}{20 \div 2} = \frac{9}{10}
\][/tex]
iii.) [tex]\(\frac{144}{156}\)[/tex]
Find the GCD of 144 and 156, which is 12.
Divide both the numerator and the denominator by 12:
[tex]\[
\frac{144 \div 12}{156 \div 12} = \frac{12}{13}
\][/tex]
iv.) [tex]\(\frac{288}{512}\)[/tex]
Find the GCD of 288 and 512, which is 32.
Divide both the numerator and the denominator by 32:
[tex]\[
\frac{288 \div 32}{512 \div 32} = \frac{9}{16}
\][/tex]
### b.) What should be added to [tex]\(\frac{1}{5}\)[/tex] to get 15?
First, convert [tex]\(\frac{1}{5}\)[/tex] to a decimal, which is 0.2.
To find the number to add, subtract 0.2 from 15:
[tex]\[
15 - 0.2 = 14.8
\][/tex]
So, you need to add 14.8 to [tex]\(\frac{1}{5}\)[/tex] to get 15.
### c.) Check if the following are in proportion.
i.) [tex]\(5: 25\)[/tex] and [tex]\(15: 45\)[/tex]
Calculate the ratios:
- Ratio of [tex]\(5: 25\)[/tex] is [tex]\(\frac{5}{25} = 0.2\)[/tex]
- Ratio of [tex]\(15: 45\)[/tex] is [tex]\(\frac{15}{45} = 0.333...\)[/tex]
Since [tex]\(0.2\)[/tex] is not equal to [tex]\(0.333...\)[/tex], they are not in proportion.
ii.) Check if [tex]\(5: 25\)[/tex] is the same as [tex]\(1.5\)[/tex].
As calculated above, the ratio of [tex]\(5: 25\)[/tex] is [tex]\(0.2\)[/tex].
Since [tex]\(0.2\)[/tex] is not equal to [tex]\(1.5\)[/tex], they are not in proportion.
I hope this helps you understand how to approach these problems! If you have any more questions, feel free to ask.
