Answer :
Sure! Let's go through the problems step by step.
5. Numbers divisible by 3:
To check if a number is divisible by 3, you can add up its digits and see if the sum is divisible by 3.
- 36: Sum of digits = [tex]\(3 + 6 = 9\)[/tex], which is divisible by 3.
36 is divisible by 3.
- 121: Sum of digits = [tex]\(1 + 2 + 1 = 4\)[/tex], not divisible by 3.
121 is not divisible by 3.
- 342: Sum of digits = [tex]\(3 + 4 + 2 = 9\)[/tex], which is divisible by 3.
342 is divisible by 3.
- 1,011: Sum of digits = [tex]\(1 + 0 + 1 + 1 = 3\)[/tex], which is divisible by 3.
1,011 is divisible by 3.
- 732: Sum of digits = [tex]\(7 + 3 + 2 = 12\)[/tex], which is divisible by 3.
732 is divisible by 3.
- 629: Sum of digits = [tex]\(6 + 2 + 9 = 17\)[/tex], not divisible by 3.
629 is not divisible by 3.
- 3,241: Sum of digits = [tex]\(3 + 2 + 4 + 1 = 10\)[/tex], not divisible by 3.
3,241 is not divisible by 3.
Divisible by 3: 36, 342, 1,011, 732
---
6. Numbers divisible by 4:
To check divisibility by 4, look at the last two digits of the number. If they form a number divisible by 4, then the whole number is divisible by 4.
- 600: Last two digits = 00, which is divisible by 4.
600 is divisible by 4.
- 318: Last two digits = 18, not divisible by 4.
318 is not divisible by 4.
- 424: Last two digits = 24, which is divisible by 4.
424 is divisible by 4.
- 936: Last two digits = 36, which is divisible by 4.
936 is divisible by 4.
- 502: Last two digits = 02, not divisible by 4.
502 is not divisible by 4.
- 925: Last two digits = 25, not divisible by 4.
925 is not divisible by 4.
- 1,016: Last two digits = 16, which is divisible by 4.
1,016 is divisible by 4.
Divisible by 4: 600, 424, 936, 1,016
---
7. Numbers divisible by 5:
A number is divisible by 5 if it ends in 0 or 5.
- 127: Ends in 7.
127 is not divisible by 5.
- 265: Ends in 5.
265 is divisible by 5.
- 1,016: Ends in 6.
1,016 is not divisible by 5.
- 515: Ends in 5.
515 is divisible by 5.
- 100: Ends in 0.
100 is divisible by 5.
- 803: Ends in 3.
803 is not divisible by 5.
- 735: Ends in 5.
735 is divisible by 5.
Divisible by 5: 265, 515, 100, 735
---
8. Reduce the fractions completely:
To reduce a fraction, divide the numerator and the denominator by their greatest common divisor (GCD).
a. [tex]\(\frac{36}{72}\)[/tex]:
The GCD is 36.
[tex]\(\frac{36 \div 36}{72 \div 36} = \frac{1}{2}\)[/tex].
b. [tex]\(\frac{24}{76}\)[/tex]:
The GCD is 4.
[tex]\(\frac{24 \div 4}{76 \div 4} = \frac{6}{19}\)[/tex].
c. [tex]\(\frac{84}{198}\)[/tex]:
The GCD is 6.
[tex]\(\frac{84 \div 6}{198 \div 6} = \frac{14}{33}\)[/tex].
d. [tex]\(\frac{325}{400}\)[/tex]:
The GCD is 25.
[tex]\(\frac{325 \div 25}{400 \div 25} = \frac{13}{16}\)[/tex].
e. [tex]\(\frac{72}{81}\)[/tex]:
The GCD is 9.
[tex]\(\frac{72 \div 9}{81 \div 9} = \frac{8}{9}\)[/tex].
f. [tex]\(\frac{144}{168}\)[/tex]:
The GCD is 24.
[tex]\(\frac{144 \div 24}{168 \div 24} = \frac{6}{7}\)[/tex].
g. [tex]\(\frac{50}{75}\)[/tex]:
The GCD is 25.
[tex]\(\frac{50 \div 25}{75 \div 25} = \frac{2}{3}\)[/tex].
h. [tex]\(\frac{125}{625}\)[/tex]:
The GCD is 125.
[tex]\(\frac{125 \div 125}{625 \div 125} = \frac{1}{5}\)[/tex].
Reduced fractions: [tex]\(\frac{1}{2}\)[/tex], [tex]\(\frac{6}{19}\)[/tex], [tex]\(\frac{14}{33}\)[/tex], [tex]\(\frac{13}{16}\)[/tex], [tex]\(\frac{8}{9}\)[/tex], [tex]\(\frac{6}{7}\)[/tex], [tex]\(\frac{2}{3}\)[/tex], [tex]\(\frac{1}{5}\)[/tex]
5. Numbers divisible by 3:
To check if a number is divisible by 3, you can add up its digits and see if the sum is divisible by 3.
- 36: Sum of digits = [tex]\(3 + 6 = 9\)[/tex], which is divisible by 3.
36 is divisible by 3.
- 121: Sum of digits = [tex]\(1 + 2 + 1 = 4\)[/tex], not divisible by 3.
121 is not divisible by 3.
- 342: Sum of digits = [tex]\(3 + 4 + 2 = 9\)[/tex], which is divisible by 3.
342 is divisible by 3.
- 1,011: Sum of digits = [tex]\(1 + 0 + 1 + 1 = 3\)[/tex], which is divisible by 3.
1,011 is divisible by 3.
- 732: Sum of digits = [tex]\(7 + 3 + 2 = 12\)[/tex], which is divisible by 3.
732 is divisible by 3.
- 629: Sum of digits = [tex]\(6 + 2 + 9 = 17\)[/tex], not divisible by 3.
629 is not divisible by 3.
- 3,241: Sum of digits = [tex]\(3 + 2 + 4 + 1 = 10\)[/tex], not divisible by 3.
3,241 is not divisible by 3.
Divisible by 3: 36, 342, 1,011, 732
---
6. Numbers divisible by 4:
To check divisibility by 4, look at the last two digits of the number. If they form a number divisible by 4, then the whole number is divisible by 4.
- 600: Last two digits = 00, which is divisible by 4.
600 is divisible by 4.
- 318: Last two digits = 18, not divisible by 4.
318 is not divisible by 4.
- 424: Last two digits = 24, which is divisible by 4.
424 is divisible by 4.
- 936: Last two digits = 36, which is divisible by 4.
936 is divisible by 4.
- 502: Last two digits = 02, not divisible by 4.
502 is not divisible by 4.
- 925: Last two digits = 25, not divisible by 4.
925 is not divisible by 4.
- 1,016: Last two digits = 16, which is divisible by 4.
1,016 is divisible by 4.
Divisible by 4: 600, 424, 936, 1,016
---
7. Numbers divisible by 5:
A number is divisible by 5 if it ends in 0 or 5.
- 127: Ends in 7.
127 is not divisible by 5.
- 265: Ends in 5.
265 is divisible by 5.
- 1,016: Ends in 6.
1,016 is not divisible by 5.
- 515: Ends in 5.
515 is divisible by 5.
- 100: Ends in 0.
100 is divisible by 5.
- 803: Ends in 3.
803 is not divisible by 5.
- 735: Ends in 5.
735 is divisible by 5.
Divisible by 5: 265, 515, 100, 735
---
8. Reduce the fractions completely:
To reduce a fraction, divide the numerator and the denominator by their greatest common divisor (GCD).
a. [tex]\(\frac{36}{72}\)[/tex]:
The GCD is 36.
[tex]\(\frac{36 \div 36}{72 \div 36} = \frac{1}{2}\)[/tex].
b. [tex]\(\frac{24}{76}\)[/tex]:
The GCD is 4.
[tex]\(\frac{24 \div 4}{76 \div 4} = \frac{6}{19}\)[/tex].
c. [tex]\(\frac{84}{198}\)[/tex]:
The GCD is 6.
[tex]\(\frac{84 \div 6}{198 \div 6} = \frac{14}{33}\)[/tex].
d. [tex]\(\frac{325}{400}\)[/tex]:
The GCD is 25.
[tex]\(\frac{325 \div 25}{400 \div 25} = \frac{13}{16}\)[/tex].
e. [tex]\(\frac{72}{81}\)[/tex]:
The GCD is 9.
[tex]\(\frac{72 \div 9}{81 \div 9} = \frac{8}{9}\)[/tex].
f. [tex]\(\frac{144}{168}\)[/tex]:
The GCD is 24.
[tex]\(\frac{144 \div 24}{168 \div 24} = \frac{6}{7}\)[/tex].
g. [tex]\(\frac{50}{75}\)[/tex]:
The GCD is 25.
[tex]\(\frac{50 \div 25}{75 \div 25} = \frac{2}{3}\)[/tex].
h. [tex]\(\frac{125}{625}\)[/tex]:
The GCD is 125.
[tex]\(\frac{125 \div 125}{625 \div 125} = \frac{1}{5}\)[/tex].
Reduced fractions: [tex]\(\frac{1}{2}\)[/tex], [tex]\(\frac{6}{19}\)[/tex], [tex]\(\frac{14}{33}\)[/tex], [tex]\(\frac{13}{16}\)[/tex], [tex]\(\frac{8}{9}\)[/tex], [tex]\(\frac{6}{7}\)[/tex], [tex]\(\frac{2}{3}\)[/tex], [tex]\(\frac{1}{5}\)[/tex]
