Answer :
Sure, let's simplify each fraction or ratio step-by-step:
13. Simplifying the ratio 16:32
- Find the greatest common divisor (GCD) of 16 and 32. The GCD is 16.
- Divide both numbers by their GCD:
[tex]\( \frac{16}{16} = 1 \)[/tex] and [tex]\( \frac{32}{16} = 2 \)[/tex].
- So, the simplest form is 1:2.
14. Simplifying the fraction 50/75
- Find the GCD of 50 and 75. The GCD is 25.
- Divide both numbers by their GCD:
[tex]\( \frac{50}{25} = 2 \)[/tex] and [tex]\( \frac{75}{25} = 3 \)[/tex].
- So, the simplest form is 2/3.
15. Simplifying the ratio 32:70
- Find the GCD of 32 and 70. The GCD is 2.
- Divide both numbers by their GCD:
[tex]\( \frac{32}{2} = 16 \)[/tex] and [tex]\( \frac{70}{2} = 35 \)[/tex].
- So, the simplest form is 16:35.
16. Simplifying the fraction 17/35
- Find the GCD of 17 and 35. The GCD is 1 (since 17 is prime and doesn't divide 35).
- Since the GCD is 1, the fraction is already in its simplest form: 17/35.
17. Simplifying the ratio 44:200
- Find the GCD of 44 and 200. The GCD is 4.
- Divide both numbers by their GCD:
[tex]\( \frac{44}{4} = 11 \)[/tex] and [tex]\( \frac{200}{4} = 50 \)[/tex].
- So, the simplest form is 11:50.
18. Simplifying the fraction 44/160
- Find the GCD of 44 and 160. The GCD is 4.
- Divide both numbers by their GCD:
[tex]\( \frac{44}{4} = 11 \)[/tex] and [tex]\( \frac{160}{4} = 40 \)[/tex].
- So, the simplest form is 11/40.
19. Simplifying the ratio 200:500
- Find the GCD of 200 and 500. The GCD is 100.
- Divide both numbers by their GCD:
[tex]\( \frac{200}{100} = 2 \)[/tex] and [tex]\( \frac{500}{100} = 5 \)[/tex].
- So, the simplest form is 2:5.
20. Simplifying the fraction 80/96
- Find the GCD of 80 and 96. The GCD is 16.
- Divide both numbers by their GCD:
[tex]\( \frac{80}{16} = 5 \)[/tex] and [tex]\( \frac{96}{16} = 6 \)[/tex].
- So, the simplest form is 5/6.
I hope this helps! If you have any more questions, feel free to ask.
13. Simplifying the ratio 16:32
- Find the greatest common divisor (GCD) of 16 and 32. The GCD is 16.
- Divide both numbers by their GCD:
[tex]\( \frac{16}{16} = 1 \)[/tex] and [tex]\( \frac{32}{16} = 2 \)[/tex].
- So, the simplest form is 1:2.
14. Simplifying the fraction 50/75
- Find the GCD of 50 and 75. The GCD is 25.
- Divide both numbers by their GCD:
[tex]\( \frac{50}{25} = 2 \)[/tex] and [tex]\( \frac{75}{25} = 3 \)[/tex].
- So, the simplest form is 2/3.
15. Simplifying the ratio 32:70
- Find the GCD of 32 and 70. The GCD is 2.
- Divide both numbers by their GCD:
[tex]\( \frac{32}{2} = 16 \)[/tex] and [tex]\( \frac{70}{2} = 35 \)[/tex].
- So, the simplest form is 16:35.
16. Simplifying the fraction 17/35
- Find the GCD of 17 and 35. The GCD is 1 (since 17 is prime and doesn't divide 35).
- Since the GCD is 1, the fraction is already in its simplest form: 17/35.
17. Simplifying the ratio 44:200
- Find the GCD of 44 and 200. The GCD is 4.
- Divide both numbers by their GCD:
[tex]\( \frac{44}{4} = 11 \)[/tex] and [tex]\( \frac{200}{4} = 50 \)[/tex].
- So, the simplest form is 11:50.
18. Simplifying the fraction 44/160
- Find the GCD of 44 and 160. The GCD is 4.
- Divide both numbers by their GCD:
[tex]\( \frac{44}{4} = 11 \)[/tex] and [tex]\( \frac{160}{4} = 40 \)[/tex].
- So, the simplest form is 11/40.
19. Simplifying the ratio 200:500
- Find the GCD of 200 and 500. The GCD is 100.
- Divide both numbers by their GCD:
[tex]\( \frac{200}{100} = 2 \)[/tex] and [tex]\( \frac{500}{100} = 5 \)[/tex].
- So, the simplest form is 2:5.
20. Simplifying the fraction 80/96
- Find the GCD of 80 and 96. The GCD is 16.
- Divide both numbers by their GCD:
[tex]\( \frac{80}{16} = 5 \)[/tex] and [tex]\( \frac{96}{16} = 6 \)[/tex].
- So, the simplest form is 5/6.
I hope this helps! If you have any more questions, feel free to ask.
