Answer:
Explanation is given below.
Step-by-step explanation:
Given:
Number of Trumpets = 40
Number of tubas = 35
Carlee says, the ratio of trumpets to tubas = 40 : 35
Danny says, the ratio of trumpets to tubas = 8 : 7
To explain why the two ratios are equivalent.
Solution:
Equivalent ratios are all ratios which are equal to each other in their reduced to simplest form.
The ratio of trumpets to tubas can be given as = [tex]\frac{40}{35}[/tex]
To reduce the ratio to its simplest form, we divide both numbers by their G.C.F.
The G.C.F. for 40 and 35 is 5.
So, we divide numerator and denominator by 5.
⇒ [tex]\frac{40\div5}{35\div 5}[/tex]
⇒ [tex]\frac{8}{7}[/tex]
Thus, the simplest ratio of trumpets to tubas can be given as = 8:7
This is why both Danny and Carlee are correct with the ratios of trumpets to tubas.
Carlee gave the direct ratio, while Danny gave the simplest ratio.
