Question

Altogether Central High School's bands have 40 trumpets and 35 tubas. Carlee says the ratio of trumpets to tubas is 40:35. Danny disagrees and says the ratio is 8:7.
Actually, they are both correct. Explain why these are equivalent ratios.

Answer 1

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 = $\frac{40}{35}$

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.

⇒ $\frac{40\div5}{35\div 5}$

⇒ $\frac{8}{7}$

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.