Question

In each of the following find the smallest ratio:
(d) 10:20, 20:30, 40:50​

Answer 1

Answer:

10:20 is the smallest ratio

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Answer 2

Answer:

1) 1:2

2) 2:3

3) 4:5

OVERALL ANSWER: 10:20

Step-by-step explanation:

We can use prime factorization to solve these problems:

1) The prime factorization of 10 is 2 × 5.

The prime factorization of 20 is 2² × 5.

So, we see the GCF/HCF is 2 × 5 = 10. Dividing both sides by 10 gives our answer for 1): 1:2.

2) The prime factorization of 30 is 2 × 3 × 5.

We already know the prime factorization of 20.

We see that the GCF/HCF is 2 × 5 = 10. Dividing both sides by 10 gives our answer for 2): 2:3.

3) The prime factorization of 40 is 2³ × 5.

The prime factorization of 50 is 2 × 5².

We see that the GCF/HCF is 2 × 5 = 10. Dividing both sides by 10 gives our answer for 3): 4:5.

We know see the smallest ratio is 10:20.