Question

4\15 : 12\23 8/21 : 32\49 9/5 : 3\10 m/t : b/t(b m t принаднежит N)

Answer 1

4/15:12/23=4/15*23/12=23/45

8/21:32/49=8/21*49/32=7/12

9/5:3/10=9/5*10/3=3*2=6

m/t:b/t=m/t*t/b=m/b

Answer 2

To find the pattern in the given ratios, let's examine the numerator and denominator separately.

In the first ratio, 4/15 : 12/23, if we multiply the numerator and denominator of the first fraction by 23 and the numerator and denominator of the second fraction by 15, we get:

(4 * 23) / (15 * 23) : (12 * 15) / (23 * 15) 92/345 : 180/345

Simplifying this further, we have: 92/345 : 180/345 = 92 : 180

We can observe that the numerator of the second fraction is twice the numerator of the first fraction.

Now let's apply the same pattern to the second ratio, 8/21 : 32/49:

(8 * 49) / (21 * 49) : (32 * 21) / (49 * 21) 392/1029 : 672/1029

Simplifying this, we get: 392/1029 : 672/1029 = 392 : 672

Again, the numerator of the second fraction is twice the numerator of the first fraction.

Applying the same pattern to the third ratio, 9/5 : 3/10:

(9 * 10) / (5 * 10) : (3 * 5) / (10 * 5) 90/50 : 15/50

Simplifying this, we have: 90/50 : 15/50 = 90 : 15

Here, the numerator of the second fraction is half the numerator of the first fraction.

Based on the observed pattern, in the ratio m/t : b/t, the numerator of the second fraction will be half the numerator of the first fraction.

Therefore, in the given ratio m/t : b/t, we can conclude that b is equal to 2m.

Answer 3

To determine the relationship between the fractions, let's analyze the given examples:

1. 4/15 : 12/23 In this case, if we cross-multiply, we get (4 * 23) = (15 * 12), which simplifies to 92 = 180. Since 92 is not equal to 180, the fractions are not equivalent.

2. 8/21 : 32/49 Cross-multiplying, we have (8 * 49) = (21 * 32), which simplifies to 392 = 672. Again, these values are not equal, so the fractions are not equivalent.

3. 9/5 : 3/10 Cross-multiplying, we get (9 * 10) = (5 * 3), which simplifies to 90 = 15. Once again, these values are not equal, so the fractions are not equivalent.

Based on the pattern observed from the given examples, we can conclude that the fractions m/t : b/t are not equivalent for any value of b, m, and t belonging to the set of natural numbers (N).