Question 1. (3 points)
a. Show that the ratios 14/18 and 28/36 form a proportion by finding a common multiplier.
b. Show that 14/18 and 28/36 are equal by writing them in simplest form.
please help, i'm desprate
14*2 / 18*2
a. To determine if the ratios 14/18 and 28/36 form a proportion, we can find a common multiplier.
To find a common multiplier, we multiply the numerator of the first fraction by the denominator of the second fraction, and the denominator of the first fraction by the numerator of the second fraction.
14/18 * 36/28 = (14 * 36) / (18 * 28)
= 504 / 504
The result is 504/504, which simplifies to 1. Since the result is 1, we can conclude that the ratios 14/18 and 28/36 form a proportion.
b. To show that 14/18 and 28/36 are equal by writing them in simplest form, we can simplify both fractions.
To simplify a fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD).
For the fraction 14/18:
The GCD of 14 and 18 is 2.
Dividing both the numerator and denominator by 2, we get:
14/18 = 7/9
For the fraction 28/36:
The GCD of 28 and 36 is 4.
Dividing both the numerator and denominator by 4, we get:
28/36 = 7/9
So, both fractions simplify to 7/9. Therefore, we have shown that 14/18 and 28/36 are equal by writing them in simplest form.
Sure, I can help you with that! Let's start with part (a) where we need to determine if the ratios 14/18 and 28/36 form a proportion.
To find a common multiplier, we need to determine if the cross-products of the ratios are equal. The cross-products are found by multiplying the numerators and denominators of the ratios diagonally. For the first ratio, the cross-products would be 14 * 36, and for the second ratio, it would be 18 * 28.
So, the cross-products are:
14/18 = (14 * 36) / (18 * 36) = 504 / 648
28/36 = (28 * 36) / (36 * 28) = 1008 / 1008
Now, we can see that the cross-products of both ratios are equal. In other words, 504/648 = 1008/1008. Thus, the ratios 14/18 and 28/36 form a proportion.
Moving on to part (b), where we need to show that 14/18 and 28/36 are equal by writing them in simplest form.
To write a fraction in simplest form, we need to find the greatest common divisor (GCD) of the numerator and denominator and divide both by it. In this case, the GCD of 14 and 18 is 2, and the GCD of 28 and 36 is 4.
Dividing both the numerator and denominator of the first ratio by 2 gives us:
14/18 = (14 ÷ 2) / (18 ÷ 2) = 7/9
Similarly, dividing both the numerator and denominator of the second ratio by 4 gives us:
28/36 = (28 ÷ 4) / (36 ÷ 4) = 7/9
As you can see, both fractions simplify to 7/9 when written in simplest form. Therefore, 14/18 and 28/36 are equal.
I hope this helps! Let me know if you have any further questions.