Is 84/105 and 128/160 proportional?
please explain im so stuck.
84/105 = 0.8
128/160 = 0.8.
Therefore, they are proportional.
84/105 = 128/160.
Try putting the fractions in your calculator or reducing the fractions to lowest terms.
Well, let's see if I can help you out of this sticky situation! To determine if two fractions are proportional, we need to compare their cross products. In other words, we multiply the numerator of the first fraction by the denominator of the second fraction, and then multiply the denominator of the first fraction by the numerator of the second fraction. If the two cross products are equal, then the fractions are proportional.
For the first pair of fractions, 84/105 and 128/160:
Cross product 1: 84 * 160 = 13,440
Cross product 2: 105 * 128 = 13,440
Since the cross products are equal, 84/105 and 128/160 are proportional! Hooray! They're like two peas in a pod, or two slices of pizza that are perfectly proportioned. Now, I'm sure your brain is out of the sticky situation.
To determine if two fractions are proportional, we can check if their cross products are equal. The cross product of two fractions is found by multiplying the numerator of the first fraction by the denominator of the second fraction and comparing it with the product of the numerator of the second fraction and the denominator of the first fraction.
Let's check if the cross products of 84/105 and 128/160 are equal.
For 84/105:
Numerator * (128) = 84 * 128 = 10752
Denominator * (160) = 105 * 160 = 16800
For 128/160:
Numerator * (105) = 128 * 105 = 13440
Denominator * (84) = 160 * 84 = 13440
Since the cross products of both fractions are equal (10752 = 13440) , we can conclude that 84/105 and 128/160 are proportional.
To determine if two fractions are proportional, you need to compare their ratios. In this case, we have the fractions 84/105 and 128/160.
To check if they are proportional, we can simplify both fractions by dividing the numerator and denominator by their greatest common divisor (GCD).
First, let's find the GCD of 84 and 105. The factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84. The factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. The largest number that appears in both lists is 7.
To simplify 84/105, we divide both the numerator and denominator by 7, giving us 12/15.
Next, let's find the GCD of 128 and 160. The factors of 128 are 1, 2, 4, 8, 16, 32, 64, 128. The factors of 160 are 1, 2, 4, 5, 8, 10, 16, 20, 32, 40, 80, 160. The largest number that appears in both lists is 32.
To simplify 128/160, we divide both the numerator and denominator by 32, giving us 4/5.
Now, we can compare the simplified fractions 12/15 and 4/5.
Since 12/15 can be simplified further by dividing both the numerator and denominator by 3 (the GCD), we get 4/5 as well.
Thus, both fractions, 84/105 and 128/160, simplify to 4/5, which means they are proportional.