Which of the following ratios is equivalent to 1215 4510 to 1260 to 86 60/45
Not to be mean or anything but some people can't understand when you write like that. Try this.
Which of the following ratios are equivalent to 12/15?
A. 4:5
B. 10:12
C. 60 to 80
D. 60/45
What's your guess?
I think it’s A
To determine which of the following ratios is equivalent to the ratio 1215 4510 to 1260 to 86 60/45, we need to simplify the given ratio.
Let's begin by converting the mixed fraction 86 60/45 into an improper fraction:
86 60/45 = (86 * 45 + 60) / 45 = 3870/45
Now, the ratio becomes:
1215 4510 : 1260 : 3870/45
To simplify further, we can multiply all the terms by the common denominator, which is 45:
1215 4510 × 45 : 1260 × 45 : 3870/45 × 45
= (1215 * 45) : (4510 * 45) : 3870
= 54675 : 202950 : 3870
Therefore, the ratio equivalent to 1215 4510 to 1260 to 86 60/45 is 54675 : 202950 : 3870.
To find the ratio that is equivalent to 1215:4510:1260:(60/45), we need to simplify the numbers and find a common factor.
Step 1: Simplify the numbers
The given ratio is 1215:4510:1260:(60/45). Let's simplify each of these numbers individually.
1215 can be simplified by dividing both the numerator and denominator by their greatest common factor (GCF), which is 135. 1215 ÷ 135 = 9.
4510 can be simplified by dividing both the numerator and denominator by their GCF, which is 10. 4510 ÷ 10 = 451.
1260 can be simplified by dividing both the numerator and denominator by their GCF, which is 60. 1260 ÷ 60 = 21.
(60/45) can be simplified by reducing the fraction to its simplest form. Since both the numerator and denominator are divisible by 15, we can simplify it further. (60/45) ÷ 15 = (4/3).
After simplifying, the numbers become: 9:451:21:(4/3).
Step 2: Finding a common factor
To create an equivalent ratio, we need to find a common factor that can be multiplied to all the numbers to give us a whole number ratio.
Looking at the simplified numbers, we can see that the common factor of 3 can be multiplied to all the numbers to give us whole numbers.
9 × 3 = 27
451 × 3 = 1353
21 × 3 = 63
4/3 × 3 = 4
Therefore, the equivalent ratio to 1215:4510:1260:(60/45) is 27:1353:63:4.