Answer: The ratio is 58:1, and the division is = 58. Scroll for solving, check, and notes.
Step-by-step explanation:
What we know:
- The question wants us to use equivalent ratios
- The numbers 3,712 and 64 have common denominators
- An equivalent ratio is a ratio that is something of a simplified form of large numbers, written in a fraction, with a colon, or with the word 'to'
How to solve:
We need to find the equivalent ratio of 3,712 and 64, and then solve the question based on that.
Process:
Finding equivalent ratios
Set up equation 3712/64
Rewrite into colon-ratio form 3712:64
Divide by common denominator /64 /64*
Solution: =58:1
*Read bottom of notes to find out how I found this denominator
Answer: The ratio is 58:1; the solution to the division is 58.
Notes:
There is no way to always know the ratio's common denominator. However, there are some general rules of thumb that may help:
-All numbers have a common denominator of 1. Sometimes, that's the most simplified form.
-All even numbers (Those that end in {0, 2, 4, 6, or 8}) have a common denominator of 2
-All numbers whose digits add up to {3, 6, or 9} (such as 12: 1+2 = 3) have a common denominator of 3.
-These three numbers serve as basic building blocks. You can keep simplifying with them until you get to a prime number. Let's use our problem as an example:
3712 and 64 - both are even, simplify by 2
1856 and 32 - both are even, simplify by 2
928 and 16 - both are even, simplify by 2
464 and 8 - both are even, simplify by 2
232 and 4 - both are even, simplify by 2
116 and 2 - both are even, simplify by 2
58 and 1 - there is a prime number, so this is the simplest form.
Now we take all of our simplifications: 2^6. 2^6 = 64, so the common denominator is 64.
Check:
Our ratio, 58:1, is the simplified form of 3,712 div. 64. This is seen better by rewriting both into a fraction-ratio form:
58:1 3712 div. 64
58/1 3712/64
Luckily, our ratio has a 1 in it. This means that when we multiply the ratio by 64 (what the 1 represents), it should yield the original equation.
3712/64 = 58/1
3712/64 = (58/1)*64
3712/64 = 3712/64
Therefore, 58:1 is the correct ratio.