Now you see that the new version has a numerator and denominator divisible by 3.
It took two steps instead of one, but you have the same answer.
11 . Yes, this is completely reduced. You can write 14 as and 15 as , but they don’t share any common factors.
12 . No. Both 39 and 26 are divisible by 13. You may not be completely familiar with the multiples of 13, but if you just note that 39 is divisible by 3 and 26 is divisible by 2, you come up with and and you can reduce the fraction:
13 . No. Here’s another situation where you look for common factors. Both of these numbers are divisible by 3. (Chapter 8 contains all the rules of divisibility you’ll be needing.)
You can stop right there, because 47 is a prime number.
14 . Yes. This is completely reduced.
Just to check the factors: . The numerator shows a prime factorization. You see more of this in Chapter 8.
15 . The left fraction can be reduced by dividing by 7. Then the two denominators can be reduced by dividing by 3. Then find the cross-product.
16 . The right fraction can be reduced by dividing by 20. Then the two numerators can be reduced by dividing by 3. Then find the cross-product.
17 . The right fraction can be reduced by dividing by 12. Then the two denominators can be reduced by dividing by 9. Then find the cross-product.
18 . The left fraction can be reduced by dividing by 2. Then the two numerators can be reduced by dividing by 13. Then find the cross-product.
19 . Fill in the proportion: . Then let x represent the new cinnamon:
20 . Set up the proportion:
21 and. The largest common factor of 7 and 8 is 1. So the least common denominator is 56, the product of the denominators: . Here are the details:
22 and. The largest common factor of 12 and 18 is 6. The least common denominator is 36. . Here are the details:
23 and. The largest common factor of x and 6 is 1. The least common denominator is their product: 6x. Break it down: and .
24 and. The largest common factor of x and is 1. Their least common denominator is their product: . Here’s the long of it: and .
25 ,, and. The least common denominator of fractions with denominators of 2, 3, and 5 is 30. Write it out:
