Mary Jane Sterling - Algebra I All-in-One For Dummies

But let’s say you do this in two steps — both dividing by a common factor.

You see that both 63 and 84 are divisible by 7. So divide both the numerator and denominator by 7.

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 8contains 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: