Answer/Discussion on Fractions

(Back to the tutorial on fractions)

Beginning Algebra
Answer/Discussion to Practice Problems
on Fractions

Answer/Discussion to 1a

100

*Rewrite 100 as a product of primes

(return to problem 1a)

Answer/Discussion to 2a

Step 1: Write the numerator and denominator as a product of prime numbers.

*Rewrite 75 as a product of primes
*Rewrite 30 as a product of primes

Step 2: Use the Fundamental Principle of Fractions to cancel out the common factors.

*Div. the common factors of 3 and 5 out of both num. and den.

(return to problem 2a)

Answer/Discussion to 2b

Step 1: Write the numerator and denominator as a product of prime numbers.

*Rewrite 9 as a product of primes

Step 2: Use the Fundamental Principle of Fractions to cancel out the common factors.

*There are no common factors to divide out

(return to problem 2b)

Answer/Discussion to 3a

*Write as prod. of num. over prod. of den.

*Div. the common factors of 2 and 5
out of both num. and den.

(return to problem 3a)

Answer/Discussion to 3b

*Rewrite as the mult. of the reciprocal

*Write as prod. of num. over prod. of den.

*Div. the common factor of 7 out of both num. and den.

(return to problem 3b)

Answer/Discussion to 3c

Step 1: Combine the numerators together.
AND
Step 2: Put the sum or difference found in step 1 over the common denominator.

*Write the sum over the common den.

Step 3: Reduce to lowest terms if necessary.

*Div. the common factor of 7 out of both num. and den.

(return to problem 3c)

Answer/Discussion to 3d

Rewriting the numbers as fractions we get:

*Rewrite whole number 5 as 5/1
*Rewrite mixed number 2 1/4 as 9/4

Step 1: Find the Least Common Denominator (LCD) for all denominators.

The first fraction has a denominator of 1 and the second fraction has a denominator of 4. What is the smallest number that is divisible by both 1 and 4. If you said 4, you are correct?

Therefore, the LCD is 4.

Step 2: Rewrite fractions into equivalent fractions with the common denominator.

*What number times 1 will result in 4?

*Multiply num. and den. by 4.

The fraction 9/4 already has a denominator of 4, so we do not have to rewrite it.

Step 3: Add and subtract the fractions with common denominators as described above.

*Write the difference over the common den.

Note that this fraction is in simplest form. There are no common factors that we can divide out of the numerator and denominator

(return to problem 3d)

Answer/Discussion to 3e

Step 1: Find the Least Common Denominator (LCD) for all denominators.

The first fraction has a denominator of 4, the second has a denominator of 5, and the third has a denominator of 10. What is the smallest number that is divisible by 4, 5, and 10? If you said 20, you are correct?

Therefore, the LCD is 20.

Step 2: Rewrite fractions into equivalent fractions with the common denominator.

Writing an equivalent fraction of 3/4 with the LCD of 20 we get: