Linear Equations with Fractions

Help Questions

Basic Math › Linear Equations with Fractions

Questions 1 - 10
1

Solve for x

Explanation

Start by adding 10 to both sides.

Multiply both side by 9 to get rid of the fraction.

Divide by 5

Since all the answer choices have mixed fractions, you will also need to reduce down to a mixed fraction

2

Solve for x

Explanation

Start by adding 10 to both sides.

Multiply both side by 9 to get rid of the fraction.

Divide by 5

Since all the answer choices have mixed fractions, you will also need to reduce down to a mixed fraction

3

What's the least common denominator of and ?

Explanation

When finding the least common denominator, the quickest way is to multiply the numbers out. In this case and share a factor other than which is . We can divide those numbers by to get and leftover. Now, they don't share a common factor so basically multiply them out with the shared factor. Answer is .

Another approach is to list out the factors of each number. The factor that appears first in both set is the least common denominator.

We see that appears first in both sets and thus, is the least common denominator.

4

What's the least common denominator of and ?

Explanation

When finding the least common denominator, the quickest way is to multiply the numbers out. In this case and share a factor other than which is . We can divide those numbers by to get and leftover. Now, they don't share a common factor so basically multiply them out with the shared factor. Answer is .

Another approach is to list out the factors of each number. The factor that appears first in both set is the least common denominator.

We see that appears first in both sets and thus, is the least common denominator.

5

Find the least common denominator for the following fractions:

Explanation

The least common denominator is the lowest common multiple of the denominators.

Multiple of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270

Multiple of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

6

Find the least common denominator for the following fractions:

Explanation

The least common denominator is the lowest common multiple of the denominators.

Multiple of 27: 27, 54, 81, 108, 135, 162, 189, 216, 243, 270

Multiple of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90

7

What is the least common denominator for the fractions and ?

Explanation

To find the least common denominator, list out the multiples of both denominators until you find the smallest multiple that is shared by both.

4: 4, 8, 12, 16, 20, 24, 28, 32

7: 7, 14, 21, 28, 35

Because 28 is the first shared multiple of 4 and 7, it must be the least common denominator for these two fractions.

8

What is the least common denominator for the fractions and ?

Explanation

To find the least common denominator, list out the multiples of both denominators until you find the smallest multiple that is shared by both.

4: 4, 8, 12, 16, 20, 24, 28, 32

7: 7, 14, 21, 28, 35

Because 28 is the first shared multiple of 4 and 7, it must be the least common denominator for these two fractions.

9

Solve for .

Explanation

Start by adding 9 to both sides.

Next, multiply both sides by 3.

Finally, divide both sides by 2.

10

Solve for .

Explanation

Start by adding 9 to both sides.

Next, multiply both sides by 3.

Finally, divide both sides by 2.

Page 1 of 4