Author: Lensyl Urbano

A Review of Fractions: Based on Khan Academy Lessons

This is a basic review of working with fractions using lessons and practice sets from the Khan Academy.

1. Adding Fractions with a Common Denominator

The first topic — adding fractions –ought to be really easy for algebra students, but it allows them to become familiar with the Khan Academy website and doing the practice sets.

Now do the Practice Set.

OPTIONAL: Subtracting fractions with a common denominator works the same way. Students may do this practice set if they find it useful.

2. Adding Fractions with a Different Denominator

This is usually a helpful review.

The practice set.

3. Multiplying and Dividing Fractions

A good review that helps build up to working with radical numbers.

Multiplying fractions:

Do the multiplying fractions practice set.

Dividing Fractions:

Dividing fractions practice set.

4. Converting Fractions to Decimals

The last review is on how to convert fractions to decimals.

Now try the practice set for ordering numbers.

5. Next: Working with Square Roots

Quick Reference: Adding Fractions with Different Denominators

To add fractions with different denominators you just need to multiply each fraction to get the same denominator:

Take:
\frac{3}{5} + \frac{5}{9}

The easiest common denominator will be the product of both denominators ( 5 × 9 = 45 ). So multiply each fraction.

\frac{3}{5}\times\frac{9}{9} + \frac{5}{9} \times\frac{5}{5}

Notice that you’re really multiplying each fraction by 1 (since 9/9 = 1 and 5/5 = 1) and anything multiplied by one remains the same number. So you’re not changing the value of the fraction, just how it looks.

Now doing the multiplication gives:
\frac{3}{5}\times\frac{9}{9} + \frac{5}{9} \times\frac{5}{5} = \frac{27}{45} + \frac{25}{45}

Which we can add because we now have a common denominator:
\frac{27}{45} + \frac{25}{45} = \frac{52}{45}

And simplify to give a mixed number:
\frac{52}{45} = 1\frac{7}{45}

Resonance Frequencies: MythBusters investigate Tesla’s Earthquake Machine

The whole episode is worth watching, but this little section (at 10:52) of MythBusters’ attempt to build an earthquake machine there demonstrate the resonance frequency in a water tank provides a nice visualization.