Post 2b: Are You Ready? Rational Number Operations: Common Denominators

(by Chris B. with help from Sage the intrepid student dog)

Now that you and Sage reviewed multiplying and dividing fractions in Post 2a: Are You Ready? Rational Number Operations: Multiplying and Dividing Fractions, it is time to review adding and subtracting fractions. Before we jump into Addition and Subtraction, let's first refresh on making Common Denominators

Making a Common Denominators

Remember from your coursework that the value "1" can be written as a number over itself such as 2/2 or 3/3 or 4/4. A ratio like these can be multiplied by any fraction in order to make an equivalent fraction with a new denominator.

In the case of 1/2, equivalent fractions can be generated as follows

1/2 = 1/2 * 2/2 = 2/4

1/2 = 1/2 * 4/4 = 4/8

If you have two fractions with different denominators, you can gain a common denominator by multiplying the numerator and denominator of the first fraction by the denominator of the second fraction. You can then multiply the numerator and denominator of the second fraction by the denominator of the first fraction. Deeper explanation of Common Denominators and Least Common Denominators can be found searching through web sites like this.

Two sets of blocks have transformed into tiles to span the chasm. The next stack of blocks glows and Sage knows what to do now. After solving the multiplication and division challenges, Sage is ready to attempt Addition and Subtraction of fractions. Sage returns to the wall mounted touchscreen TV which now shows an example for how to create a common denominator for fractions.

Here's an example problem for creating a Common Denominator before addition or subtraction of fractions.

There's a second problem in this scratchpad so that Sage can attempt to make a common denominator.

Sage paws through the example problem and is excited that his denominator of 30 matched the hints on the right.

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Catch your algebra mistakes before they cost you

The scratchpad in this guide runs on moment.of.math — a free Chrome extension that checks your algebra line by line, on any problem. It can generate new variations problems, so you can get as much practice as you need. On many homework sites, it automatically detects the math on the page, so you don't have to copy anything over. Try it on tonight's homework.

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