Grade 10 Algebraic Fractions - addition and subtraction 1.mp4

Main Ideas

The tutorial explains how to add and subtract algebraic fractions. The key requirement is to rewrite every fraction with a common denominator before combining the numerators.

Method

1. Find the lowest common denominator (LCD).

   • For simple numerical denominators, use the smallest number they both divide into.
   • For algebraic denominators, factor them first. Building the LCD from the factors often keeps it simpler.
   • A whole number can be written as a fraction with denominator (1).

2. Convert each fraction to an equivalent fraction.

   • Multiply the numerator and denominator by the same factor.
   • This changes the form of the fraction without changing its value.

3. Use brackets around numerators when adding or subtracting.

   • A numerator with multiple terms is a single unit. When multiplying to make an equivalent fraction, multiply the entire numerator.
   • When subtracting, subtract the entire second numerator. For example, (-(x+1)=-x-1), not (-x+1).

4. Combine the numerators and simplify.

   • Distribute any factors, then collect like terms.
   • Keep the common denominator.

5. Check whether the result can be simplified further.

   • Factor the numerator and denominator if possible, then cancel common factors.
   • Do not cancel individual terms across a fraction.

Examples and Lessons

• A subtraction with denominators (2) and (6) uses (6) as the LCD. Converting both fractions and carefully distributing the subtraction gives (\frac{2x-7}{6}), which cannot be simplified further.
• When working with whole numbers, writing each whole number over (1) makes the LCD clear. The result is (\frac{3}{2}), which the tutorial prefers to leave as a fraction rather than a decimal.

• For more complicated algebraic denominators, factor expressions such as (a^2-b^2) using the difference-of-squares identity: [ a^2-b^2=(a-b)(a+b). ]

• The order of subtraction matters: (b-a) is not the same as (a-b). They are negatives of one another: [ b-a=-(a-b). ] The tutorial calls changing the order while accounting for the negative sign the “switcher” rule.

• After finding the LCD and combining terms, factor the result again to see whether common factors can be cancelled. The tutorial’s more complex example illustrates that further simplification may be possible after collecting like terms.

The next example is left for a subsequent tutorial.

Speakers or Sources Featured

• A single teacher/narrator explains the lesson; no individual name is given in the subtitles.
• The video is from the Pinelands High School channel.