How to Calculate Faster using Cancellation Part 1

Cancellation is one of the great techniques in making calculations faster. This technique is used in simplifying fractions, rational expressions, and equations in Algebra. In this post, we are going to learn some of the cancellation techniques that are usually not in schools but can be a helpful strategy in taking examinations like the Civil Service Exam.

1. Getting the Lowest Terms of a Fraction

Cancellation can be used to simplify fractions in order to convert them to lowest terms. In general, in order to simplify fractions, we have to get the greatest common denominator of the numerator and the denominator; however, making use of cancellation several times until the fraction is in lowest terms is also a good strategy especially for large numbers .

cancellation

 

In the first example above, cancellation is used to simplify 6/9 to 2/3 by dividing both the numerator and denominator by 3.  In the second example, cancellation was used twice: first, 24/32 is divided by 4 to obtain 6/8, and then was divided by 2 to obtain 3/4.

2. Multiplying Fractions

Cancellation can also be used to simplify multiplication of fractions. You can cancel any pair of number where one is on the numerator and the other is on the denominator.

cancellation

In the example above, 4/9 is multiplied by 3/16.

(1) We can cancel out 3 and 9 by dividing both of them by 3. We get 1 in the numerator and 3 in the denominator.

(2) We can also cancel out 4 and 16 by dividing both of them by 4. This gives us 1 and 4 respectively.

cancellation

Click image to enlarge

In the last example, we have

\dfrac{7}{15} \times \dfrac{9}{8} \times \dfrac{4}{21}.

(1)  9 and 15 are cancelled by dividing both of them by 3. This results to 3 and 5, respectively.
(2) 4 and 8 are cancelled out by dividing both of them by 4. This results to 1 and 2, respectively.
(3) 7 and 21 are cancelled out by dividing both of them by 7. This results to 1 and 3, respectively.
(4) 3 and 3 are cancelled out by dividing both of them by 3. The result is 1.

This results to the simplified fraction to

\dfrac{1}{5} \times \dfrac{1}{2} \times \dfrac{1}{1} = \dfrac{1}{10}.

The examples above are discussed in the following video. The language used is mixed Tagalog and English.

In the next post, we will discuss more about cancellation.

Civil Service Exam Rescheduled to December 6, 2015

The  suspended Paper-and-Pencil Examination of the Civil Service Professional and Subprofessional Examinations on October 18, 2015 was reset to December. The new schedule of the exam is on December 6, 2015 according to an advisory from the official website of the Civil Service Commission. The suspension in some areas due to typhoon Lando.

According to CSC, for Regions 4 and 5, and City of San Fernando, Pampanga, and Malolos City Testing Centers, affected examinees are required to register with the CSCRO or the CSCFO nearest them.

For areas with full suspensions (NCR, CAR, Regions 1 and 2, Cabanatuan City, Olongapo City and Bongao, Tawi-tawi), affected examinees will have the same testing center and school assignment and are not required to register again.

For the full requirements, visit the CSC Examination Advisory or download here.  The download file was copied and pasted from the CSC website. This is because sometimes, the CSC website is very slow.

Civil Service Commission Cancels October 18 Exam in 5 Areas

The Civil Service Commission has canceled the October 18 examination in selected areas due to typhoon Lando. The Civil Service examination is cancelled in the following areas.

  • National Capital Region
  • Region 1
  • Region 2
  • Cordillera Administrative Region
  • Tawi-tawi

Examinees are advised to wait for further announcements.

Source: GMA News

3 Helpful Strategies in Comparing Fractions

There are questions in Civil Service Examinations that may require you to compare fractions or even arrange them in order. In this post, I am going to teach you three strategies in comparing fractions.

Strategy 1: Cross Multiplication

Which is greater, 5/7 or 8/11?

If only two fractions are compared, the easiest way is to cross multiply. However, take note of the following:

1.) You multiply the denominator of the fraction to the numerator of the other fraction.
2.) Place the product above the numerator.

Screen Shot 2015-10-08 at 11.02.23 PM

The larger product is the larger fraction. As shown in the example above, 56 is larger than 55, therefore, 8/11 is larger than 5/7.

Strategy 2: Converting to Similar Fractions

Sample Question: Which is the largest: 13/16, 5/8, 3/4?

We can get the least common denominators of these fractions. Now, the LCM of these denominators is 16. So, we convert everything to fractions whose denominators is 16.

To convert 5/8 to something over 16, we divide 16 by 8 then multiply by 5 which gives us 10. So, 5/8 is equal to 10/16.

To convert ¾ to 16, we divide 16 by 4, then multiply by 3. This gives us 12.

So, we have converted all fractions to fractions whose denominator is 16.

We have 13/16, 10/16, and 12/16. Obviously, the largest is 13/16. Note that using this strategy does not only tell us which is the largest. In fact, we can order the fractions from smallest to largest or vice versa.

Strategy 3: Converting to Decimals

Which is larger: 2/5, 3/4, or 7/10.

We can convert them to decimal by manually dividing the numerator by the denominator (watch video above). The equivalent of 2/5 = 0.4, 3/4 is 0.75 and 7/10 = 70.

The strategies above can be used effectively by looking at the fractions. If two fractions are compared, use Strategy 1. If the numerators are not very large, you can use strategy 2 or 3.

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