APPLYING GCF AND LCM TO FRACTION OPERATIONS

About "Applying GCF and LCM to Fraction Operations"

Applying GCF and LCM to fraction operations :

Generally we have the following kinds of operations in fraction.

In which if we want to add or subtract two or more fractions, then we may have to use the concept LCM if the denominator of those fractions are not same.

For multiplying and dividing two fractions we may have to use the concept GCF. If we want to reduce the fraction into its lowest form,then we have to apply the concept GCF.

Now let us see some example problems to understand how we use the concept LCM and GCF while adding and subtracting two fractions.

Question 1 :

Solution :

To simplify the fraction, we have to find the GCF of both numerator and denominator.

Now we have to divide both numerator and denominator by the GCF as given below.

Therefore, the simplified form of 9/12 is 3/4.

Let us see the next example "Applying GCF and LCM to Fraction Operations".

Question 2 :

Solution :

Since the denominators are not same, we have to take LCM to make the denominators same.

To simplify the fraction, we have to find the GCF of both numerator and denominator.

Now we have to divide both numerator and denominator by the GCF as given below.

Let us see the next example "Applying GCF and LCM to Fraction Operations".

Subtracting two fractions using LCM

If the denominators of the fractions are not co-prime (there is a common divisor other than 1), we have to apply this method.

Fro example, let us consider the two fractions 5/12,  1/20.

In the above two fractions, denominators are 12 and 20.

For 12 and 20, if there is at least one common divisor other than 1, then 12 and 20 are not co-prime.

For 12 & 20, we have the following common divisors other than 1.

2 & 4

So 12 and 20 are not co-prime.

In the next step, we have to find the L.C.M (Least common multiple) of 12 and 20.

12 =  2² x 3

20 = 2² x 5

When we decompose 12 and 20 in to prime numbers, we find 2, 3 and 5 as prime factors for 12 and 20.

To get L.C.M of 12 and 20, we have to take 2, 3 and 5 with maximum powers found above.

So, L.C.M of 12 and 20 = 2² x 3 x 5

= 4 x 3 x 5

= 60

Now we have to make the denominators of both the fractions to be 60 and subtract the two fractions 5/12 and 1/20 as given below.

How to multiply two fractions?

To multiply two or more fractions, we have to multiply the numerators with numerators and denominators with denominators.

If it is possible we can simplify the fraction into its lowest form using GCF.

Question 3 :

Multiply (3/20)  x (30/12)

Solution :

Considering the numerators and denominators we can simplify the above fraction by using the concept GCF.

By simplifying the given fractions using GCF, We get

So the final answer is 3/8.

How to simplify fractions using gcf?

Problem 1 :

Simplify 42/60 in simplest form

Solution :

Step 1 :

Write the two numbers on one line

Step 2 :

Draw the L shape

Step 3 :

Divide out common prime numbers starting from the smallest.

7 and 10 is not divisible by any common number.

7/10 is the simplified form of the given fraction 42/60.

After having gone through the stuff and examples, we hope that the students would have understood "Applying GCF and LCM to Fraction Operations".

WORD PROBLEMS

HCF and LCM  word problems

Word problems on simple equations

Word problems on linear equations

Algebra word problems

Word problems on trains

Area and perimeter word problems

Word problems on direct variation and inverse variation

Word problems on unit price

Word problems on unit rate

Word problems on comparing rates

Converting customary units word problems

Converting metric units word problems

Word problems on simple interest

Word problems on compound interest

Word problems on types of angles

Complementary and supplementary angles word problems

Double facts word problems

Trigonometry word problems

Percentage word problems

Profit and loss word problems

Markup and markdown word problems

Decimal word problems

Word problems on fractions

Word problems on mixed fractrions

One step equation word problems

Linear inequalities word problems

Ratio and proportion word problems

Time and work word problems

Word problems on sets and venn diagrams

Word problems on ages

Pythagorean theorem word problems

Percent of a number word problems

Word problems on constant speed

Word problems on average speed

Word problems on sum of the angles of a triangle is 180 degree

OTHER TOPICS

Profit and loss shortcuts

Percentage shortcuts

Times table shortcuts

Time, speed and distance shortcuts

Ratio and proportion shortcuts

Domain and range of rational functions

Domain and range of rational functions with holes

Graphing rational functions

Graphing rational functions with holes

Converting repeating decimals in to fractions

Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

Translating the word problems in to algebraic expressions

Remainder when 2 power 256 is divided by 17

Remainder when 17 power 23 is divided by 16

Sum of all three digit numbers divisible by 6

Sum of all three digit numbers divisible by 7

Sum of all three digit numbers divisible by 8

Sum of all three digit numbers formed using 1, 3, 4

Sum of all three four digit numbers formed with non zero digits

Sum of all three four digit numbers formed using 0, 1, 2, 3

Sum of all three four digit numbers formed using 1, 2, 5, 6