Check fractions in the lowest terms here. It means that the fractions can be written in the simplest forms. Refer to the steps to reduce the fractions and get the simplified answer. Know the terms greatest common divisor and greatest common factor. Also, know how these terms reflect in reducing the fractions to the lowest terms. Follow the below sections to know more about Simplifying Fractions to Lowest Terms using different methods.
Fraction in Lowest Terms – Definition
Reducing the fraction or simplifying the fraction means that the numerator and denominator can no longer be divided further. These fractions cannot be divided by the whole numbers evenly or exactly other than 1.
Even though the fractions look unique or different, they actually represent the same value or amount. In other words, we can also tell that one of the fraction values will have simplified or reduced terms compared to other values. You have to reduce the terms by dividing by the common factor of numerator and denominator.
Learn the formal way of reducing the fractions which really works in all the cases. There is also an informal way that helps for reducing the fractions and you can use them whenever you are more comfortable.
Example:
Suppose that 2/3 is a fraction value. Now check for the whole numbers other than 1 which helps in dividing both the numbers without having a remainder. Other examples of these king of fully reduced fractions include 5/9,7/8 and 11/20.
There are also fractions that can be reduced further. Suppose that 2/4 is the fraction. Now check for the common factor which divides both the numbers i.e., 2 and 4. 2 is the common factor that divides both the numbers. On further simplification of the fractions, we get the final result as 1/2.
How to Reduce to Lowest Terms?
There are several methods to reduce to the lowest terms. We have outlined all of the methods in detail by considering few examples. They are as follows
Method 1: Dividing out the Common Primes
- Note down the numerator and denominator values as a product of primes.
- Now that you know the common prime factor, divide the numerator and denominator by each of the common prime factors. Division of fractions is indicated by the slanted line through each factor. This complete process is called canceling common factors.
- The product value of the remaining factors in the numerator and also the product value of the remaining factors in the denominator are prime numbers and the fraction value is reduced to the lowest terms.
Example:
Suppose that 6/18 is the fraction number. On dividing the fractions we can write it as 2*3/2*3*3 = 1/3 is the final result.
In the above equation, 1 and 3 are relative primes.
Method 2: Dividing Out Common Factors
- First, divide the denominator and numerator by a number of factors which is common to both. Note down the quotient which is above the original number.
- Continue the process till the denominator and numerator are relatively prime numbers.
Example:
Suppose 25/30 is the fraction number. Now, consider the common whole number which divides both the numbers. Therefore, 5 is the common number that divides both numerator and denominator. After dividing the numbers by 5, the result will be 5/6. Here 5 and 6 are prime relatively.
Method 3: HCF Method
To reduce the fractions, find the HCF of the denominator and numerator of the given fraction. To reduce the fraction to its lowest terms, we divide the denominator and numerator by their HCF numbers.
Example:
Reduce the fraction 21/56 to its reduced form?
First of all, divide the number 21 by the number 56
The final quotient when dividing the values is 7.
Therefore HCF of 21 and 56 is 7.
Now, divide the denominator and numerator in the fraction by HCF value 7.
Then the final result value will be 3/8
Method 4: Prime Factorization Method
First, find the common factors of both numerators and denominators. Then express both the denominator and numerator of the fraction as the product values of the prime factors. Once you find the equation, then cancel the common factors from them to get the final result value.
Example:
Reduce 120/360 to the lowest term
First of all, find the factors of both numerators and denominators.
The factors of 120 are 2,2,2,3,5
The factors are 360 are 2,2,2,3,3,5
On further simplification, we get the final result as 1/3.
Example Problems on Reducing Fractions to Lowest Terms
Problem 1:
Mr. Lee is planting a vegetable garden. The garden will have no more than 16 equal sections. 3/4 of the garden will have tomatoes. What other fractions could represent the part of the garden that will have tomatoes?
Solution:
As given in the question,
No of equal sections the garden will have = 16
Part of the garden will have tomatoes = 3/4
Now, we have to find fractions that are equivalent to 3/4.
We can use multiplication to find equivalent fractions.
3*2/4*2 = 6/8
3*3/4*3 = 9/12
3*4/4*4 = 12/16
Few parts = Larger Parts = Smaller Parts
Each numerator represents the parts of Mr. Lee’s garden that have tomatoes
Each denominator represents how many parts there are in all the gardens.
As the denominator becomes the greater number, the size of the parts becomes smaller.
Therefore the final result is 1/16
Thus, 1/16th part of the garden has tomatoes.
Problem 2:
Sophia is making bracelets with beads. Each bracelet has 4 beads and 3/4 of the beads are red. If Sophia makes 5 bracelets, how many red beads does she need?
Solution:
As given in the problem,
No of beads each bracelet has = 4
No of red beads = 3/4
No of bracelets = 5
For 1 bracelet, the number of red beads = 3
For 5 bracelets, the number of red beads = 15
Therefore, the total no of beads = 20
Hence, Sophia will need 15 red beads to make 5 bracelets.
Problem 3:
Tala cut a pizza in half. She cuts each half into 2 pieces and cut each piece into 2 slices. What fraction of the pizza did Tala eat?
Solution:
As given in the question,
No of halves she cut = 1
No of pieces she cut half piece = 2
Therefore, Tala ate = 2/8 or 1/4
Problem 4:
2/5 of the students voted for Tala to be the class president, 1/3 voted for Emma, and 4/15 voted for Tim. Which candidate got the most votes?
Solution:
As given in the question,
We need to make equivalent fractions to solve this
Multiples of 5: 5,10,15…
Multiples of 3: 3,6,9,12,15….
Tals’s voting = 2/5*3/3 = 6/15
Emma’s voting = 1/3*5/5 = 5/15
Hence, Tala got the most votes