Simplest Form Of 618? The 127 Detailed Answer

The simplest form of a fraction is a fraction whose numerator and denominator are relatively prime. This means that the numerator (upper part or upper part) and denominator (lower part or lower part) of the fraction have no common divisor other than 1.

A fraction is a value that represents part of a whole. The simplest form is also called the reduced fraction form. For example, ¾ is the simplest form of a fraction that has a common divisor equal to 1. But 2/4 is not the simplest form because 2/4 can be further simplified and written as ½. Here we can also say that ½ and 2/4 are equivalent fractions.

In this article, let’s find out how to write the fraction in its simplest form using the given steps and examples.

How do I find the simplest form of a fraction?

A fraction, in its simplest form, is when the top and bottom of the fraction are integers that are relatively prime.

Finding the simplest form of any fraction is an easy technique. We need to simplify the numerator and denominator of the fraction by dividing both the numerator and denominator by the greatest common divisor that divides them completely. After division, the numerator and denominator should remain integers. This method of simplifying fractions is also known as reducing fractions.

For example, if the fraction is ac/bc, then the simplified form of ac/bc is a/b because the common factor “c” is divided by both the numerator and denominator.

ac/bc = a/b

Steps to find the simplest shape

Learn the step-by-step method of simplifying fractions here:

Find the GCF of the numerator and denominator of the fraction

Divide the numerator and denominator by the generated GCF

Write the simplified fraction of the given fraction

Also Read: Simplifying Fractions?

Solved examples

Let’s solve examples based on simplifying fractions.

Simplify the fractions given below:

(i) 3/6

(ii) 2/10

(iii) 15/35

(iv) 15.10

(v) 16.4

Solution:

(i) 3/6

Let’s find the GCF of 3 and 6.

GCF(3.6) = 3

So 3/6 = (3 x 1)/(3 x 2) = ½

So ½ is the answer.

(ii) 2/10

GCF of 2 and 10 is 2.

Therefore we can write

2/10 = (1×2)/(5×2)

Dividing the numerator and denominator by 2, we get;

2/10 = ⅕

So ⅕ is the solution.

(iii) 15/35

HCF of 15 and 35 is 5

If we divide the numerator and denominator by 5, we get;

15/5 = 3

35/5 = 7

Therefore 15/35 = 3/7 is the required fraction.

(iv) 15.10

GCF (10, 15) = 5

Divide 10 and 15 by 5 to get;

10/5 = 2

15/5 = 3

Therefore, the simplified fraction of 10/15 is:

10/15 = 2/3

(v) 16.4

GCD of 4 and 16 = 4

Divide the numerator and denominator (4 and 16) by 4 to get;

4/4 = 1

16/4 = 4

Therefore, the simplified fraction of 4/16 is:

4/16 = ¼

Simplest form of adding fractions

When adding two fractions, the sum of the fractions must be written in the simplest form.

For example, if we add ¼ and ¼, we get; ¼ + ¼ = 2/4 But 2/4 is not the simplest form. Hence we get the division of the numerator and denominator by the greatest common divisor of 2 and 4 i.e. 2; 2/4 = ½ So ¼ + ¼ = ½

Note: If the denominators of the two fractions are also not equal, then they are unlike fractions. So we need to convert these fractions into equal fractions by making the denominators equal and then adding them up.

Simplest form ratio

A ratio is represented by a:b, where a and b are integers. When we write a ratio in its simplest form, we reduce the ratio to its lowest terms.

Example: Simplify 32:40. We can use the same method to simplify the ratio as we used to simplify the fraction. 32 is here the antecedent and 40 the consequent. So we need to find the highest possible factor of 32 and 40 to get the simplified form. Therefore 8 is the common factor of 32 and 40. Therefore the simplest form of 32:40 is 4:5 (because 8 x 4 = 32 and 8 x 5 = 40)

Decimal to Simplest Form

Follow these steps to convert decimals to the simplest fractional form:

Remove the decimal and write it as a whole number, which will be the numerator of the fraction.

Write the denominator as a multiple of 10 equal to the digits after the decimal point. (For example, if there are 2 digits after the decimal point, then the denominator is 10 x 10 = 100)

Now simplify the fraction

Example: Write 0.5 in a fraction. By following the steps given above, we get; 0.5 = 5/10 [Since there is only one decimal place] = ½ [By taking out the HCF from the numerator and denominator and then simplifying]

practice questions

Simplify the following fractions: 10/45 2/18 4/60 9/81 What is the equivalent fraction of 5/9? Solve and write in the simplest form: ⅗ + 7/5 ⅘ + 8/3 Fill in the gaps: 36/54 = 18/___ 30/54 = ___/9 ¼ = 7/___ 180/___ = 9/10

Fractions Related Articles

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Simplest Form – Definition & Examples – Expii

In its simplest form, a fraction is when the numerator and denominator do not have a common divisor.

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Here,

# 5% = 5/100 #

# => 1/20 #

Therefore, #5%# can be written as #1/20# in its simplest form.

Fractions in the simplest form

A fraction is said to be in its simplest form when its numerator and denominator are relatively prime, that is, they have no common factors other than 1. (Some books use “written in the lowest terms” to mean the same thing.)

So 5 9 is the simplest form, since 5 and 9 have no common factors except 1. But 6 is not 9; 6 and 9 have a factor 3 in common.

To write 6 9 in the simplest form, divide both the numerator and denominator by the greatest common factor, in this case 3:

6 ÷ 3 9 ÷ 3 = 2 3

So 6 9 in the simplest form is 2 3 .

This is called reducing fractions.

One to every power is one.

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simplify fractions

A fraction is a part of a whole. It has a numerator and a denominator.

For example: 12 here 1 is the numerator and 2 is the denominator. It is represented by the following figure:

Here the shape is divided into 2 equal parts, hence the denominator is 2 and 1 of 2 parts is shaded, hence the numerator is 1.

Simplest form of a fraction

A fraction is called in its simplest form if 1 is the only common divisor of the numerator and denominator. For example, 89 because 1 is the only common divisor of 8 and 9 in that fraction.

We simplify fractions because there is always work to do or math when the fractions are in their simplest form.

Simplifying proper and improper fractions

Steps:

Find the highest common factor (HCF) of the numerator and denominator.

Divide both the numerator and denominator by HCF.

Example 1: Check if the fraction 715 is in its simplest form?

Solution: Factors of numerator 7 = 1, 7

Factors of denominator 15 = 1, 3, 5, 15

We can see that 1 is the only common divisor of 7 and 15

Hence 715 in its simplest form.

Example 2: Reduce 1218 in its simplest form.

Solution: Factors of 12 = 1, 2, 3, 4, 6, 12

Factors of 18 = 1, 2, 3, 6, 9, 18

Highest common factor (HCF) of 12 and 18 = 6

If we divide the numerator and denominator by 6 (HCF), we get

12÷6 18÷6 = 2 3

Therefore 23 is the simplest form of the fraction 1218.

Simplify a mixed fraction

Steps:

Find the highest common factor (HCF) of the numerator and denominator of the fraction.

Divide both the numerator and denominator by HCF to get the simplified fraction.

Write the whole and the simplified fraction together.

Example 4: Matthew has 31216 ice cream. How much ice does he have in his simplest form?

Solution: Factors of 3 12 16 = 1 4 12 = 1, 2, 3, 4, 6, 12

Factors of 16 = 1, 2, 4, 8, 16

Highest common factor (HCF) of 12 and 16 = 4

If we divide the numerator and denominator by 4 (HCF), we get

12÷4 16÷4 = 3 4

So Matthew 31216 is carrying ice cream in its simplest form.

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