Multiplication of Fractions With the Same Numerator and Same Denominator

7/27/2019 Multiplication of Fractions With the Same Numerator and Same Denominator

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Multiplication of fractions with the same Numerator and sameDenominator:

We know that the fraction is a part of the whole. Let us study the following diagram.

In the above diagrams, the first one shows the fraction 13.

The second diagram shows 13 of the shaded region of the first., which is 13 of13

= 1313

= 19

The third diagram shows the 13 of the previous shaded region, which is 13 of19

= 1319

= 127

Hence when we multiply the fractions with the same denominator and same numerator, we get the resulting fraction

as the same part of each part.

For example :

25 of25 is the same as 2525

= 2255

= 425Hence when we find the same part of the part, we group the numerators, and denominators separately and multiplythem separetly.

(i.e) 252525

= 222555

= 8125

Exponent form of the product of fractions with the same numeratorand same denominator:Back to Top
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We are aware that the product 2 x 2 x 2 x 2 x 2 can be expressed in exponent form as 25

We use the same procedure for the fractions as well.

252525 = (25)5

= 2555

= 323125

Multiplication of fractions with same denominator but differentnumerator:Back to Top

In the above figure, first picture shows the fraction 25

Where as the second picture, shows the 35 of25 of the first picture.

Hence overall among 25 small boxes, 6 boxes are shaded, which is shown in the third picture.Hence 35 of25 is the same as 625

For example : 372747 = 324777

=24343

Hence we observe that when we find the product of the fractions with the same denominator, we get the smallerportion of the whole.

Arithmetically when we multiply the fractions with the same denominator, we follow the following steps.Step 1: Group the numerators and multiply them.Step 2: Group the denominators and multiply them.Step 3: The resulting fraction from steps 1 and 2 is the product of the fractions with the same denominators.Step 4: If the resulting fraction in step 3 is an improper fraction and has factors common, we divide the numeratorand denominator by the Highest Common Factor and write the simplest form and convert into mixed fraction, else wehighlight the obtained fraction as the final answer.

Note: When we multiply proper fractions with the same denominators, the resulting product will be the smallest of the


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whole. Hence it will definitely be a proper fraction.

Example 1: 51115112011

Solution: We have 41115112011

= 41520111111 [ grouping the numerators and the denominators separately ]

= 12001331 [ multiplying the numbers in the numerator and denominator as grouped inthe previous step ]

Example 2: 294969

Solution: We have 294969

=246999 [ grouping the numerators and the denominators separately ]

= 48729 [ multiplying the numbers in the numerator and denominator as grouped in the

previous step ]

=4837293 [ dividing the numerator and the denominator by the common factor 3 ]

= 16243 Final Answer in the simplest form.

Practice Question:Back to Top

Multiply the following fractions and express your answer in the simplest form.

1. 161616

2. 3107102710

3. 32122412


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How to Multiply Mixed Numbers by Fractions

Introduction:

When we multiply whole numbers and integers we use the multiplication tables and the rule of signs and

multiply the numbers. When we come across the problems like " Find the area of a rectangle whose length is 534 cm

and width 212 cm" , we need to multiply the mixed fractions. In this section let us see how we multiply these types of

fractions.

Conversion of Mixed Fractions:

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Mixed Numbers: Mixed numbers are those which are the combination of whole number greater than zero and a

proper fraction.

Before multiplying the mixed numbers we should convert them into improper fractions.

Conversion of Mixed Fractions into Improper Fractions:

We follow the following procedure to convert a mixed fraction into its improper fraction.

For any fraction of the form, kpq , 'k' is the whole number, 'q' is the divisor and 'p' is the remainder.
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the improper fraction is (kq)+pq

Example : 534

Solution:534

=534=(54)+34

= 20+34

= 234

Note: When we convert a mixed fraction into improper fractions we see that the numerator is greater than that of the

denominator.

Multiplication of mixed numbers by fractions:

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When we multiply two or more mixed numbers we follow the following rules.

Step 1. Convert the mixed fractions into improper fractions of the form ab

Step 2. Group the numerators and multiply them.

Step 3. Group the denominators and multiply them.

Step 4. Find the Highest Common Factor (HCF) of the fraction obtained from Steps 2 and 3.

Step 5. Divide the numerator and denominator by the HCF obtained from step 4.

Step 6. If the fraction obtained is is a proper fraction or a whole number highlight this as the final answer else

convert the improper fraction into mixed fraction and highlight this as the answer.

Example : Multiply and express the answer in the simplest form

631627925

Solution:631627925

= 991625925 [ converting the mixed fraction into improper fraction ]

= 992521695 [ grouping the numerators and the denominators separately ]


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= 4950720 [ multiplying the numbers in the numerator and denominator ]

= 49509072090 [ dividing the numerator and the denominator by the HCF ]

= 558 [ simplest form of the fraction which is in improper form ]

= 678 Final answer in the form of mixed fraction.

Working:

To find the Highest Common Factor of 4950 and 720, let us find the prime factors of each.

4950 = 2 x 3 x3 x 5 x 5 x 11

720 = 2 x 2 x 2 x 2 x 3 x 3 x 5

The common factors are , 2, 3, 3, 5

Highest Common Factor HCF = 2 x 5 x 3 x 3 = 90

Practice Questions:

Back to Top

Multiply the following fractions and express your result in simplest form.

1. 24557

2. 3342121625


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Multiplication of Fractions With the Same Numerator and Same Denominator

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