• Home
  • /
  • Blog
  • /
  • How To Find Equivalent Fractions? (With Examples)

How To Find Equivalent Fractions? (With Examples)

what is an equivalent fraction

This post is also available in: हिन्दी (Hindi)

Equivalent fractions are the fractions that represent the same value, even though they look different. For example, if you have a cake, cut it into two equal pieces, and eat one of them, you will have eaten half the cake. If you cut a cake into eight equal pieces and eat four of them, you will still have eaten half the cake. These are equivalent fractions.

Let’s understand what is an equivalent fraction.

What are Equivalent Fractions?

Equivalent fractions are the fractions that have different numerators and denominators but still, the values of the two fractions are equal. 

For example, $\frac{1}{2}$ and $\frac {3}{6}$ are equivalent fractions. Also, $\frac{6}{12}$ is equivalent to both $\frac{1}{2}$ and $\frac {3}{6}$.  Both of these fractions $\frac {3}{6}$, $\frac{6}{12}$ can be reduced to the lowest form of $\frac{1}{2}$.

Visual Representation of Equivalent Fractions

Let’s visualize fractions $\frac{1}{2}$, $\frac{2}{4}$ and $\frac{3}{6}$ by dividing a circle into equal parts (sectors).

what is an equivalent fraction
$1$ part of $2$ parts
what is an equivalent fraction
$2$ parts of $4$ parts
what is an equivalent fraction
$4$ part of $8$ parts

All these fractions have different numerators and denominators. But they all represent half part of a circle. Hence, the fractions $\frac{1}{2}$, $\frac{2}{4}$ and $\frac{3}{6}$ are equivalent fractions and they all reduce to the lowest/simplest form $\frac{1}{2}$.

Let’s consider one more example.

what is an equivalent fraction
$3$ parts of $4$ parts = $\frac {3}{4}$
what is an equivalent fraction
$12$ parts of $16$ parts = $\frac {12}{16}$
what is an equivalent fraction
$48$ parts of $64$ parts = $\frac {48}{64}$

All these fractions also have different numerators and denominators. But they all represent three-fourths of a square. Hence, the fractions $\frac{3}{4}$, $\frac{12}{16}$ and $\frac{48}{64}$ are equivalent fractions and they all reduce to the lowest/simplest form $\frac{3}{4}$.

girl-with-teacher-happy
Maths can be really interesting for kids

How to Find Equivalent Fractions?

You can find equivalent fractions of any given fraction by 

  • multiplying both the numerator and the denominator by a number
  • dividing both the numerator and the denominator by a number

Note:

  • The method of multiplying is generally used when the numerator and denominator of the given fraction are smaller
  • The method of dividing is generally used when the numerator and denominator of the given fraction are larger

Finding Equivalent Fractions by Multiplying

In order to find the equivalent fractions of any fraction multiply both the numerator and the denominator by the same number.

Let’s understand it by the following example.

You want to find equivalent fractions of $\frac {5}{7}$. Let’s multiply both the numerator and the denominator by numbers $3$, $5$, $6$, $7$, $8$ and $10$. 

Note: You can choose any number.

Multiplying the numerator and the denominator of $\frac {5}{7}$ by $3$: $\frac {5 \times 3}{7 \times 3}$ = $\frac {15}{21}$

Multiplying the numerator and the denominator of $\frac {5}{7}$ by $5$: $\frac {5 \times 5}{7 \times 5}$ = $\frac {25}{35}$

Multiplying the numerator and the denominator of $\frac {5}{7}$ by $6$: $\frac {5 \times 6}{7 \times 6}$ = $\frac {30}{42}$

Multiplying the numerator and the denominator of $\frac {5}{7}$ by $7$: $\frac {5 \times 7}{7 \times 7}$ = $\frac {35}{49}$

Multiplying the numerator and the denominator of $\frac {5}{7}$ by $8$: $\frac {5 \times 8}{7 \times 8}$ = $\frac {40}{56}$

Multiplying the numerator and the denominator of $\frac {5}{7}$ by $10$: $\frac {5 \times 10}{7 \times 10}$ = $\frac {50}{70}$

$5$ equivalent fractions of $\frac {5}{7}$ are $\frac {15}{21}$, $\frac {25}{35}$, $\frac {30}{42}$, $\frac {35}{49}$, and $\frac {40}{56}$.

Note: 

  • For any fraction, there are countless equivalent fractions.
  • You can find any number of equivalent fractions by multiplying the numerator and the denominator by the same number.
Is your child struggling with Maths?
frustrated-kid
We can help!
Country
  • Afghanistan 93
  • Albania 355
  • Algeria 213
  • American Samoa 1-684
  • Andorra 376
  • Angola 244
  • Anguilla 1-264
  • Antarctica 672
  • Antigua & Barbuda 1-268
  • Argentina 54
  • Armenia 374
  • Aruba 297
  • Australia 61
  • Austria 43
  • Azerbaijan 994
  • Bahamas 1-242
  • Bahrain 973
  • Bangladesh 880
  • Barbados 1-246
  • Belarus 375
  • Belgium 32
  • Belize 501
  • Benin 229
  • Bermuda 1-441
  • Bhutan 975
  • Bolivia 591
  • Bosnia 387
  • Botswana 267
  • Bouvet Island 47
  • Brazil 55
  • British Indian Ocean Territory 246
  • British Virgin Islands 1-284
  • Brunei 673
  • Bulgaria 359
  • Burkina Faso 226
  • Burundi 257
  • Cambodia 855
  • Cameroon 237
  • Canada 1
  • Cape Verde 238
  • Caribbean Netherlands 599
  • Cayman Islands 1-345
  • Central African Republic 236
  • Chad 235
  • Chile 56
  • China 86
  • Christmas Island 61
  • Cocos (Keeling) Islands 61
  • Colombia 57
  • Comoros 269
  • Congo - Brazzaville 242
  • Congo - Kinshasa 243
  • Cook Islands 682
  • Costa Rica 506
  • Croatia 385
  • Cuba 53
  • Cyprus 357
  • Czech Republic 420
  • Denmark 45
  • Djibouti 253
  • Dominica 1-767
  • Ecuador 593
  • Egypt 20
  • El Salvador 503
  • Equatorial Guinea 240
  • Eritrea 291
  • Estonia 372
  • Ethiopia 251
  • Falkland Islands 500
  • Faroe Islands 298
  • Fiji 679
  • Finland 358
  • France 33
  • French Guiana 594
  • French Polynesia 689
  • French Southern Territories 262
  • Gabon 241
  • Gambia 220
  • Georgia 995
  • Germany 49
  • Ghana 233
  • Gibraltar 350
  • Greece 30
  • Greenland 299
  • Grenada 1-473
  • Guadeloupe 590
  • Guam 1-671
  • Guatemala 502
  • Guernsey 44
  • Guinea 224
  • Guinea-Bissau 245
  • Guyana 592
  • Haiti 509
  • Heard & McDonald Islands 672
  • Honduras 504
  • Hong Kong 852
  • Hungary 36
  • Iceland 354
  • India 91
  • Indonesia 62
  • Iran 98
  • Iraq 964
  • Ireland 353
  • Isle of Man 44
  • Israel 972
  • Italy 39
  • Jamaica 1-876
  • Japan 81
  • Jersey 44
  • Jordan 962
  • Kazakhstan 7
  • Kenya 254
  • Kiribati 686
  • Kuwait 965
  • Kyrgyzstan 996
  • Laos 856
  • Latvia 371
  • Lebanon 961
  • Lesotho 266
  • Liberia 231
  • Libya 218
  • Liechtenstein 423
  • Lithuania 370
  • Luxembourg 352
  • Macau 853
  • Macedonia 389
  • Madagascar 261
  • Malawi 265
  • Malaysia 60
  • Maldives 960
  • Mali 223
  • Malta 356
  • Marshall Islands 692
  • Martinique 596
  • Mauritania 222
  • Mauritius 230
  • Mayotte 262
  • Mexico 52
  • Micronesia 691
  • Moldova 373
  • Monaco 377
  • Mongolia 976
  • Montenegro 382
  • Montserrat 1-664
  • Morocco 212
  • Mozambique 258
  • Myanmar 95
  • Namibia 264
  • Nauru 674
  • Nepal 977
  • Netherlands 31
  • New Caledonia 687
  • New Zealand 64
  • Nicaragua 505
  • Niger 227
  • Nigeria 234
  • Niue 683
  • Norfolk Island 672
  • North Korea 850
  • Northern Mariana Islands 1-670
  • Norway 47
  • Oman 968
  • Pakistan 92
  • Palau 680
  • Palestine 970
  • Panama 507
  • Papua New Guinea 675
  • Paraguay 595
  • Peru 51
  • Philippines 63
  • Pitcairn Islands 870
  • Poland 48
  • Portugal 351
  • Puerto Rico 1
  • Qatar 974
  • Romania 40
  • Russia 7
  • Rwanda 250
  • Réunion 262
  • Samoa 685
  • San Marino 378
  • Saudi Arabia 966
  • Senegal 221
  • Serbia 381 p
  • Seychelles 248
  • Sierra Leone 232
  • Singapore 65
  • Slovakia 421
  • Slovenia 386
  • Solomon Islands 677
  • Somalia 252
  • South Africa 27
  • South Georgia & South Sandwich Islands 500
  • South Korea 82
  • South Sudan 211
  • Spain 34
  • Sri Lanka 94
  • Sudan 249
  • Suriname 597
  • Svalbard & Jan Mayen 47
  • Swaziland 268
  • Sweden 46
  • Switzerland 41
  • Syria 963
  • Sao Tome and Principe 239
  • Taiwan 886
  • Tajikistan 992
  • Tanzania 255
  • Thailand 66
  • Timor-Leste 670
  • Togo 228
  • Tokelau 690
  • Tonga 676
  • Trinidad & Tobago 1-868
  • Tunisia 216
  • Turkey 90
  • Turkmenistan 993
  • Turks & Caicos Islands 1-649
  • Tuvalu 688
  • U.S. Outlying Islands
  • U.S. Virgin Islands 1-340
  • UK 44
  • US 1
  • Uganda 256
  • Ukraine 380
  • United Arab Emirates 971
  • Uruguay 598
  • Uzbekistan 998
  • Vanuatu 678
  • Vatican City 39-06
  • Venezuela 58
  • Vietnam 84
  • Wallis & Futuna 681
  • Western Sahara 212
  • Yemen 967
  • Zambia 260
  • Zimbabwe 263
Age Of Your Child
  • Less Than 6 Years
  • 6 To 10 Years
  • 11 To 16 Years
  • Greater Than 16 Years

Finding Equivalent Fractions by Dividing

In order to find the equivalent fractions of any fraction divide both the numerator and the denominator by the same number.

Let’s understand it by the following example.

You want to find equivalent fractions of $\frac {42}{126}$. 

Factors of $42$ are $1$, $2$, $3$, $6$, $7$, $14$, $21$, and $42$.

Factors of $126$ are $1$, $2$, $3$, $6$, $9$, $14$, $18$, $21$, $42$, $63$, and $126$.

Common factors of $42$ and $126$ are $1$, $2$, $3$, $6$, $14$, $21$, and $42$

You can divide numerator and denominator by any of these numbers – $2$, $3$, $6$, $14$, $21$, and $42$.

Note: $1$ is not considered as dividing by $1$ results in the same number.

Dividing the numerator and the denominator of $\frac {42}{126}$ by $2$: $\frac {42 \div 2}{126 \div 2}$ = $\frac {21}{63}$

Dividing the numerator and the denominator of $\frac {42}{126}$ by $3$: $\frac {42 \div 3}{126 \div 3}$ = $\frac {14}{42}$

Dividing the numerator and the denominator of $\frac {42}{126}$ by $6$: $\frac {42 \div 6}{126 \div 6}$ = $\frac {7}{21}$

Dividing the numerator and the denominator of $\frac {42}{126}$ by $14$: $\frac {42 \div 14}{126 \div 14}$ = $\frac {3}{9}$

Dividing the numerator and the denominator of $\frac {42}{126}$ by $21$: $\frac {42 \div 21}{126 \div 21}$ = $\frac {2}{6}$

Dividing the numerator and the denominator of $\frac {42}{126}$ by $42$: $\frac {42 \div 42}{126 \div 42}$ = $\frac {1}{3}$

$6$ equivalent fractions of $\frac {42}{126}$ are $\frac {21}{63}$, $\frac {14}{42}$, $\frac {7}{21}$, $\frac {3}{9}$, $\frac {2}{6}$ and $\frac {1}{3}$.

How Do You Know Fractions Are Equivalent?

You can check whether two or more fractions are equivalent or not by simplifying the fractions. The idea behind the process of simplification is that every equivalent fraction reduces to the same fraction when written in the simplest form.

The methods that you can use to check whether given fractions are equivalent or not are

  • Making Denominators Same 
  • Converting Fractions to Decimals
  • Cross Multiplication Method

Let’s use these methods one by one.

Making Denominators Same

The denominators of two or more equivalent fractions can be made the same by finding the L.C.M. of the denominators of the fractions.

Let’s consider the following examples to understand the process.

Ex 1: $ \frac {12}{20}$ and $ \frac {18}{30}$

The two denominators are $20$ and $30$.

L.C.M. of $20$ and $30$ is $60$.

For first fraction $60 \div 20 = 3$

For first fraction $60 \div 30 = 2$

Now, multiplying the numerators and the denominators of the first fraction by $3$ and the second by $2$.

$ \frac {12 \times 3}{20 \times 3} = \frac {36}{60}$

$ \frac {18 \times 2}{30 \times 2} = \frac {36}{60}$

Since, both the fractions $ \frac {12}{20}$ and $ \frac {18}{30}$ can be written as \frac {36}{60}$, therefore these fractions are equivalent fractions.

Ex 2: $ \frac {18}{36}$ and $ \frac {5}{9}$  

L.C.M. of $36$ and $9$ is $36$.

For first fraction $36 \div 36 = 1$

For first fraction $36 \div 9 = 4$

Note: The quotient obtained for $ \frac {18}{36}$ is $1$, therefore, there no need to multiply, as multiplying any number by $1$ gives the same number.

Multiply the numerator and the denominator of the second fraction by $4$.

$ \frac {5 \times 4}{9 \times 4} = \frac {20}{36}$  

As the fractions $ \frac {18}{36}$ and $ \frac {20}{36}$ are not the same, therefore, the fractions $ \frac {18}{36}$ and $ \frac {5}{9}$ are not equivalent.

Converting Fractions to Decimals

Two or more fractions will be equivalent fractions if they convert to the same decimal numbers.

Ex 1: $\frac {12}{18}$ and $\frac {4}{6}$ 

$\frac {12}{18} = 0.666666…$

$\frac {4}{6} = 0.666666…$

Here, the decimal represent of both the fractions is $0.666666…$, therefore, these fractions are equivalent fractions.

Ex 2: $\frac {5}{12}$ and $\frac {35}{48}$ 

$\frac {5}{12} = 0.666666…$

$\frac {35}{48} = 0.7291666…$

The fractions $\frac {5}{12}$ and $\frac {35}{48}$  are not equivalent fractions.

Cross Multiplication Method

In the cross multiplication method, multiply the numerator of the first fraction by the denominator of the second fraction and then multiply the denominator of the first fraction by the numerator of the second fraction. If the two products are equal, the fractions are equivalent otherwise not.

what is an equivalent fraction
Cross Multiplication method

Ex 1: $\frac {3}{7}$ and $\frac {18}{42}$

$3 \times 42 = 126$ and $7 \times 18 = 126$

$\frac {3}{7}$ and $\frac {18}{42}$ and are equivalent fractions.

Ex 2: $\frac {35}{55}$ and $\frac {60}{75}$

$35 \times 75 = 2625$ and $55 \times 60 = 3300$

$\frac {35}{55}$ and $\frac {60}{75}$ are not equivalent fractions.

Conclusion

The two or more fractions are called equivalent fractions if they have different numerators and denominators but represent the same value. There exist countless equivalent fractions for any fraction and these equivalent fractions can be checked by using either of these methods – by making denominators the same, converting fractions to decimals, or cross multiplication method.

Practice Problems

  1. Find five equivalent fractions for each of the following fractions:
    1. $\frac {1}{2}$
    2. $\frac {4}{5}$
    3. $\frac {18}{33}$
    4. $\frac {65}{75}$
    5. $\frac {42}{77}$
  2. Check whether given fractions are equivalent or not
    1. $\frac {5}{6}$ and $\frac {45}{54}$
    2. $\frac {3}{9}$ and $\frac {18}{54}$
    3. $\frac {7}{13}$ and $\frac {77}{169}$
    4. $\frac {56}{91}$ and $\frac {49}{84}$
    5. $\frac {60}{135}$ and $\frac {64}{144}$

Recommended Reading

{"email":"Email address invalid","url":"Website address invalid","required":"Required field missing"}
>