• Home
• /
• Blog
• /
• What is Proportion? (With Meaning & Examples)

# What is Proportion? (With Meaning & Examples)

September 30, 2022

This post is also available in: हिन्दी (Hindi)

Proportion in math is a comparison of two numbers that represent things or people, and it is often written as a fraction or with a colon. The concept of proportion is related to ratio and fractions, which represents a relation between two values.

We use proportions in solving many daily life problems such as in business while dealing with transactions or while cooking, etc. It establishes a relation between two or more quantities and thus helps in their comparison.

Let’s understand what is proportion and how it is used.

## What is Proportion?

Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or ratios.

For example, a car moving at a certain speed and covering a distance of $60 km$ in $1hr$ is the same as a car covering a distance of $300 km$ in $5 hr$. So, we can say that the numbers $60$, $1$, $300$, and $5$ are in proportion or $300 : 5 = 60 : 1$ or $\frac{300}{5} = \frac{60}{1}$.

A proportion involves two ratios. The meaning of proportion is that the two ratios are equal to each other. As in the above example, the two ratios $300: 5$ and $60: 1$ are equal.

In general four numbers $a$, $b$, $c$, and $d$ are said to be in proportion, when $a:b = c:d$, or $\frac{a}{b} = \frac{c}{d}$, and the ratios $a:b$ and $c:d$ are called equivalent ratios.

Proportions are denoted using the symbol  “::” or “=”.

When the values $a$, $b$, $c$ and $d$ are in proportion, i.e., $a:b :: c:d$ or $\frac{a}{b} = \frac{c}{d}$, the numbers $a$ and $d$ are called extremes and the numbers $b$ and $d$ are called means.

## Difference Between Ratio and Proportion

The following differences help in distinguishing between ratio and proportion.

Is your child struggling with Maths?
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
• 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
• Cape Verde 238
• Caribbean Netherlands 599
• Cayman Islands 1-345
• Central African Republic 236
• 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
• Egypt 20
• 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
• 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
• 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
• 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
• 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
• Less Than 6 Years
• 6 To 10 Years
• 11 To 16 Years
• Greater Than 16 Years

## Checking for Values in Proportion

Four numbers $a$, $b$, $c$ and $d$ are said to be in proportion, when $a:b = c:d$. To check whether the numbers $a$, $b$, $c$, and $d$ are in proportion, you can use any of the following methods.

• Fraction Method
• Multiplication Method

The numbers $a$, $b$, $c$ and $d$ will be in proportion, if $\frac{a}{b}$ and \frac{c}{d}$are equivalent fractions. Let’s consider the following examples to understand the method. The numbers$12$,$20$,$21$,$35$are in proportion, since,$\frac{12}{20} = \frac{21}{35}$.$\frac{12}{20} = $\frac{3 \times 4}{5 \times 4} =$\frac{3}{5}$and$\frac{21}{35} = \frac{3 \times 7}{5 \times 7} \frac{3}{5}$. The fractions$\frac{12}{20}$and$\frac{21}{35}$are called equivalent fractions. The numbers$6$,$9$,$4$,$10$are not in proportion, since,$\frac{6}{9} \ne \frac{4}{10}$.$\frac{6}{9} = \frac{2 \times 3}{3 \times 3} = \frac{2}{3}$and$\frac{4}{10} = \frac{2 \times 2}{5 \times 2} = \frac{2}{5}$. ### Multiplication Method The numbers$a$,$b$,$c$and$d$will be in proportion if the products of means is equal to the product of extremes. To understand this method, let’s again consider the above examples. The numbers$12$,$20$,$21$,$35$are in proportion, since,$12 \times 35 = 420$and$20 \times 21 = 420$. And the numbers$6$,$9$,$4$,$10$are not in proportion, since,$6 \times 10 = 60$and$9 \times 4 = 36$. ## Properties of Proportion Proportion establishes an equivalent relation between two ratios. Following are the properties of proportion. ### Addendo The property states that if$a$,$b$,$c$, and$d$are in proportion, i.e.,$a : b = c : d$, then value of each ratio is$a + c : b + d$. In other words, we can say that if$a$,$b$,$c$, and$d$are in proportion, then$a : b = c : d = a + c : b + d$. Let’s consider a proportion$2$,$3$,$4$,$6$to understand the Addendo property.$2 + 4 = 6$and$3 + 6 = 9$And,$\frac{6}{9} = \frac{2}{3} = \frac{4}{6}$. ### Subtrahendo The property states that if$a$,$b$,$c$, and$d$are in proportion, i.e.,$a : b = c : d$, then value of each ratio is$a – c : b – d$. In other words, we can say that if$a$,$b$,$c$, and$d$are in proportion, then$a : b = c : d = a – c : b – d$. Let’s consider a proportion$5$,$10$,$1$,$2$to understand the Subtrahendo property.$5 – 1 = 4$and$10 – 2 = 8$And,$\frac{4}{8} = \frac{5}{10} = \frac{1}{2}$. ### Dividendo The property states that if$a$,$b$,$c$, and$d$are in proportion, i.e.,$a : b = c : d$, then$a – b : b = c – d : d$. Let’s consider a proportion$3$,$2$,$6$,$4$to understand the Dividendo property.$\left(3 – 2 \right) : 2 = 1 : 2$and$\left(6 – 4 \right) : 4 = 2:4 = 1:2$. ### Componendo The property states that if$a$,$b$,$c$, and$d$are in proportion, i.e.,$a : b = c : d$, then$a + b : b = c + d : d$. Let’s consider a proportion$2$,$3$,$4$,$6$to understand the Componendo property.$\left(2 + 3 \right) : 3 = 5 : 3$and$\left(4 + 6 \right) : 6 = 10:6 = 5:3$. ### Alternendo The property states that if$a$,$b$,$c$, and$d$are in proportion, i.e.,$a : b = c : d$, then$a : c = b: d$. Let’s consider a proportion$2$,$3$,$4$,$6$to understand the Alternendo property.$2 : 4 = 1 : 2$and$3 : 6 = 1:2$. ### Invertendo The property states that if$a$,$b$,$c$, and$d$are in proportion, i.e.,$a : b = c : d$, then$b : a = d : c$. Let’s consider a proportion$2$,$3$,$4$,$6$to understand the Invertendo property.$3 : 2$and$6 : 4 = 3:2$. ### Componendo and Dividendo The property states that if$a$,$b$,$c$, and$d$are in proportion, i.e.,$a : b = c : d$, then$\left(a + b \right) : \left(a – b \right) = \left(c + d \right) : \left(c – d \right)$. Let’s consider a proportion$3$,$2$,$6$,$4$to understand the Componendo and Dividendo property.$\left(3 + 2 \right) : \left(3 – 2 \right) = 5 : 1$and$\left(6 + 4 \right) : \left(6 – 4 \right) = 10:2 = 5:1$. ## Examples Ex 1: Check whether the numbers$27$,$33$,$54$,$66$are in proportion or not. Let$a = 27$,$b = 33$,$c = 54$,$d = 66\frac{a}{b} = \frac{27}{33} = \frac{9 \times 3}{11 \times 3} = \frac{9}{11}$And,$\frac{c}{d} = \frac{54}{66} = \frac{9 \times 6}{11 \times 6} = \frac{9}{11}$Since,$\frac{27}{33} = \frac{54}{66} = \frac{9}{11}$, therefore, the numbers$27$,$33$,$54$,$66$are in proportion. Alternatively, it can be solved as$a \times d = 27 \times 66 = 1782$and$b \times d = 33 \times 54 = 1782$. Since,$27 \times 66 = 33 \times 54$, therefore, the numbers$27$,$33$,$54$,$66$are in proportion. Ex 2: Find the value of$x$, such that$2$,$x$,$3$, and$15$are in proportion. For$2$,$x$,$3$, and$15$to be in proportion,$2 \times 15 = x \times 3 => 3x = 30 => x = \frac{30}{3} = 10$. ## Conclusion Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or ratios. If any four numbers$a$,$b$,$c$and$d$are in proportion, then$a:b = c:d$. ## Practice Problems 1. Check whether the following numbers are in proportion or not. •$1$,$2$,$3$,$4$•$2$,$3$,$4$,$6$•$2$,$3$,$4$,$8$•$1$,$5$,$10$,$15$2. For what value of$x$, the following numbers will be in proportion? •$2$,$8$,$x$,$20$•$x$,$75$,$1$,$5$•$7$,$x$,$5$,$15$•$9$,$36$,$11$,$x$## Recommended Reading ## FAQs ### What is a proportion in math? Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or ratios. The four numbers$a$,$b$,$c$, and$d$are said to be in proportion, when$a:b = c:d$, or$\frac{a}{b} = \frac{c}{d}$, and the ratios$a:b$and$c:d$are called equivalent ratios. ### How do you know if two ratios form a proportion? The two ratios will form a proportion, if they are equivalent fractions, i.e., the ratios$a:b$and$c:d$will form a proportion, if$\frac{a}{b} = \frac{c}{d}$. ### What are the different properties of proportion? When four numbers$a$,$b$,$c$, and$d\$ are in proportion, they exhibit the following properties:
Addendo: If a : b = c : d, then value of each ratio is a + c : b + d
Subtrahendo: If a : b = c : d, then value of each ratio is a – c : b – d
Dividendo: If a : b = c : d, then a – b : b = c – d : d
Componendo: If a : b = c : d, then a + b : b = c+d : d
Alternendo: If a : b = c : d, then a : c = b: d
Invertendo: If a : b = c : d, then b : a = d : c
Componendo and Dividendo: If a : b = c : d, then a + b : a – b = c + d : c – d