4.2: Proportions - Mathematics

4.2: Proportions - Mathematics

Proportions Worksheets

This series of printable proportion worksheets are prepared specifically for learners of grade 6, grade 7, and grade 8. A variety of pdf exercises like finding proportions using a pair of ratios, determining proportions in function tables, creating a proportion with a given set of numbers and solving word problems are included here. Students will also learn to identify if the coordinates on a graph share a proportional relationship. Begin your proportions practice with our free worksheets!

To ascertain whether a pair of ratios forms a proportion or not, cross multiply and simplify the fractions. If the obtained products are equal, the ratios form a proportion.

Determine the ratios between the x and y values for each table. If all ratios obtained across the table are equal, then the values are proportional.

Packed with sets of four numbers, these printable worksheets requires 6th grade and 7th grade students to form two equivalent sets of ratios and create a proportion.

Observe the coordinates on each graph to determine if they are proportional. The coordinates are in proportion if the graph is a straight line and passes through the origin.

Trying to form a proportion? You could use any of the four numbers from the given set of five numbers and set up two equal ratios to form a proportion.

Plot the x and y coordinates on the graphs provided. Draw a graph through the points to ascertain whether x and y values are in proportional relationship.

Test the skills of 7th grade and 8th grade students with these printable worksheets! Observe the proportional graphs based on real-life scenarios and answer the word problems.

Inculcate the concept of proportion with these pdf worksheets. Create a proportion by utilizing the cross product method to form two sets of equal ratios.

Access this assortment of proportion worksheets to find the constant of proportionality for the graphs, linear equations, tables and a lot more!

This batch of proportion worksheets includes multi-level exercises like solving the proportions involving integers, decimals, algebraic expressions and a lot more!

Employ this series of worksheets to determine the unit rate of a graph, expressing phrases in rates and unit rates, solve well-researched word problems and much more!

How to solve proportions?

Solving proportional equations is fairly trivial, if you know the basic equation transformation laws - multiplying and dividing both sides by the same number is all that is required. Of course, with the help of our proportion calculator all the work is done for you.

Example calculation

Say you have the proportion 4/5 = 12/x and need to find x. To solve for x, you need to first multiply both sides by x, resulting in x · 4/5 = 12. Then you divide both sides by 4/5, getting x = 12 / (4 / 5) = 12 / 4 * 5 = 3 * 5 = 15. Therefore, 4 is to 5 as 12 is to 15.

Business mathematics

The blog contains different types of business mathematics concepts. It describes the concepts with formulas and example problems. This information is very very useful in lot of competitive exams.

Ratio and Proportions problems

Ratio and Proportions problems

1.If a:b =5:9 and b:c=4:7 Find a:b:c?

Sol: a:b=5:9 and b:c=4:7=4*9/4:9*4/9=9:63/9

2.Find the fourth proportion to 4,9,12

Sol: d is the fourth proportion to a,b,c

3.Find third proportion to 16,36

Sol: If a:b=b:c then c is the third proportion to a,b

4.Find mean proportion between 0.08 and 0.18

Sol: mean proportion between a and b=square root of ab
mean proportion =square root of 0.08*0.18=0.12

5.If a:b=2:3 b:c=4:5, c:d=6:7 then a:b:c:d is

Sol: a:b=2:3 and b:c=4:5=4*3/4:5*3/4=3:15/4

Sol: let 2A=3B=4C=k then
A=k/2, B=k/3, C=k/4

7.15% of x=20% of y then x:y is

Sol: let a/3=b/4=c/7=k

9.Rs 3650 is divided among 4 engineers, 3 MBA’s and 5 CA’s
such that 3 CA’s get as much as 2 MBA’s and 3 Eng’s as
much as 2 CA’s .Find the share of an MBA.

Sol: 4E+3M+5C=3650
3C=2M, that is M=1.5C
3E=2C that is E=.66 C
Then, (4*0.66C)+(3*1.5C)+5C=3650
M=1.5 and C=450.

1.Three containers A,B and C are having mixtures of milk and
water in the ratio of 1:5 and 3:5 and 5:7 respectively. If
the capacities of the containers are in the ratio of all the
three containers are in the ratio 5:4:5, find the ratio of
milk to water, if the mixtures of all the three containers
are mixed together.

Sol: Assume that there are 500,400 and 500 liters respectively
in the 3 containers.
Then ,we have, 83.33, 150 and 208.33 liters of milk in each of
the three containers.
Thus, the total milk is 441.66 liters. Hence, the amount of
water in the mixture is 1400-441.66=958.33liters.
Hence, the ratio of milk to water is
441.66:958.33 => 53:115(using division by .3333)
The calculation thought process should be
Dividing by 25 => 53:115.

2.A certain number of one rupee,fifty parse and twenty five
paise coins are in the ratio of 2:5:3:4, add up to Rs 210.
How many 50 paise coins were there?

Sol: the ratio of 2.5:3:4 can be written as 5:6:8
let us assume that there are 5 one rupee coins,6 fifty
paise coins and 8 twenty-five paise coins in all.
their value=(5*1)+(6*.50)+(8*.25)=5+3+2=Rs 10
If the total is Rs 10,number of 50 paise coins are 6.
if the total is Rs 210, number of 50 paise coins would be

3.The incomes of A and B are in the ratio of 4:3 and their
expenditure are in the ratio of 2:1 . if each one saves
Rs 1000,what are their incomes?

Sol: Ratio of incomes of A and B=4:3
Ratio of expenditures of A and B=2:1
Amount of money saved by A=Amount of money saved by B=Rs 1000
let the incomes of A and B be 4x and 3x respectively
let the expense of A and B be 2y and 1yrespectively
Amount of money saved by A=(income-expenditure)=4x-2y=Rs 1000
Amount of money saved by B=3x-y=Rs 1000
this can be even written as 6x-2y=Rs 2000
now solve 1 and 3 to get
x=Rs 500
therefore income of A=4x=4*500=Rs 2000
income of B=3x=3*500=Rs 1500

4.A sum of Rs 1162 is divided among A,B and C. Such that 4
times A's share share is equal to 5 times B's share and 7
times C's share . What is the share of C?

Sol: 4 times of A's share =5 times of B's share=7 times of
C's share=1
therefore , the ratio of their share =1/4:1/5:1/7
LCM of 4,5,7=140
therefore, ¼:1/5:1/7=35:28:20
the ratio now can be written as 35:28:20
therefore C's share=(20/83)*1162=20*14=Rs 280.

5.The ratio of the present ages of saritha and her mother is
2:9, mother's age at the time of saritha's birth was 28 years,
what is saritha's present age?

Sol: ratio of ages of saritha and her mother =2:9
let the present age of saritha be 2x years.
then the mother's present age would be 9x years
Difference in their ages =28 years
9x-2x=28 years
therefore saritha's age =2*4=8 years

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  • Rates (4-2)
  • Rates (4-2) Videos
  • Identifying and Writing Proportions (4-3)
  • Solving Proportions (4-4)
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Identifying and Writing Proportions (4-3)

Identifying and Writing Proportions

Equivalent Ratios - Two or more ratios that simplify to same comparative ratio.

Proportion - An equation beginning with two rations that are equivalent are called proportion.

A proportion is simply a statement that two ratios are equal. It can be written in two ways: as two equal fractions a/b = c/d or using a colon, a:b = c:d. The following proportion is read as "twenty is to twenty-five as four is to five."

Progress and Info

The impact of the COVID-19 pandemic on schooling is a ‘generational catastrophe’. Before the pandemic, progress made was already slow and insufficient to reach the SDG education targets. School closures brought by the pandemic have had devastating consequences for children’s learning and wellbeing. Hundreds of millions of children and youth are falling behind in their learning, which will have long-term impacts. One year into the COVID-19 crisis, 2 in 3 students worldwide are still affected by full or partial school closures. The most vulnerable children and those unable to access remote learning are at an increased risk of never returning to school, and even being forced into child marriage or child labor.

It is estimated that an additional 101 million children and youth (from grades 1 to 9) fell below the minimum reading proficiency level due to COVID-19 in 2020, which wiped out the education gains achieved over the last 20 years. Recovery could occur by 2024, but only if exceptional efforts are devoted to the task through remedial and catch-up strategies.

Just before the pandemic struck, 53% of young people were completing secondary school globally, but only 29% in sub-Saharan Africa. Depending on the duration of school closures, which is causing learning losses and affecting the motivation to be in school, and the extent to which poverty might increase, which add to the obstacles faced by disadvantaged children, the growth in school completion rates may slow down or even reverse.

Pre-COVID-19 data from 76 countries and territories (mostly low- and middle-income) for the period 2012-2020, indicate that around 7 in 10 children aged 3 and 4 are developmentally on track, with no significant differences by child’s sex. However, many young children are unable to attend early childhood education due to the pandemic and are therefore now entirely reliant on their caregivers for nurturing care. Unsafe conditions, negative interactions with caregivers and lack of educational opportunities during the early years can lead to irreversible outcomes, affecting a child’s potential for the remainder of his/her life.

The participation rate in organized learning one year before the official primary entry age rose steadily in the years before the COVID-19 outbreak, from 65% in 2010 to 73% in 2019, but with considerable variation between countries ranging from 12% to nearly 100%. Gender parity has been achieved in every region. This progress over the past years is threatened since 2020, as early education facilities and primary schools closed in most countries, preventing or limiting access to education, especially for children from low- and middle-income countries.

Disparities in access to education and learning outcomes remain persistent across a range of education indicators. For example, there were still only 92 literate women aged 15 years or older for every 100 literate men of the same age in 2019. Almost half of countries with recent data did not meet gender parity in primary completion, and only a handful of countries demonstrate parity in tertiary enrolment ratios. Disparities by location (urban vs rural) and household wealth are typically more extreme, with a respective one third and one sixth of countries meeting parity in primary completion, and no countries with recent data reaching parity in tertiary attendance. The COVID-19 pandemic is expected to lead to a reversal of recent progress towards equity. With the shift to remote learning, those from the poorest households and other vulnerable groups are less equipped to participate and more likely to drop out permanently or for extended periods.

Based on data between 2017 and 2019, globally, more than a fifth of primary schools do not have access to basic drinking water and more than a third do not have basic handwashing facilities. Across the LDCs, more than two thirds of primary schools do not have access to electricity. Availability of internet and computers for pedagogical purposes in schools is even lower.

ODA for scholarships amounted to $1.7 billion in 2019, up from $1.3 billion in 2017. France, Japan, EU Institutions, Saudi Arabia and Turkey accounted for 55% of this total.

In 2019, 81% of primary school teachers are trained but the proportion is lower in sub-Saharan Africa (65%) and Southern Asia (74%). With the unprecedented lockdown due to the COVID-19 pandemic, leading to total or partial school closures in most countries, the teaching workforce was severely affected.

Source: Advance unedited copy of 2021 report of the Secretary-General on Progress towards the Sustainable Development Goals

At the end of 2019, millions of children and young people were still out of school, and more than half of those in school were not meeting minimum proficiency standards in reading and numeracy. The closure of schools to slow the spread of COVID-19 is having an adverse impact on learning outcomes and the social and behavioural development of children and young people. It has affected more than 90 per cent of the world’s student population, 1.5 billion children and young people. Although remote learning is provided to many students, children and young people in vulnerable and disadvantaged communities, such as those living in remote areas, extreme poverty, fragile states and refugee camps, do not have the same access thereto. The digital divide will widen existing gaps in equality with regard to education.

In 74 countries with comparable data for the 2011–2019 period, around 7 in 10 children 3 and 4 years of age were on track developmentally in at least three of the following domains: literacy-numeracy, physical development, social-emotional development and learning.

Participation in organized learning one year before the official primary age of entry grew steadily, from 62 per cent in 2010 to 67 per cent in 2018. However, variation among countries is still wide, with values ranging from 9 to nearly 100 per cent.

The primary school completion rate reached 84 per cent in 2018, up from 70 per cent in 2000. Under current trends, the rate is expected to reach 89 per cent globally by 2030. In 2018, 258 million children, adolescents and young people 6 to 17 years of age were still out of school, representing 17 per cent of the global population of that age group. Parity between children or adolescents from the richest and poorest quintiles of the population was achieved in 25 per cent of countries for primary education, 21 per cent of countries for lower secondary education and only 1 per cent of countries for upper secondary education.

In 2018, some 773 million adults, two thirds of them women, remained illiterate in terms of reading and writing skills. The global adult literacy rate, for the population 15 years of age and older, was 86 per cent in 2018, while the youth literacy rate, for the population 15 to 24 years of age, was 92 per cent. Southern Asia is home to nearly half of the global illiterate population, and sub-Saharan Africa is home to one quarter thereof.

In 2019, less than one half of primary and lower secondary schools in subSaharan Africa had access to electricity, the Internet, computers and basic handwashing facilities, key basic services and facilities necessary to ensure a safe and effective learning environment for all students.

ODA for scholarships amounted to $1.6 billion in 2018, up from $1.3 billion in 2017.

Based on data from 129 countries, the percentage of primary school teachers receiving the minimum pedagogical training according to national standards throughout the world has stagnated at 85 per cent since 2015. The percentage is lowest in sub-Saharan Africa (64 per cent) and Southern Asia (72 per cent).

Source: Progress towards the Sustainable Development Goals, Report of the Secretary-General,

Despite the considerable progress on education access and participation over the past years, 262 million children and youth aged 6 to 17 were still out of school in 2017, and more than half of children and adolescents are not meeting minimum proficiency standards in reading and mathematics. Rapid technological changes present opportunities and challenges, but the learning environment, the capacities of teachers and the quality of education have not kept pace. Refocused efforts are needed to improve learning outcomes for the full life cycle, especially for women, girls and marginalized people in vulnerable settings.

  • In 72 countries with recent data, approximately 7 in 10 children aged 3 and 4 were developmentally on track in at least three of the following domains: literacy-numeracy, physical development, social-emotional development and learning.
  • In 2015, an estimated 617 million children and adolescents of primary and lower secondary school age worldwide – more than 50 per cent – were not achieving minimum proficiency levels in reading and mathematics. Of these, about two thirds were attending school but were not learning in the classroom, or dropped out school.
  • Some 750 million adults – two thirds of them women – remained illiterate in 2016. Half of the global illiterate population lives in South Asia, and a quarter live in sub-Saharan Africa.
  • Many developing countries still lack basic infrastructure and facilities to provide effective learning environments. Sub-Saharan Africa faces the biggest challenges: at the primary and lower secondary levels, less than half of schools have access to electricity, the Internet, computers and basic drinking water.
  • ODA for scholarships amounted to $1.3 billion in 2017. Australia, France, Japan, the United Kingdom of Great Britain and Northern Ireland and institutions of the European Union accounted for nearly two thirds of this total.
  • Globally, there has been little progress in the percentage of primary school teachers who are trained: it has been stagnating at about 85 per cent since 2015. The proportion is lowest in sub-Saharan Africa (64 per cent).

More than half of children and adolescents worldwide are not meeting minimum proficiency standards in reading and mathematics. Refocused efforts are needed to improve the quality of education. Disparities in education along the lines of gender, urban-rural location and other dimensions still run deep, and more investments in education infrastructure are required, particularly in LDCs.

  • At the global level, the participation rate in early childhood and primary education was 70 per cent in 2016, up from 63 per cent in 2010. The lowest rates are found in sub-Saharan Africa (41 per cent) and Northern Africa and Western Asia (52 per cent).
  • An estimated 617 million children and adolescents of primary and lower secondary school age worldwide—58 per cent of that age group—are not achieving minimum proficiency in reading and mathematics.
  • In 2016, an estimated 85 per cent of primary school teachers worldwide were trained the proportion was only 71 per cent for Southern Asia and 61 per cent for sub-Saharan Africa
  • In 2016, only 34 per cent of primary schools in LDCs had electricity and less than 40 per cent were equipped with basic handwashing facilities.

Achieving inclusive and equitable quality education for all will require increasing efforts, especially in sub-Saharan Africa and Southern Asia and for vulnerable populations, including persons with disabilities, indigenous people, refugee children and poor children in rural areas.

  • In 2014, about 2 in 3 children worldwide participated in pre-primary or primary education in the year prior to official entry age for primary school. However, in the least developed countries, the ratio was only 4 in 10.
  • Despite considerable gains in education enrolment over the past 15 years, worldwide, the adjusted net enrolment rates were 91 per cent for primary education, 84 per cent for lower secondary education and 63 per cent for upper secondary education in 2014. About 263 million children and youth were out of school, including 61 million children of primary school age. Sub-Saharan Africa and Southern Asia account for over 70 per cent of the global out-ofschool population in primary and secondary education.
  • Even though more children than ever are going to school, many do not acquire basic skills in reading and mathematics. Recent learning assessment studies show that in 9 of 24 sub-Saharan African countries and 6 of 15 Latin American countries with data, fewer than half of the students at the end of primary education had attained minimum proficiency levels in mathematics. In 6 of 24 sub-Saharan African countries with data, fewer than half of the students who finished their primary schooling had attained minimum proficiency levels in reading.
  • Equity issues constitute a major challenge in education according to a recent assessment. In all countries with data, children from the richest 20 per cent of households achieved greater proficiency in reading at the end of their primary and lower secondary education than children from the poorest 20 per cent of households. In most countries with data, urban children scored higher in reading than rural children.
  • The lack of trained teachers and the poor condition of schools in many parts of the world are jeopardizing prospects for quality education for all. Sub -Saharan Africa has a relatively low percentage of trained teachers in pre -primary, primary and secondary education (44 per cent, 74 per cent and 55 per cent, respectively). Moreover, the majority of schools in the region do not have access to electricity or potable water.
  • On the basis of data from 65 developing countries, the average percentage of schools with access to computers and the Internet for teaching purposes is above 60 per cent in both primary and secondary education. However, the share is less than 40 per cent in more than half of sub-Saharan countries with data.
  • Official development assistance (ODA) for scholarships amounted to $1 billion in 2015, a decrease from $1.2 billion in 2014. Australia, France and the United Kingdom of Great Britain and Northern Ireland were the largest contributors.

Source: Report of the Secretary-General, "Progress towards the Sustainable Development Goals", E/2017/66

  • Despite progress, the world failed to meet the Millennium Development Goal of achieving universal primary education by 2015. In 2013, the latest year for which data are available, 59 million children of primary-school age were out of school. Estimates show that, among those 59 million children, 1 in 5 of those children had dropped out and recent trends suggest that 2 in 5 of out-of-school children will never set foot in a classroom. The Sustainable Development Goals clearly recognize that this gap must be closed, even as the international community more explicitly addresses the challenges of quality and equity.
  • Measuring learning achievement, starting in the early grades, will help to identify where schools are failing to meet their commitments to children and to formulate appropriate remedial action. For example, data for 2013 from 15 Latin American countries show that in six countries, fewer than 50 per cent of third graders had a minimum level of proficiency in mathematics in three countries, fewer than half were proficient in reading.
  • At the end of primary school, children should be able to read and write and to understand and use basic concepts in mathematics. However, in 2014, between 40 per cent and 90 per cent of children failed to achieve even minimum levels of proficiency in reading, in 10 African countries, and in nine of those countries, between 40 per cent and 90 per cent of children failed to achieve minimum levels of proficiency in mathematics.
  • The end of lower secondary education often coincides with the end of compulsory education. By this stage, young people should be able to master subject-related knowledge and skills and possess personal and social skills. Data from 38 countries in the developed regions show that, in the majority of those countries, at least 75 per cent of young people achieved at least a minimum proficiency in reading and/or mathematics the same was true for only 5 out of 22 countries, in developing regions, for which data were available.
  • Completion rates for both primary and lower secondary education has been rising steadily since 2000. Completion rates for primary education in both developed and developing regions exceeded 90 per cent in 2013. At the lower secondary level, the gap between developed and developing regions has narrowed substantially, but still stood at nearly 20 percentage points in 2013 (91 per cent for developed regions and 72 per cent for developing regions).
  • Quality early education provides children with basic cognitive and language skills and fosters emotional development. In the majority of the 58 countries with available data for the period 2009-2015, more than half of children between the ages of 3 and 4 were developmentally on track in at least three of the following domains: literacy, numeracy, physical development, social-emotional development and learning.
  • Goal 4 strongly supports the reduction of persistent disparities. Worldwide, in 2013, two thirds of the 757 million adults (aged 15 and over) who were unable to read and write were women. Globally, in 2013, 1 in 10 girls were out of school, compared to 1 in 12 boys. Children from the poorest 20 per cent of households are nearly four times more likely to be out of school than their richest peers. Out-of-school rates are also higher in rural areas and among children from households headed by someone with less than a primary education.
  • To fulfil the promise of universal primary and secondary education, new primary school teachers are needed, with current estimates showing a need for nearly 26 million of them by 2030. Africa faces the greatest challenges in this regard, with nearly 7 in 10 countries experiencing acute shortages of trained primary school teachers. In 2013, only 71 per cent of teachers in sub-Saharan Africa and 84 per cent in Northern Africa were trained in accordance with national standards.
  • Official development assistance for educational scholarships amounted to around $1.1 billion annually from 2011 to 2013. It totalled $1.2 billion in 2014, with Australia, France and Japan being the largest contributors.

Source: Report of the Secretary-General, "Progress towards the Sustainable Development Goals", E/2016/75

Proportion Calculator

The calculator uses cross multiplication to convert proportions into equations which
are then solved using ordinary equation solving methods.
Be sure to enter something in each input box before clicking
solve. Use the following as a guide:


Any lowercase letter may be used as a variable.


Exponents are supported on variables using the ^ (caret) symbol. For example, to express x 2 , enter x^2.
Note: exponents must be positive integers, no negatives, decimals, or variables. Exponents may not be placed
on numbers, brackets, or parentheses.

Parentheses and Brackets

Parentheses ( ) and brackets [ ] may be used to group terms as in a standard equation or expression.

Multiplication, Addition, and Subtraction

For addition and subtraction, use the standard + and – symbols respectively. For multiplication, use the *
symbol. A * symbol is not necessiary when multiplying a number by a variable. For instance: 2 * x can also
be entered as 2x. Similarly, 2 * (x + 5) can also be entered as 2(x + 5) 2x * (5) can be entered as 2x(5).
The * is also optional when multiplying parentheses, example: (x + 1)(x – 1).

Order of Operations

The calculator follows the standard order of operations taught by most algebra books – Parentheses, Exponents,
Multiplication and Division, Addition and Subtraction. The only exception is that division is not supported
attempts to use the / symbol will result in an error.

Division, Square Root, Radicals, Fractions

The above features are not supported.

Special Note

If either side of the proportion has a numerator and denominator that share a common factor with a variable,
the calculator will report an erroneous solution. Example: 1/2 = x/x will cause the calculator to report
0 as a solution, even though there is no solution.


A proportionality constant is a number that is used to convert a measurement in one system to the equivalent measurement in another system. For instance, people who are familiar with the traditional system of units used in the United States (pounds, feet, inches, etc.) may need to find out the metric equivalent for these measures in grams and meters. To make these calculations, they would need some proportionality constants.

One way to write a formula showing how to use a proportionality constant K is:

For example, people may know that they have 100 eggs and want to know how many dozen eggs they have. The proportionality constant K is then 1 dozen/ 12 eggs.


Three cups of water weigh 12 ounces. How heavy is 10 cups of water?

This means 10 cups will weigh 40 ounces.

If five boys can eat 16 slices of pizza, then how many slices can 20 boys eat?

Boys Pizza What was done
5 16
20 64 multiplied top row by 4

This means 20 boys can eat 64 slices of pizza.

Martin can read 45 pages in 30 minutes. At this rate, how long will it take him to read a 300-page book?

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