What are equal groups?

Two groups are called equal groups if they have the same number of objects. So, in equal groups, equal number of objects or things are grouped.

Jack has a total of $36.00, and each app costs $2.00. Using the formula, the product and group size can be checked off, this means that the number of groups is unknown.

Since the size of the groups is moved to the other side of the equation, the operation used to identify the number of groups is division.

{eq}36 \div 2 = 18 {/eq}

Therefore, Jack will be able to purchase 18 apps.

Sample 2:

At the farmer's market, a carton of eggs has 6 white large eggs.

How many eggs are there if Ginny purchases 5 cartons?

In this sample, two factors are identified: The number of cartons purchased, also known as the number of groups; and the number of eggs in each carton, also known as the size of the group. Using the equation, we can check off, number of groups and size of groups, leaving the product as the unknown.

This means that the operation used is multiplication.

5 X 6 = 30

Therefore, Ginny will have 30 eggs in total.

Sample 3:

Kenneth can finish reading one chapter book in two weeks. Assuming he keeps this same pace, how many books will he finish reading in one year?

In this sample, the number of groups needs to be identified. As we can see that the size of the group has been provided by stating "two weeks", so the digit 2. The product or total was provided by stating "one year", so the digit is 52, as there are 52 weeks in a year. Using the equations, the only factor not checked off is the number of groups.

Since we need to move to the other side of the equation, the operation used will be division.

{eq}52 \div 2 = 28 {/eq}

Therefore, Kenneth will read 26 chapter books in one year.

Equal groups is a way of solving word problems that allow for visualization of the items in the problem, uses multiplication or division to solve the problems, and all groups must have the same size. There are three types of equal group math problems:

1) Unknown products: The number of groups and the group size is provided, but the product is unknown. Multiply number group and group size to find the product.

Usually, the uniform groups concept is made through word problems where students will also understand problem-solving skills. These problems have several such, even groups, and your work is to find out the missing number. Let us understand this concept of equal groups math with the help of an example in detail.

Suppose you have 21 balls, and you need to put them inside 3 bags so that each bag has an equal amount. How will you solve this problem?

The problem is of division among three bags. Each bag will get 7 balls with the solution as 21 ÷ 3 = 7.

In the above diagram, you can see 3 bags get 7 balls in each.

When the concept of uniform groups comes into maths, your problem becomes quite easy and simpler. It is because you are given total items and groups. Your only work is to distribute. The problems can be either solved through division or multiplication. These two basic operations are used because both division and multiplication deal with this concept of equal division.

When we divide, the name clearly defines that we will separate total items into equal parts from identical groups. Each group will be having the same number of items. But how will you bring uniformity in the groups? The concept is based upon our visualisation.

Suppose we have a term 6 ÷ 2 = 3. It means there are a total of 6 items, and we need to make 2 groups having the same number of items. Here the result is 3. There will be two groups having three items.

In the above diagram, we have created two groups with three parallelograms in each of them.

Suppose now the question is 6 ÷ 3. Here, we have 6 items, and we need to divide these items into three groups as in the below diagram.

We get,

In the above diagram, there are three groups, each having 2 parallelograms in them.

The name clearly says equal groups meaning. But in the case of equal groups multiplication, we will be given groups and items in each of them. Our task is to find the total number of items added.

Consider the below example:

We have 4 even groups with 3 items in each of them. How will you find the total number of items you have?

In multiplication. 4 x 3 will give your answer, as in the below diagram.

In the above picture, there are 4 groups with three parallelograms in each. Thus the total items will be 12, which is equal to 4 x 3.

Adding equal groups contains two different types of identical groups. One group has an even number of items, and the second one has an odd number of items. Let us study each of them in detail one by one.

Even items:

Suppose we have 4 groups with 2 capsules in each. We need to perform basic addition and find the total number of capsules we have, as in the below diagram.

In the above diagram, 4 groups have 2 capsules in each. Thus addition of all will be 2 + 2+ 2 + 2 = 8 capsules.

Odd Items:

Counting the total of the items in odd-even groups having odd items is as follows.

In the above diagram, there are three groups with 5 telephones in each. Thus the total telephones will be given by 5 + 5 + 5 = 15.

It is how we do counting equal groups and adding them to get a total number of items.