Adding and subtracting money are two of the most common money transactions. You would undoubtedly add money to find out your total store expenses, how much you owe somebody, or how much money you have in total. You would subtract money to find out how much change you owe, how much somebody owes you, or how much money you have left after you go shopping. The ability to add and subtract money is very important.

Adding money. First, we will practice counting money. Adding money is very similar to adding numbers. There is only one critical component that you need to remember. When adding money, you first need to add cents to each other, then add dollars. When you report your answer, you say both dollars and cents. Let’s practice a little.

At the grocery store, you are going to buy two things. You want a gallon of milk that will cost you $2.79. You also want a loaf of bread that costs $1.99. What will be your amount? To do this, you require to add two numbers. The task will look like this:

You would add the numbers together as you normally would, starting from the right column to the left. Don’t forget to carry your numbers with you when you need to. Add-on looks like this:

The most critical components to remember below are the alignment of your decimals and writing down a dollar sign ($) in front of your solution. Without the dollar, your answer is sure to be flagged as wrong.

Let’s try another addition problem. This time the task will be a little more complicated. At the grocery store, you’re going to buy a can of soup for $1.39, a head of lettuce for $1.69, a gallon of orange juice for $2.99, a pack of chicken for $5.95, and a frozen pizza for $7.89. What will be your total? Here’s what the task looks like:

To begin, add the quantities together (from right to left), adding numbers when necessary, for example:

Therefore, your correct answer is $19.91. Don’t neglect the dollar indicator as well as the decimal point! These two most important things will help you find the right solution.

Subtracting money. Subtracting money is very similar to adding money. You will solve the problem in the same way. Only you will subtract, not add. When you subtract money, you first subtract cents and then dollars (you move from right to left, similar to how we added). Sometimes, you will need to borrow to complete a subtraction problem.

Here’s an example problem: You spent $18.95 on a new set of jeans at the store. How much change will you get back if you pay the cashier with a $20 bill? The problem will certainly look like this (make sure the decimal multipliers are aligned!):

And here’s what the substruction (with borrowing) would look like:

Let’s try another example of the money subtraction problem. George spent $15.62 at the supermarket and $19.48 at the electronics store. He had $50 before he made the purchases. How much did he have left when he got home (assuming he didn’t buy something else)?

This is a 2 step task. Initially, you must add the two amounts he spent together. After that, you take that amount and also subtract it from where he should have started. Let’s solve the addition problem first:

Now we will take the answer from the addition and also subtract it from the $50, for example:

Therefore, George would come home with $14.90 after his shopping.

Fractions comprise a numerator and a denominator. Also, when two fractions have the same number in the denominator, it is identified as a common, or like, denominator. Adding fractions to each other when they have a common denominator is easy, as you can add all the numerators to each other! The new fraction will undoubtedly have the same original common denominator, so all you have to worry about is adding numbers above the line. The same applies to subtracting fractions that have common denominators. The task gets a little more complicated when the fractions don’t have the same common denominator, but still, they can be added or subtracted once the common denominator has been found.

Part 1

Adding Fractions With Common Denominators

1. Recognize the numerator and denominator. 

All fractions have two parts: the numerator, the number above the line, and the denominator, which is the number below the line. While the denominator tells you the number of components of the whole into which it is broken, the numerator tells you the number of elements of that whole.

* In the fraction 1/2, for example, the numerator is 1, the denominator is 2, and the fraction is one-half. 

Step 2

Identify the denominator. 

In case when two or more fractions have a common denominator, it means that they all have the same number in the denominator or that they all represent a whole that has been broken into the same number of parts. To summarize, fractions with a common denominator are elementary, and the resulting fraction will necessarily have the same common denominator as the original fractions. 

For example:

  • The fractions 4/5 and 3/5 have a common denominator of 5. 
  • The fractions 3/8, 5/8, and 17/8 have a common denominator of 8.

Step 3

Locate the numerators. 

To add fractions to each other when they have a common denominator, you sum up all the numerators and rewrite the sum over the original denominator.

  • In fractions 4/5 and 3/5, the numerators are 4 and 3.
  • In fractions 3/8, 5/8, and 17/8, the numerators are 3, 5, and 17.

Step 4

Add the numerators. 

  • In the example 4/5 + 3/5 add the numerators 4 + 3 = 7. 
  • In the example 3/8 + 5/8 + 17/8 add the numerators 3 + 5 + 17 = 25.

Step 5

Rewrite the fraction with the new numerator. 

Remember to use the same common denominator because the number of components the whole is divided into remains the same, and you’re just adding the number of individual elements.

  • Fractions 3/5 + 2/5 = 5/5 
  • Fractions 3/8 + 5/8 + 17/8 = 25/8

Step 6

Solve the fraction if needed. 

Often a fraction can be represented in a simpler form. This includes dividing it to get a number that is not a fraction or decimal. In example 5/5, this fraction can be easily rewritten because when the numerator and denominator are the same will equal 1.

Think of it like an apple that has been divided into three parts. If you eat all three pieces of the apple, you have eaten one whole apple.

  • Any fraction can be transformed from a fraction by dividing the numerator by the denominator. As a result, you will usually get a decimal number. For example, 5/8 can also be written as 5 ÷ 8, which is 0.625.

Step 7

Reduce the fraction if you can. 

A fraction is said to have the simplest form if both the numerator and denominator do not have any common factor by which they can be divided.

  • For example, in the 3/6 fraction, the numerator and denominator have a common factor of 3, meaning they can be divided by 3. Therefore, the fraction 3/6 can be taken as 3 ÷ 3/ 6 ÷ 3 = 1/2.

Step 8

Transform improper fractions to mixed numbers if needed. 

When a fraction has a numerator greater than the denominator, such as 25/8, it is said to be an improper fraction (conversely, when the numerator is less than the common denominator, it is a proper fraction). It can be modified to a mixed number, a number consisting of a digit and a proper fraction. To convert an improper fraction, such as 25/8, to a mixed number, you:

  • Divide the numerator of the improper fraction by its denominator to find out exactly how many whole numbers 8 are in 25, where the answer is 25 ÷ 8 = 3 (0.125).
  • Establish what’s left. If 8 x 3 = 24, then subtract that from the original numerator: 25 – 24 = 1, where the difference would be the new numerator.
  • Change the mixed number. The denominator will be the same as the original fraction, meaning 25/8 can be reformulated as 3 1/8.

Part 2 

Subtracting Fractions With Common Denominators

Step 1 

Find the numerators as well as denominators. 

For example, 12/26 – 4/26 – 1/26. In this example: 

  • The numerators are 12, 4, and 1. 
  • The common denominator is 26.

Step 2

Subtract the numerators.

As with addition, you don’t have to worry about doing anything with the denominator, so find the difference between the numerators: 

  • 12 – 4 – 1 = 7
  • Write the fraction with a new numerator: 12/26 – 4/26 – 1/26 = 7/26.

Step 3 

Reduce or solve the fraction if needed. 

Comparable to adding fractions, when you subtract fractions, you can still end up with: 

  • An improper fraction that can be modified to a mixed number 
  • A fraction that can be solved by division
  • A fraction that can be transformed into a simpler type by locating a common denominator 

Part 3

Locate Common Denominators. 

Step 1

Find the denominators.

Fractions do not always have the same denominators; to add or subtract those fractions, you must first locate a common one. To begin, find the denominators in the fractions you’re dealing with.

  • For example, in the formula 5/8 + 6/9, the denominators are 8 and 9.

Step 2 

Establish the least common multiple. 

Locate the least common multiple of both numbers to discover a common denominator. The smallest positive number would be a multiple of both initial numbers. To discover the least common multiple of 8 and 9, you should initially look through the multiples of each number: 

  • The multiples of 8 would be: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, 104, and so on.
  • The multiples of 9 would be: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, 108, and so on.
  • The least common multiple of numbers 8 and 9 is 72.

Step 3 

Multiply the fractions to find the least common multiple. 

Multiply each common denominator by the appropriate number to achieve the common denominator. Remember that what you do to the denominator must do to its numerator.

  • For the fraction 5/8, to find the common denominator of 72, you need to multiply 8 x 9. Therefore, you must multiply the numerator by 9, presenting you 5 x 9 = 45 
  • For the fraction 6/9, to find the common denominator of 72, you multiply 9 x 8. Therefore, you have to also multiply the numerator by 8, giving you 6 x 8 = 48 

Step 4 

Rewrite the fractions. 

A new fraction will have the common denominator as well as the product of the numerators multiplied by the same values: 

  • The fraction 5/8 ends up being 45/72, and the fraction 6/9 becomes 48/72
  • Because they now have a common denominator, you can add the fractions 45/72 + 48/72 = 93/72.
  • Don’t forget to reduce, solve, or transform improper fractions to mixed numbers when applicable and also necessary.