Fractions

What are Fractions? – Definitions and Properties of Fractions

A fraction is a number that represents a part of a whole. The numerator is the top number and the denominator is the bottom number. The numerator tells how many parts are being represented and the denominator tells what size the parts are.

There are three properties of fractions that are always true.

• The first property is that the sum of the numerators is always equal to the sum of the denominators.
• The second property is that the product of the numerators is always equal to the product of the denominators.
• The third property is that the quotient of the numerators is always equal to the quotient of the denominators.

What is a Fraction?

A fraction is a number that is written as a ratio of two integers. The numerator is the number on top of the fraction and the denominator is the number on the bottom of the fraction. A fraction can also be written as a decimal or a percentage.

Commutative Property of Addition

The commutative property of addition states that when two numbers are added together, the order of the numbers doesn’t matter. This means that 5 + 4 = 4 + 5 and that -3 + 7 = 7 + -3.

Associative Property

The associative property is a mathematical property that states that when two or more items are combined, the order of the items does not affect the result. The associative property can be represented by the equation a + (b + c) = (a + b) + c.

Distributive Property

If a and b are numbers and a + b = c, then a = c – b.

For example, if 4 + 5 = 9, then 4 = 9 – 5.

Equivalent Fraction

An equivalent fraction is a fraction that has the same value as another fraction, but is in a different form. For example, the fractions ¾ and 3/4 are equivalent, because they both represent the value of three quarters.

Facts About the Equivalent fractions

Equivalent fractions are fractions that have the same value, regardless of the size of the numerator and denominator. For example, the fractions 1/2 and 2/4 are equivalent, because they both represent the value of 1/2.

How to Simplify the Equivalent Fractions?

There are a few steps in simplifying fractions. In general, fractions can be simplified by dividing both the numerator and the denominator by the same number. This number can be any number other than zero.

For example, the fraction
can be simplified by dividing both the numerator and the denominator by 2. This will result in the fraction

Similarly, the fraction
can be simplified by dividing both the numerator and the denominator by 3. This will result in the fraction

Finally, the fraction
can be simplified by dividing both the numerator and the denominator by 5. This will result in the fraction

How to Check Two Fractions are Equivalent Fraction

• To check if two fractions are equivalent, cross-multiply the numerators and denominators. If the cross-multiplication results in a product of 1, then the fractions are equivalent.
• For example, to check if 3/4 and 2/3 are equivalent fractions, cross-multiply 3 and 4 with 2 and 3. The cross-multiplication results in a product of 12, which is not equal to 1. Therefore, 3/4 and 2/3 are not equivalent fractions.

Addition and Subtraction

• Addition and subtraction are two of the most basic operations in mathematics. They are used to calculate the result of combining or separating two numbers.
• Addition is the process of combining two numbers to get a single result. The numbers are combined by adding their values together. For example, if you want to find the total cost of three items that cost $2.50, $5.00, and $7.50, you would add the values of the three items together to get a total cost of $19.00.
• Subtraction is the process of separating two numbers to get a single result. The numbers are separated by subtracting their values together. For example, if you want to find out how much money you have left after spending $9.00, you would subtract the value of $9.00 from your total amount of money to get a result of $0.00.

Converting Between Decimals and Fractions

• To convert a decimal to a fraction, divide the decimal number by 1.000.
• To convert a fraction to a decimal, divide the numerator by the denominator.