Rational and Irrational Numbers: Background You’ll Need 2

Recognize the numerator and denominator of a fraction

Fractions are everywhere! Whether you’re splitting a pizza with friends or measuring ingredients for a recipe, understanding fractions is a life skill.

Let’s look at some fractions.  

Carlos and Idris love pizza. On Monday night, they share a pizza equally. How much of the pizza does each one get? Are you thinking that each boy gets half of the pizza? That’s right. There is one whole pizza, evenly divided into two parts, so each boy gets one of the two equal parts.

In math, we write [latex]\Large{\frac{1}{2}}[/latex] to mean one out of two parts.

An image of a round pizza sliced vertically down the center, creating two equal pieces. Each piece is labeled as one half.

 

On Tuesday, Carlos and Idris share a pizza with their parents, Liam and Rose, with each person getting an equal amount of the whole pizza. How much of the pizza does each person get? There is one whole pizza, divided evenly into four equal parts. Each person has one of the four equal parts, so each has [latex]\Large{\frac{1}{4}}[/latex] of the pizza.

An image of a round pizza sliced vertically and horizontally, creating four equal pieces. Each piece is labeled as one fourth.

 

On Wednesday, the family invites some friends over for a pizza dinner. There are a total of [latex]12[/latex] people. If they share the pizza equally, each person would get [latex]\Large{\frac{1}{12}}[/latex] of the pizza.

An image of a round pizza sliced into twelve equal wedges. Each piece is labeled as one twelfth.

fractions

A fraction represents a part of a whole.  A fraction is written [latex]\Large{\frac{a}{b}}[/latex], where [latex]a[/latex] and [latex]b[/latex] are integers and [latex]b\ne 0[/latex]. In a fraction, [latex]a[/latex] is called the numerator and [latex]b[/latex] is called the denominator.

Numerator

The numerator tells us how many parts of the whole we are considering. For example, if you have a fraction [latex]\frac{3}{4}[/latex], the numerator is [latex]3[/latex]. This means you’re considering [latex]3[/latex] parts out of a total of [latex]4[/latex].

Imagine you have [latex]4[/latex] quarters, and you give [latex]3[/latex] to a friend; you’ve essentially given them [latex]\frac{3}{4}[/latex] of your quarters.

Denominator

The denominator is the total number of equal parts that make up the whole. In the fraction [latex]\frac{3}{4}[/latex] the denominator is [latex]4[/latex]. It’s like saying the whole is divided into [latex]4[/latex] equal parts.

 If you have a chocolate bar divided into [latex]4[/latex] pieces, the denominator tells you that you started with [latex]4[/latex] pieces.

Recognizing the numerator and denominator in a fraction helps you understand how much of a whole you’re dealing with. It’s the first step in performing operations like addition, subtraction, multiplication, and division with fractions. So the next time you see a fraction, you’ll know exactly what each number represents!