{"id":8237,"date":"2023-09-29T14:20:08","date_gmt":"2023-09-29T14:20:08","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&p=8237"},"modified":"2025-08-28T03:49:02","modified_gmt":"2025-08-28T03:49:02","slug":"rational-and-irrational-numbers-background-youll-need-2","status":"web-only","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/rational-and-irrational-numbers-background-youll-need-2\/","title":{"raw":"Rational and Irrational Numbers: Background You\u2019ll Need 2","rendered":"Rational and Irrational Numbers: Background You\u2019ll Need 2"},"content":{"raw":"
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Recognize the numerator and denominator of a fraction<\/span><\/p>\r\n<\/section>\r\n

Fractions are everywhere! Whether you're splitting a pizza with friends or measuring ingredients for a recipe, understanding fractions is a life skill.<\/p>\r\n

Let's look at some fractions.\u00a0\u00a0<\/p>\r\n

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\u2019s right. There is one whole pizza, evenly divided into two parts, so each boy gets one of the two equal parts.<\/p>\r\n

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

\r\n[caption id=\"\" align=\"aligncenter\" width=\"211\"]\"An Figure 1. This pizza is cut into two halves[\/caption]\r\n<\/center>\r\n

 <\/p>\r\n

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.<\/p>\r\n

\r\n[caption id=\"\" align=\"aligncenter\" width=\"211\"]\"An Figure 2. The pizza is cut into quarters, each piece is 1\/4 of the whole pizza[\/caption]\r\n<\/center>\r\n

 <\/p>\r\n

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.<\/p>\r\n

\r\n[caption id=\"\" align=\"aligncenter\" width=\"212\"]\"An Figure 3. The pizza is cut into twelve pieces, each piece is 1\/12 of the whole pizza[\/caption]\r\n<\/center>\r\n
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fractions<\/h3>\r\n

A fraction<\/strong> represents a part of a whole.\u00a0 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.<\/p>\r\n<\/div>\r\n<\/section>\r\n

Numerator<\/h2>\r\n

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].<\/p>\r\n

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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]\u00a0of your quarters.<\/p>\r\n<\/section>\r\n

Denominator<\/h2>\r\n

The denominator is the total number of equal parts that make up the whole. In the fraction [latex]\\frac{3}{4}[\/latex]\u00a0the denominator is [latex]4[\/latex]. It's like saying the whole is divided into [latex]4[\/latex] equal parts.<\/p>\r\n

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\u00a0If you have a chocolate bar divided into [latex]4[\/latex] pieces, the denominator tells you that you started with [latex]4[\/latex] pieces.<\/p>\r\n<\/section>\r\n

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!<\/p>\r\n

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[ohm2_question hide_question_numbers=1]13824[\/ohm2_question]<\/p>\r\n<\/section>","rendered":"

\n

Recognize the numerator and denominator of a fraction<\/span><\/p>\n<\/section>\n

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

Let’s look at some fractions.\u00a0\u00a0<\/p>\n

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\u2019s right. There is one whole pizza, evenly divided into two parts, so each boy gets one of the two equal parts.<\/p>\n

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

\n
\"An
Figure 1. This pizza is cut into two halves<\/figcaption><\/figure>\n<\/div>\n

 <\/p>\n

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.<\/p>\n

\n
\"An
Figure 2. The pizza is cut into quarters, each piece is 1\/4 of the whole pizza<\/figcaption><\/figure>\n<\/div>\n

 <\/p>\n

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.<\/p>\n

\n
\"An
Figure 3. The pizza is cut into twelve pieces, each piece is 1\/12 of the whole pizza<\/figcaption><\/figure>\n<\/div>\n
\n
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fractions<\/h3>\n

A fraction<\/strong> represents a part of a whole.\u00a0 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.<\/p>\n<\/div>\n<\/section>\n

Numerator<\/h2>\n

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].<\/p>\n

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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]\u00a0of your quarters.<\/p>\n<\/section>\n

Denominator<\/h2>\n

The denominator is the total number of equal parts that make up the whole. In the fraction [latex]\\frac{3}{4}[\/latex]\u00a0the denominator is [latex]4[\/latex]. It’s like saying the whole is divided into [latex]4[\/latex] equal parts.<\/p>\n

\n

\u00a0If you have a chocolate bar divided into [latex]4[\/latex] pieces, the denominator tells you that you started with [latex]4[\/latex] pieces.<\/p>\n<\/section>\n

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!<\/p>\n

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