Learn on PengiBig Ideas Math, Course 2Chapter 2: Rational Numbers

Lesson 1: Rational Numbers

In this Grade 7 lesson from Big Ideas Math Course 2, students learn to define rational numbers as any number expressible as a ratio of two integers, and practice converting fractions and mixed numbers into terminating or repeating decimals using long division. Students also use a number line to compare and order rational numbers, including negative fractions, mixed numbers, and decimals. The lesson aligns with Florida Standards MAFS.7.NS.1.2b and MAFS.7.NS.1.2d.

Section 1

Decimal Form of a Rational Number

Property

A rational number is one that can be expressed as a quotient (or ratio) of two integers, where the denominator is not zero. The decimal representation of a rational number has one of two forms.

The decimal representation terminates, or ends.

The decimal representation repeats a pattern.

Section 2

Convert fractions to decimals

Property

To convert a fraction to a decimal, divide the numerator of the fraction by the denominator of the fraction. The fraction bar indicates division, so a fraction like $\frac{a}{b}$ can be written as $a \div b$ .

Examples

To write $\frac{3}{4}$ as a decimal, we divide 3 by 4. The calculation $3.00 \div 4$ gives us $0.75$ . So, $\frac{3}{4} = 0.75$ .

To convert the improper fraction $\frac{9}{5}$ to a decimal, we divide 9 by 5. The calculation $9.0 \div 5$ results in $1.8$ . So, $\frac{9}{5} = 1.8$ .

Section 3

Convert decimals to fractions

Property

To convert a terminating decimal to a fraction: $0.abc = \frac{abc}{1000}$ (denominator is power of 10 based on decimal places)

To convert a repeating decimal to a fraction: Let $x$ equal the decimal, multiply by appropriate power of 10 to align repeating parts, then subtract and solve for $x$

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Decimal Form of a Rational Number

Property

A rational number is one that can be expressed as a quotient (or ratio) of two integers, where the denominator is not zero. The decimal representation of a rational number has one of two forms.

The decimal representation terminates, or ends.

The decimal representation repeats a pattern.

Section 2

Convert fractions to decimals

Property

Examples

To write $\frac{3}{4}$ as a decimal, we divide 3 by 4. The calculation $3.00 \div 4$ gives us $0.75$ . So, $\frac{3}{4} = 0.75$ .

To convert the improper fraction $\frac{9}{5}$ to a decimal, we divide 9 by 5. The calculation $9.0 \div 5$ results in $1.8$ . So, $\frac{9}{5} = 1.8$ .

Section 3

Convert decimals to fractions

Property

To convert a terminating decimal to a fraction: $0.abc = \frac{abc}{1000}$ (denominator is power of 10 based on decimal places)

To convert a repeating decimal to a fraction: Let $x$ equal the decimal, multiply by appropriate power of 10 to align repeating parts, then subtract and solve for $x$

Overview

Lesson overview

Review the lesson summary and core properties without leaving the current page.

Overview

Section 1

Decimal Form of a Rational Number

Property

A rational number is one that can be expressed as a quotient (or ratio) of two integers, where the denominator is not zero. The decimal representation of a rational number has one of two forms.

The decimal representation terminates, or ends.

The decimal representation repeats a pattern.

Section 2

Convert fractions to decimals

Property

Examples

To write $\frac{3}{4}$ as a decimal, we divide 3 by 4. The calculation $3.00 \div 4$ gives us $0.75$ . So, $\frac{3}{4} = 0.75$ .

To convert the improper fraction $\frac{9}{5}$ to a decimal, we divide 9 by 5. The calculation $9.0 \div 5$ results in $1.8$ . So, $\frac{9}{5} = 1.8$ .

Section 3

Convert decimals to fractions

Property

To convert a terminating decimal to a fraction: $0.abc = \frac{abc}{1000}$ (denominator is power of 10 based on decimal places)

To convert a repeating decimal to a fraction: Let $x$ equal the decimal, multiply by appropriate power of 10 to align repeating parts, then subtract and solve for $x$