I can convert fractions to decimals and vice versa.

Ability to change fractions into decimals and decimals back into fractions.

I can convert fractions and decimals to percentage.

Skill in transforming fractions and decimals into percentages.

I can order rational numbers on a number line.

Capability to arrange rational numbers in sequence on a number line.

Definition of Rational Numbers

Rational Numbers are real numbers that can be expressed as the ratio of an integer to a non-zero integer.

Form of Rational Numbers

Rational Numbers are of the form q = $$\frac{m}{n}$$ where n \neq 0.

Examples of Rational Numbers

Examples include , , , 0.75, 14\%, and 1.63.

How is a fraction represented?

By $$\frac{m}{n}$$ where $$n \neq 0$$ .

Visual representation of fractions using a pizza.

A visual representation of fractions using a pizza.

A fraction where the numerator is less than the denominator. Its value is less than 1. Examples: $$\frac{1}{2}$$ , $$\frac{5}{6}$$ , $$\frac{10}{17}$$

A fraction where the numerator is greater than or equal to the denominator. Its value is greater than 1. Examples: $$\frac{7}{4}$$ , $$\frac{11}{3}$$ , $$\frac{34}{19}$$

A mixed fraction is a combination of a whole number and a proper fraction. Its value is greater than 1.

Fractions with the same denominators. Examples: $$\frac{4}{3}$$ , $$\frac{7}{3}$$ , $$\frac{8}{3}$$

Fractions with different denominators. Examples: $$\frac{1}{4}$$ , $$\frac{7}{6}$$ , $$\frac{2}{3}$$

Decimals that have a finite number of digits after the decimal point. Example: 0.5, 0.86, 0.25

Decimals that have a pattern of digits that repeat infinitely after the decimal point. Example: 0.3333..., 0.257257..., 0.123123...

Mixed Fraction to Improper Fraction

To convert a mixed fraction to an improper fraction, multiply the whole number by the denominator, add the numerator, and place the result over the original denominator.

Improper Fraction to Mixed Fraction

To convert an improper fraction to a mixed fraction, divide the numerator by the denominator. The quotient is the whole number, and the remainder is the new numerator over the original denominator.

Converting improper fraction to mixed fraction

To convert an improper fraction to a mixed number, divide the numerator by the denominator to get the quotient and remainder. The quotient is the whole number part, and the remainder is the numerator of the fractional part.

Step 1 in converting $$\frac{17}{5}$$ to a mixed number

Divide 17 by 5 to get 3 remainder 2.

Step 2 in converting $$\frac{17}{5}$$ to a mixed number

Write the quotient (3) as the whole number part and the remainder (2) over the original denominator (5) as the fractional part: $$3 \frac{2}{5}$$ .

Diagram showing conversion of $$\frac{17}{5}$$ to $$3 \frac{2}{5}$$

The diagram illustrates the division of 17 by 5, resulting in a quotient of 3 and a remainder of 2, forming the mixed number $$3 \frac{2}{5}$$ .

Converting a mixed fraction to an improper fraction involves the following steps:

1. Multiply the whole number by the denominator. 2. Add the result to the numerator. 3. Write the sum over the original denominator.

The first step in converting a mixed fraction to an improper fraction is to multiply the whole number by the denominator.

Multiply the whole number by the denominator.

After multiplying the whole number by the denominator in a mixed fraction, the next step is to add the result to the numerator.

Add the result to the numerator.

To finalize the conversion of a mixed fraction to an improper fraction, write the sum over the original denominator.

Write the sum over the original denominator.

Conversion: Fraction to Decimal

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

Example of converting the fraction 7/4 to a decimal.

Converting the fraction 7/4 to a decimal results in 1.75, which is a terminating decimal.

Converting the fraction $$\frac{4}{9}$$ to a decimal

The fraction $$\frac{4}{9}$$ as a decimal is 0.444... (repeating).

Nature of the decimal 0.444...

The decimal 0.444... is non-terminating but repeating.

Converting 0.72 to a fraction

0.72 as a fraction is $$\frac{72}{100}$$ , which simplifies to $$\frac{18}{25}$$ .

Decimal places and fraction denominator

Since 0.72 has two decimal places, the denominator of the fraction should be 100.

Converting 1.498 to a fraction involves using a denominator of 1000 because it has three decimal places.

1.498 = $$\frac{1498}{1000}$$ , which simplifies to $$\frac{749}{500}$$ .

The simplified fraction $$\frac{749}{500}$$ can be expressed as a mixed fraction.

1.498 = 1 $$\frac{249}{500}$$ .

Independent work encourages self-reliance and personal responsibility in learning.

Convert the decimal 0.12 to a fraction.

0.12 = $$\frac{12}{100}$$ = $$\frac{3}{25}$$

Convert the decimal 11.5 to a fraction.

11.5 = $$\frac{115}{10}$$ = $$\frac{23}{2}$$

Rational Numbers Flashcards

Student preview

50 questions

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1.

FLASHCARD QUESTION

Front

Rational Numbers

Back

Rational numbers include fractions, decimals, and percentages.

2.

FLASHCARD QUESTION

Front

Let us all remember that we are in the holy presence of God.

Back

3.

FLASHCARD QUESTION

Front

In the name of the Father, the Son, and the Holy Spirit. Amen.

Back

4.

FLASHCARD QUESTION

Front

I will continue, o my God, to do all my actions for the love of You.

Back

5.

FLASHCARD QUESTION

Front

St. John Baptist De La Salle, pray for us. Live Jesus in our hearts, forever.

Back

6.

FLASHCARD QUESTION

Front

Rational numbers and their operations

Back

are used in real-life problems to calculate and compare quantities, manage finances, determine rates, and measure various parameters accurately.

7.

FLASHCARD QUESTION

Front

I can describe given rational numbers as fractions, decimals, or percentages.

Back

Understanding how to express rational numbers in different forms such as fractions, decimals, and percentages.

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