Learn on PengiSaxon Math, Course 1Chapter 8: Advanced Topics in Geometry and Number Operations

Lesson 76: Comparing Fractions by Converting to Decimal Form

In this Grade 6 Saxon Math Course 1 lesson, students learn how to compare fractions by converting them to decimal form through numerator-by-denominator division. The lesson covers comparing two fractions, as well as comparing a fraction directly to a decimal number, using place value alignment to determine which value is greater or less. This builds on prior methods of fraction comparison and strengthens students' understanding of the relationship between fractions and decimals.

Section 1

📘 Comparing Fractions by Converting to Decimal Form

New Concept

Another way to compare fractions is to convert the fractions to decimal form.

Why it matters

Fractions and decimals are different ways to write the same number; mastering this conversion is the first step toward true number fluency. This skill is critical in algebra, where you will constantly transform expressions to reveal hidden relationships and solve complex equations.

What’s next

Next, you’ll practice converting fractions to decimals and use this skill to compare their values.

Section 2

New Concept

Property

To compare fractions, one method is to convert the fractions into their decimal forms first.

Examples

To compare 35\frac{3}{5} and 58\frac{5}{8}, convert them: 35=0.6\frac{3}{5} = 0.6 and 58=0.625\frac{5}{8} = 0.625. Since 0.600<0.6250.600 < 0.625, we have 35<58\frac{3}{5} < \frac{5}{8}.
To compare 14\frac{1}{4} and 310\frac{3}{10}, convert them: 14=0.25\frac{1}{4} = 0.25 and 310=0.30\frac{3}{10} = 0.30. Since 0.25<0.300.25 < 0.30, we have 14<310\frac{1}{4} < \frac{3}{10}.
To compare 320\frac{3}{20} and 18\frac{1}{8}, convert them: 320=0.15\frac{3}{20} = 0.15 and 18=0.125\frac{1}{8} = 0.125. Since 0.150>0.1250.150 > 0.125, we have 320>18\frac{3}{20} > \frac{1}{8}.

Explanation

Think of fractions as secret codes. It's hard to tell if 35\frac{3}{5} is bigger than 58\frac{5}{8} just by looking. But when you decode them into decimals by dividing the top by the bottom, you get 0.60.6 and 0.6250.625. Suddenly, the secret is out, and it's easy to see which number is the true heavyweight champion!

Section 3

Fraction vs. Decimal Showdown

Property

To compare a fraction with a decimal, start by converting the fraction into a decimal number.

Examples

To compare 34\frac{3}{4} and 0.70.7, convert the fraction: 34=0.75\frac{3}{4} = 0.75. Now compare the decimals: 0.75>0.700.75 > 0.70, so 34>0.7\frac{3}{4} > 0.7.
To compare 0.50.5 and 25\frac{2}{5}, convert the fraction: 25=0.4\frac{2}{5} = 0.4. Now compare the decimals: 0.5>0.40.5 > 0.4, so 0.5>250.5 > \frac{2}{5}.
To compare 78\frac{7}{8} and 0.850.85, convert the fraction: 78=0.875\frac{7}{8} = 0.875. Now compare the decimals: 0.875>0.8500.875 > 0.850, so 78>0.85\frac{7}{8} > 0.85.

Explanation

Imagine a showdown between a fraction and a decimal. It's not a fair fight if they are in different forms! To make it an even match, transform the fraction into a decimal by dividing its numerator by its denominator. Once they're both speaking the same language, you can easily tell which one is greater and declare a winner.

Section 4

Thinking Skill: Explain

Property

To compare decimal numbers, write both numbers with the same number of decimal places. Then compare the numbers.

Examples

To compare 0.60.6 and 0.6250.625, write them with three decimal places: 0.6000.600 and 0.6250.625. Since 600<625600 < 625, we know 0.6<0.6250.6 < 0.625.
To compare 0.750.75 and 0.70.7, write them with two decimal places: 0.750.75 and 0.700.70. Since 75>7075 > 70, we know 0.75>0.70.75 > 0.7.
To compare 0.40.4 and 0.3950.395, write them with three decimal places: 0.4000.400 and 0.3950.395. Since 400>395400 > 395, we know 0.4>0.3950.4 > 0.395.

Explanation

Comparing decimals like 0.70.7 and 0.750.75 is like comparing a 7-inch stick to a 75-inch stick—it seems obvious until you realize the units are different! To fix this, we give them the same 'units' by padding with zeros. So, 0.70.7 becomes 0.700.70. Now, comparing 0.700.70 and 0.750.75 is easy. It's a fair race!

Book overview

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Chapter 8: Advanced Topics in Geometry and Number Operations

  1. Lesson 1

    Lesson 71: Parallelograms

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  2. Lesson 2

    Lesson 72: Fractions Chart

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  3. Lesson 3

    Lesson 73: Exponents

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  4. Lesson 4

    Lesson 74: Writing Fractions as Decimal Numbers

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  5. Lesson 5

    Lesson 75: Writing Fractions and Decimals as Percents, Part 1

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  6. Lesson 6Current

    Lesson 76: Comparing Fractions by Converting to Decimal Form

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  7. Lesson 7

    Lesson 77: Finding Unstated Information in Fraction Problems

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  8. Lesson 8

    Lesson 78: Capacity

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  9. Lesson 9

    Lesson 79: Area of a Triangle

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  10. Lesson 10

    Lesson 80: Using a Constant Factor to Solve Ratio Problems

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  11. Lesson 11

    Investigation 8: Geometric Construction of Bisectors

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Lesson overview

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Section 1

📘 Comparing Fractions by Converting to Decimal Form

New Concept

Another way to compare fractions is to convert the fractions to decimal form.

Why it matters

Fractions and decimals are different ways to write the same number; mastering this conversion is the first step toward true number fluency. This skill is critical in algebra, where you will constantly transform expressions to reveal hidden relationships and solve complex equations.

What’s next

Next, you’ll practice converting fractions to decimals and use this skill to compare their values.

Section 2

New Concept

Property

To compare fractions, one method is to convert the fractions into their decimal forms first.

Examples

To compare 35\frac{3}{5} and 58\frac{5}{8}, convert them: 35=0.6\frac{3}{5} = 0.6 and 58=0.625\frac{5}{8} = 0.625. Since 0.600<0.6250.600 < 0.625, we have 35<58\frac{3}{5} < \frac{5}{8}.
To compare 14\frac{1}{4} and 310\frac{3}{10}, convert them: 14=0.25\frac{1}{4} = 0.25 and 310=0.30\frac{3}{10} = 0.30. Since 0.25<0.300.25 < 0.30, we have 14<310\frac{1}{4} < \frac{3}{10}.
To compare 320\frac{3}{20} and 18\frac{1}{8}, convert them: 320=0.15\frac{3}{20} = 0.15 and 18=0.125\frac{1}{8} = 0.125. Since 0.150>0.1250.150 > 0.125, we have 320>18\frac{3}{20} > \frac{1}{8}.

Explanation

Think of fractions as secret codes. It's hard to tell if 35\frac{3}{5} is bigger than 58\frac{5}{8} just by looking. But when you decode them into decimals by dividing the top by the bottom, you get 0.60.6 and 0.6250.625. Suddenly, the secret is out, and it's easy to see which number is the true heavyweight champion!

Section 3

Fraction vs. Decimal Showdown

Property

To compare a fraction with a decimal, start by converting the fraction into a decimal number.

Examples

To compare 34\frac{3}{4} and 0.70.7, convert the fraction: 34=0.75\frac{3}{4} = 0.75. Now compare the decimals: 0.75>0.700.75 > 0.70, so 34>0.7\frac{3}{4} > 0.7.
To compare 0.50.5 and 25\frac{2}{5}, convert the fraction: 25=0.4\frac{2}{5} = 0.4. Now compare the decimals: 0.5>0.40.5 > 0.4, so 0.5>250.5 > \frac{2}{5}.
To compare 78\frac{7}{8} and 0.850.85, convert the fraction: 78=0.875\frac{7}{8} = 0.875. Now compare the decimals: 0.875>0.8500.875 > 0.850, so 78>0.85\frac{7}{8} > 0.85.

Explanation

Imagine a showdown between a fraction and a decimal. It's not a fair fight if they are in different forms! To make it an even match, transform the fraction into a decimal by dividing its numerator by its denominator. Once they're both speaking the same language, you can easily tell which one is greater and declare a winner.

Section 4

Thinking Skill: Explain

Property

To compare decimal numbers, write both numbers with the same number of decimal places. Then compare the numbers.

Examples

To compare 0.60.6 and 0.6250.625, write them with three decimal places: 0.6000.600 and 0.6250.625. Since 600<625600 < 625, we know 0.6<0.6250.6 < 0.625.
To compare 0.750.75 and 0.70.7, write them with two decimal places: 0.750.75 and 0.700.70. Since 75>7075 > 70, we know 0.75>0.70.75 > 0.7.
To compare 0.40.4 and 0.3950.395, write them with three decimal places: 0.4000.400 and 0.3950.395. Since 400>395400 > 395, we know 0.4>0.3950.4 > 0.395.

Explanation

Comparing decimals like 0.70.7 and 0.750.75 is like comparing a 7-inch stick to a 75-inch stick—it seems obvious until you realize the units are different! To fix this, we give them the same 'units' by padding with zeros. So, 0.70.7 becomes 0.700.70. Now, comparing 0.700.70 and 0.750.75 is easy. It's a fair race!

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 8: Advanced Topics in Geometry and Number Operations

  1. Lesson 1

    Lesson 71: Parallelograms

    LearnPractice
  2. Lesson 2

    Lesson 72: Fractions Chart

    LearnPractice
  3. Lesson 3

    Lesson 73: Exponents

    LearnPractice
  4. Lesson 4

    Lesson 74: Writing Fractions as Decimal Numbers

    LearnPractice
  5. Lesson 5

    Lesson 75: Writing Fractions and Decimals as Percents, Part 1

    LearnPractice
  6. Lesson 6Current

    Lesson 76: Comparing Fractions by Converting to Decimal Form

    LearnPractice
  7. Lesson 7

    Lesson 77: Finding Unstated Information in Fraction Problems

    LearnPractice
  8. Lesson 8

    Lesson 78: Capacity

    LearnPractice
  9. Lesson 9

    Lesson 79: Area of a Triangle

    LearnPractice
  10. Lesson 10

    Lesson 80: Using a Constant Factor to Solve Ratio Problems

    LearnPractice
  11. Lesson 11

    Investigation 8: Geometric Construction of Bisectors

    LearnPractice