Learn on PengiSaxon Math, Intermediate 4Chapter 5: Lessons 41–50, Investigation 5

Investigation 5: Percents, Activity Percent

In this Grade 4 lesson from Saxon Math Intermediate 4, students explore percents as parts of a whole, learning that percent means "per hundred" and can be expressed as a fraction with a denominator of 100 or as a decimal. Students practice naming percents using familiar money equivalents, estimating percents visually, finding the remaining percent of a whole, and calculating 50% of a number by dividing it in half. The activity reinforces connections between fractions, decimals, and percents through shading figures and comparing values.

Section 1

📘 Percents

New Concept

Percent means per hundred.

50% means 5010050\% \text{ means } \frac{50}{100}

What’s next

Next, you'll estimate percents, find remaining parts of a whole, and compare percents to common fractions like 12\frac{1}{2}.

Section 2

Percent

Property

A percent is a fraction with a denominator of 100. The percent sign (%) represents the denominator 100. For example, 50% means 5010050\% \text{ means } \frac{50}{100}.

Example

A quarter is what percent of a dollar? 25100=25%\frac{25}{100} = 25\%.
A dime is what percent of a dollar? 10100=10%\frac{10}{100} = 10\%.
A penny is what percent of a dollar? 1100=1%\frac{1}{100} = 1\%.

Explanation

Think of 'percent' as 'per cent,' just like there are 100 cents in a dollar. So, 25% is like 25 cents out of a dollar. The percent sign (%) is just a cool shorthand for writing a fraction with 100 on the bottom. It’s a super handy way to talk about parts of a whole, from test scores to sale prices.

Section 3

Finding the Remaining Percent of a Whole

Property

The parts of a whole total 100%. If 25% of a circle is shaded, then 75% is not shaded because 25%+75%=100%25\% + 75\% = 100\%.

Example

If 40% of a circle is shaded, what percent is not shaded? 100%40%=60%100\% - 40\% = 60\% is not shaded.
If 80% of the answers were correct, what percent were incorrect? 100%80%=20%100\% - 80\% = 20\% were not correct.
If the chance of rain is 10%, what is the chance it will not rain? 100%10%=90%100\% - 10\% = 90\% chance of no rain.

Explanation

Imagine a whole pizza is 100%. If you eat 30% of it, how much is left? Just subtract from 100! The whole of anything—a group of people, a tank of gas, or a bag of candy—always adds up to 100%. Knowing one part lets you instantly figure out the other missing part. It's a simple subtraction trick!

Section 4

Finding 50% of a Number

Property

Since 50% equals 12\frac{1}{2}, we find 50% of a number by dividing it into two equal parts.

Example

How many eggs is 50% of a dozen (12 eggs)? 12÷2=612 \div 2 = 6 eggs.
How many minutes is 50% of an hour (60 minutes)? 60÷2=3060 \div 2 = 30 minutes.
How much money is 50% of 10 dollars? 10 dollars÷2=5 dollars10 \text{ dollars} \div 2 = 5 \text{ dollars}.

Explanation

Don't let 'finding 50% of a number' scare you! It's just a math-class way of saying 'cut it in half.' Since 50% is the same as the fraction 12\frac{1}{2}, you just divide the total number by two. It’s the easiest percent calculation you'll ever do. If you can share a cookie, you can find 50%.

Book overview

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

Continue this chapter

Chapter 5: Lessons 41–50, Investigation 5

  1. Lesson 1

    Lesson 41: Subtracting Across Zero, Missing Factors

  2. Lesson 2

    Lesson 42: Rounding Numbers to Estimate

  3. Lesson 3

    Lesson 43: Adding and Subtracting Decimal Numbers, Part 1, Activity Adding and Subtracting Decimals

  4. Lesson 4

    Lesson 44: Multiplying Two-Digit Numbers, Part 1

  5. Lesson 5

    Lesson 45: Parentheses and the Associative Property, Naming Lines and Segments

  6. Lesson 6

    Lesson 46: Relating Multiplication and Division, Part 1, Activity Using a Multiplication Table to Divide

  7. Lesson 7

    Lesson 47: Relating Multiplication and Division, Part 2

  8. Lesson 8

    Lesson 48: Multiplying Two-Digit Numbers, Part 2

  9. Lesson 9

    Lesson 49: Word Problems About Equal Groups, Part 1

  10. Lesson 10

    Lesson 50: Adding and Subtracting Decimal Numbers, Part 2, Activity Adding and Subtracting Decimals

  11. Lesson 11Current

    Investigation 5: Percents, Activity Percent

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

📘 Percents

New Concept

Percent means per hundred.

50% means 5010050\% \text{ means } \frac{50}{100}

What’s next

Next, you'll estimate percents, find remaining parts of a whole, and compare percents to common fractions like 12\frac{1}{2}.

Section 2

Percent

Property

A percent is a fraction with a denominator of 100. The percent sign (%) represents the denominator 100. For example, 50% means 5010050\% \text{ means } \frac{50}{100}.

Example

A quarter is what percent of a dollar? 25100=25%\frac{25}{100} = 25\%.
A dime is what percent of a dollar? 10100=10%\frac{10}{100} = 10\%.
A penny is what percent of a dollar? 1100=1%\frac{1}{100} = 1\%.

Explanation

Think of 'percent' as 'per cent,' just like there are 100 cents in a dollar. So, 25% is like 25 cents out of a dollar. The percent sign (%) is just a cool shorthand for writing a fraction with 100 on the bottom. It’s a super handy way to talk about parts of a whole, from test scores to sale prices.

Section 3

Finding the Remaining Percent of a Whole

Property

The parts of a whole total 100%. If 25% of a circle is shaded, then 75% is not shaded because 25%+75%=100%25\% + 75\% = 100\%.

Example

If 40% of a circle is shaded, what percent is not shaded? 100%40%=60%100\% - 40\% = 60\% is not shaded.
If 80% of the answers were correct, what percent were incorrect? 100%80%=20%100\% - 80\% = 20\% were not correct.
If the chance of rain is 10%, what is the chance it will not rain? 100%10%=90%100\% - 10\% = 90\% chance of no rain.

Explanation

Imagine a whole pizza is 100%. If you eat 30% of it, how much is left? Just subtract from 100! The whole of anything—a group of people, a tank of gas, or a bag of candy—always adds up to 100%. Knowing one part lets you instantly figure out the other missing part. It's a simple subtraction trick!

Section 4

Finding 50% of a Number

Property

Since 50% equals 12\frac{1}{2}, we find 50% of a number by dividing it into two equal parts.

Example

How many eggs is 50% of a dozen (12 eggs)? 12÷2=612 \div 2 = 6 eggs.
How many minutes is 50% of an hour (60 minutes)? 60÷2=3060 \div 2 = 30 minutes.
How much money is 50% of 10 dollars? 10 dollars÷2=5 dollars10 \text{ dollars} \div 2 = 5 \text{ dollars}.

Explanation

Don't let 'finding 50% of a number' scare you! It's just a math-class way of saying 'cut it in half.' Since 50% is the same as the fraction 12\frac{1}{2}, you just divide the total number by two. It’s the easiest percent calculation you'll ever do. If you can share a cookie, you can find 50%.

Book overview

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

Continue this chapter

Chapter 5: Lessons 41–50, Investigation 5

  1. Lesson 1

    Lesson 41: Subtracting Across Zero, Missing Factors

  2. Lesson 2

    Lesson 42: Rounding Numbers to Estimate

  3. Lesson 3

    Lesson 43: Adding and Subtracting Decimal Numbers, Part 1, Activity Adding and Subtracting Decimals

  4. Lesson 4

    Lesson 44: Multiplying Two-Digit Numbers, Part 1

  5. Lesson 5

    Lesson 45: Parentheses and the Associative Property, Naming Lines and Segments

  6. Lesson 6

    Lesson 46: Relating Multiplication and Division, Part 1, Activity Using a Multiplication Table to Divide

  7. Lesson 7

    Lesson 47: Relating Multiplication and Division, Part 2

  8. Lesson 8

    Lesson 48: Multiplying Two-Digit Numbers, Part 2

  9. Lesson 9

    Lesson 49: Word Problems About Equal Groups, Part 1

  10. Lesson 10

    Lesson 50: Adding and Subtracting Decimal Numbers, Part 2, Activity Adding and Subtracting Decimals

  11. Lesson 11Current

    Investigation 5: Percents, Activity Percent