Unit 4 · Standard 6.RP.3c

Relate Fractions, Decimals, and Percents

Lesson 4-2

Name:Date:Class:

Key Vocabulary Level 1 support

Picture first, then the word, then a plain-language meaning. Say each word out loud.

25% means 25 out of 100

Percent

A way to compare a number to 100, shown with the % sign.

0.75 means seventy-five hundredths

Decimal

A number with a dot, like 0.5, that shows a part.

1/2 = 0.5 = 50%

Equivalent

Having the same value, just written a different way.

Common benchmarks: 25%, 50%, 75%

Benchmark

A familiar number you use to guess, like 50% or 1/2.

$40 shirt at 25% off: discount = $10

Discount

Money taken off the first price to make it cheaper.

Key Ideas & Notes

You're designing the scoring system for a new arcade game.
Players earn points as fractions of the total possible score.
The leaderboard shows scores as percentages, but the game engine uses decimals.
You need to convert between all three forms to build the display!
Complete the conversion table. Each row shows the same value in three forms.

Think About It

What are three different ways to write the same number?
If a player scored 3/4 of the points, what percent is that?
Are some fractions easier to convert than others?

My Notes

Guided Examples

Example 1

Convert 3/5 to a percent.

Solution: 3 ÷ 5 = 0.6 = 60%.

Answer: A. 60%

Example 2

Convert 7/20 to a percent.

Solution: 7 ÷ 20 = 0.35 = 35%.

Answer: A. 35%

Example 3

Which decimal is equivalent to 45%?

Solution: To convert a percent to a decimal, divide by 100: 45 ÷ 100 = 0.45.

Answer: A. 0.45

Write About the Math The Writing Revolution

I can explain my conversions using the words percent, decimal, equivalent, and benchmark.

1. Kernel Sentence subject + verb

Model: Percent is a way to compare a number to 100, shown with the % sign.Porcentaje es una manera de comparar un número con 100, con el signo %.

Write a kernel sentence about percent. Use a subject and a verb.Escribe una oración base sobre porcentaje. Usa un sujeto y un verbo.

2. Sentence Expansion because · but · so

Kernel: Percent matters in mathPorcentaje importa en matemáticas

Expand the kernel three ways. Add a reason, a contrast, and a result.

becauseporque

Percent matters in math because ___.Porcentaje importa en matemáticas porque ___.

butpero

Percent matters in math, but ___.Porcentaje importa en matemáticas, pero ___.

soentonces

Percent matters in math, so ___.Porcentaje importa en matemáticas, entonces ___.

3. Sentence Types 4 ways to write a math idea

StatementAfirmación

Tell one true fact about percent.Di un hecho verdadero sobre percent.

Percent ___.

QuestionPregunta

Ask a question about percent.Haz una pregunta sobre percent.

How does ___ ?¿Cómo ___ ?

ExclamationExclamación

Show excitement about percent.Muestra entusiasmo sobre percent.

Wow, ___ !¡Guau, ___ !

CommandMandato

Tell a partner what to do with percent.Dile a un compañero qué hacer con percent.

First, ___ .Primero, ___ .

4. Explain Your Reasoning use a sentence starter

___ as a percent is ___.___ como porcentaje es ___.

They are equal because ___.Son iguales porque ___.

I see this when ___.Veo esto cuando ___.

Try It

Solve on your own. Check the answer key when you are done.

1. What fraction is equal to 0.75?

3/4
7/5
3/5
7/10

Show your work:

2. A game shows your score as 7/8 complete. What percent is that?

87.5%
78%
75%
88%

Show your work:

Stretch Your Thinking Level 2 enrichment

Challenge task — explain your reasoning in full sentences.

A student says 3/8 is greater than 40% because 3 and 8 are bigger numbers than 4 and 0. Is the student correct? Convert both values to the same form and explain.

Sentence starter: The student is ___ because 3/8 = ___ = ___%, which is ___ than 40%.

Show your work:

Reflect — Exit Ticket

Which shows 0.45 as a fraction and a percent?

9/20 and 45%
45/10 and 4.5%
4/5 and 45%
9/20 and 4.5%

Your answer:

Answer Key & Teacher Guide

Try It 1: A. 3/4 — 0.75 = 75/100. Simplify by dividing both by 25: 75÷25 = 3 and 100÷25 = 4. So 0.75 = 3/4.
Try It 2: A. 87.5% — 7 ÷ 8 = 0.875, and 0.875 × 100 = 87.5%.
Exit Ticket: A. 9/20 and 45% — 0.45 = 45/100 = 9/20 (simplified). 0.45 × 100 = 45%.

Writing (TWR) — what to look for

Kernel sentence: A complete sentence needs a subject and a verb. Example: Percent is a way to compare a number to 100, shown with the % sign.
Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).