Learning to Juggle with: Fractions, Decimals, and Percents © Mike’s Math Mall

Introduction

Fractions, Decimals, and Percents Fractions, decimals, and percents are different ways of representing the same number. 𝟏 𝟐 = 0.5 = 50% Fraction Decimal Percent These numbers look different, but they all have the exact same value.

Fractions, Decimals, and Percents Because we use fractions, decimals, and percents in everyday life, it’s helpful if we can juggle or change between each form… …making these numbers easier to understand.

Fractions, Decimals, and Percents When do we use Fractions? Telling time 𝟏 𝟒 after four (a quarter after four) Cooking/Recipes 𝟐 𝟑 cups flour Reading Music 𝟏 𝟐 note Measuring Length 𝟓 𝟏 𝟖 inches Can you think of other ways we use fractions?

Fractions, Decimals, and Percents When do we use Decimals? Sports 0.375 – baseball batting averages Prices $299.99 Pi 3.141592… 𝜋 Gas Amounts 18.8959 gallons Where else do we see decimals?

Fractions, Decimals, and Percents When do we use Percents? Grades 25% Retail Sales 60% off! Thanks for reminding me! Statistics 100% of students choose shorter school days! Tipping Rates 15% to 20% Where else do we find percentages?

Changing Fractions to Decimals Part 1: 1 1 2 𝐧𝐮𝐦𝐞𝐫𝐚𝐭𝐨𝐫 𝐝𝐞𝐧𝐨𝐦𝐢𝐧𝐚𝐭𝐨𝐫 Changing Fractions to Decimals 𝟎.𝟕𝟓 𝟑 𝟒 𝒑𝒂𝒓𝒕 𝒘𝒉𝒐𝒍𝒆 𝟏.𝟓

Proper fractions, like this one, represent numbers less than 1. Focusing on Fractions A fraction is formed by two numbers; a top number, the numerator, over a bottom number, the denominator. 3 4 𝐧𝐮𝐦𝐞𝐫𝐚𝐭𝐨𝐫 𝐝𝐞𝐧𝐨𝐦𝐢𝐧𝐚𝐭𝐨𝐫 → 𝒑𝒂𝒓𝒕 𝒘𝒉𝒐𝒍𝒆 or Proper fractions, like this one, represent numbers less than 1.

Does anyone know how to turn a fraction into a decimal? Fractions to Decimals Decimals are related to fractions because they also represent numbers less than 1. Does anyone know how to turn a fraction into a decimal? Divide the numerator by the denominator! But how does that give you a decimal?

Fractions to Decimals Let’s use 𝟑 𝟒 as an example. . 7 5 4 3.0 -2 8 2 To turn 𝟑 𝟒 into a decimal, we divide the numerator, 3, by the denominator, 4. . 7 5 4 3.0 So 𝟑 𝟒 = 0.75 -2 8 2 -20 Hint: you can think of a fraction bar like a division (÷) symbol.

Fractions to Decimals Let’s try 𝟏 𝟒 . 2 5 4 1.0 - 8 2 -20 . 2 5 4 1.0 So 𝟏 𝟒 = 0.25 - 8 2 -20

Fractions to Decimals . 6 6 3 2.0 -1 8 2 -18 2 Let’s try 𝟐 𝟑 At this point, you can see the division problem will never end, and the 6 will keep repeating. . 6 6 3 2.0 -1 8 2 So 𝟐 𝟑 = 0.6 -18 2

Can someone guess what the decimal form of 3 𝟑 𝟒 would be? Fractions to Decimals Can someone guess what the decimal form of 3 𝟑 𝟒 would be? If you said 3.75, you’re right! Notice how the whole number stays the same in both forms. I think I get it, but can we do more to be sure? Absolutely!

Time to Show Your Stuff! = 0.25 = 0.4 = 0.83 = 0.7 = 0.3 = 1.5 = 2.6 Change the following fractions into decimals. 1) 𝟏 𝟒 2) 𝟐 𝟓 = 0.25 = 0.4 3) 𝟓 𝟔 4) 𝟕 𝟏𝟎 = 0.83 = 0.7 5) 𝟏 𝟑 6) 1 𝟏 𝟐 = 0.3 = 1.5 7) 2 𝟑 𝟓 8) 9 𝟓 𝟖 = 2.6 = 9.625

Changing Decimals back to Fractions

Decimals to Fractions Before we start changing decimals into fractions, we need a good understanding of how to properly say decimals. Believe it or not, when you properly say a decimal, you are automatically creating the fraction.

0. 3927 Decimals to Fractions ten thousandths thousandths hundredths Can you name the following decimal place values? ten thousandths thousandths hundredths tenths Now let’s look at how to properly “say” decimals. 0. 3927 (Sample number)

Decimals to Fractions 1) 0.7 “seven tenths” 2) 0.23 Practice saying the following decimals: 1) 0.7 “seven tenths” 2) 0.23 “twenty-three hundredths” 3) 0.034 “thirty-four thousandths” 4) 9.8 “nine and eight tenths”

Decimals to Fractions = 𝟖 𝟏𝟎 = 𝟏𝟔 𝟏𝟎𝟎 = 𝟓𝟐 𝟏,𝟎𝟎𝟎 = 4 𝟒 𝟏𝟎 1) 0.8 As you say each decimal, picture the fraction you’re saying to yourself: = 𝟖 𝟏𝟎 = 𝟏𝟔 𝟏𝟎𝟎 1) 0.8 2) 0.16 = 𝟓𝟐 𝟏,𝟎𝟎𝟎 = 4 𝟒 𝟏𝟎 3) 0.052 4) 4.4 What work still needs to be done with all of these fractions? If you said “simplify,” you’re right!

Decimals to Fractions = 𝟖 𝟏𝟎 = 𝟒 𝟓 = 𝟒 𝟐𝟓 = 𝟏𝟔 𝟏𝟎𝟎 = 𝟏𝟑 𝟐𝟓𝟎 = 𝟓𝟐 𝟏,𝟎𝟎𝟎 Simplify. 1) 0.8 = 𝟖 𝟏𝟎 = 𝟒 𝟓 I get it! But I better do some more practice. = 𝟒 𝟐𝟓 2) 0.16 = 𝟏𝟔 𝟏𝟎𝟎 = 𝟏𝟑 𝟐𝟓𝟎 3) 0.052 = 𝟓𝟐 𝟏,𝟎𝟎𝟎 4) 4.4 = 4 𝟒 𝟏𝟎 = 4 𝟐 𝟓

Time to Show Your Stuff! = 𝟐 𝟏𝟎 = 1 𝟑𝟐 𝟏𝟎𝟎 = 𝟏 𝟓 = 1 𝟖 𝟐𝟓 = 𝟏𝟐𝟒 𝟏,𝟎𝟎𝟎 Change the following decimals into fractions. Don’t forget to simplify! = 𝟐 𝟏𝟎 = 1 𝟑𝟐 𝟏𝟎𝟎 1) 0.2 2) 1.32 = 𝟏 𝟓 = 1 𝟖 𝟐𝟓 = 𝟏𝟐𝟒 𝟏,𝟎𝟎𝟎 = 𝟒𝟖𝟖 𝟏𝟎,𝟎𝟎𝟎 3) 0.124 4) 0.0488 = 𝟔𝟏 𝟏,𝟐𝟓𝟎 = 𝟑𝟏 𝟐𝟓𝟎