# Fractions, decimals, & percentages

Contents

In these tutorials, we'll explore the number system. We'll convert fractions to decimals, operate on numbers in different forms, meet complex fractions, and identify types of numbers. We'll also solve interesting word problems involving percentages (discounts, taxes, and tip calculations).

## Converting fractions to decimals

This tutorial guides you through two very important skills: converting fractions to decimals and converting decimals to fractions.

Decimal to simplified fraction

Here's an example of how we convert a decimal to a simplified fraction. Over time this will become second nature to you.

Rewrite decimals as fractions

Practice rewriting decimals as fractions. These problems use decimals with tenths and hundredths.

Rewriting decimals as fractions challenge

Practice rewriting decimals as fractions. These problems use decimals with up to four decimal places.

Fraction to decimal: 7/8

Sal writes 7/8 as a decimal.

Fraction to decimal: 11/25

Sal writes 11/25 as a decimal.

Fraction to decimal with rounding

Sal writes 21/16 as a rounded decimal.

Converting fractions to decimals

Practice converting a fraction to a decimal.

## Adding & subtracting rational numbers

We're going to mix it up a little in this set of examples. Remember that a rational number is a real number that can be written as a simple fraction, or by extension a decimal or percentage. We have to be able to add and subtract numbers when they are in different formats, whether fraction, decimal or percentage. This gets to be fun as learn to move between these expressions of rational numbers, and start to understand they're all pointing to same thing! Common Core Standards: 7.NS.A.1d

Comparing rational numbers

U09_L1_T3_we4 Comparing Rational Numbers

Comparing rational numbers

Practice comparing decimals, percents, fractions, and mixed numbers.

Adding & subtracting rational numbers: 79% - 79.1 - 58 1/10

Sal evaluates 79% - 79.1 - 58 1/10.

Adding & subtracting rational numbers: 0.79 - 4/3 - 1/2 + 150%

Sal evaluates 0.79 - 4/3 - 1/2 + 150%.

Adding & subtracting rational numbers

Practice adding and subtracting negative fractions, decimals, and percents.

## Percent word problems

At least 50% of the math that you end up doing in your real life will involve percentages. We're not really sure about that figure, but it sounds authoritative. Anyway, unless you've watched this tutorial, you're really in no position to argue otherwise. Common Core Standards: 7.EE.B.3

Growing by a percentage

In this example we grow a whole number by a percentage of itself. Growing by percentage is a common skill often used when figuring how much is owed or earned with interest.

Solving percent problems

We'll use algebra to solve this percent problem.

Percent word problem: 100 is what percent of 80?

This word problem is expressed simply which can be confusing to some. Take your time and focus on the what is being asked for.

Percent word problem: 78 is 15% of what number?

In this example, you working with us to find the number that is expressed as a given percentage. We'll create a simple algebraic equation to solve!

Discount, tax, and tip word problems

Practice solving word problems involving price discounts, taxes, and tip calculations.

Markup and commission word problems

Practice solving word problems involving price markups and commission fees.

## Rational number word problems

You already have many tools in your mathematical toolkit: addition, subtraction, multiplication, and division of decimals and fractions, as well as your understanding of units of measure. Now we'll put them all to work in solving some multi-step word problems. Common Core Standards: 7.EE.B.3

Rational number word problem: school report

First visualize this word problem then use subtraction and multiplication of decimals and fractions to get at the answer.

Rational number word problem: cosmetics

Remember units of measurement? Convert minutes into hours and put your knowledge of fractions to work in this word problem.

Rational number word problem: cab

Budgeting money is one of the most valuable math skills you'll learn. Practice with us as we figure out how much money is left after a cab fare.

Rational number word problem: ice

Word problems force us to put concepts to work using real-world applications. In this example, determine the volume of frozen water and express the answer as a fraction.

Rational number word problem: computers

In this word problem, we'll compare the weight of two objects using a ratio of integers. We'll practice simplifying a fraction, too.

Rational number word problem: stock

Use your knowledge of proportions and fractions to determine shareholders profit in this word problem.

Rational number word problem: checking account

Your checking account is overdrawn. Not good. Use your knowledge of decimals and adding negative and positive numbers to bring your account back into the black.

Rational number word problems

Practice solving multi-step word problems. The numbers in these problems may be fractions, decimals, and percents.