# Arithmetic operations

Contents

Let's begin our journey together in 5th grade with good ole fashioned arithmetic. Don't assume that this has to be boring...not at all! We're going to have fun as we learn about and practice adding, subtracting, multiplying, and dividing whole numbers and decimals. We know you're probably pretty comfortable with basic arithmetic, so we'll try to challenge you a little more in these tutorials!

## Common fractions and decimals

Learn about common fractions and their decimal forms like 1 /2 = 0.5, 3/4 = 0.75, and 2/5 = 0.4.

Article

Common fractions and decimals

Build intuition behind memorizing the decimal form of common fractions like that 1/2 equals 0.5 or 3/4 equals 0.75.

Exercise

Common fractions and decimals

Practice converting between the fraction and decimal form of common numbers like 0.5 or 3/4.

## Adding decimals

You get the general idea of decimals and what the digits in different places represent (place value). Now you're ready to do something with the decimals. Adding and subtracting is a good place to start. This will allow you to add your family's expenses to figure out if your little brother is laundering money (perhaps literally). Have fun! Common Core Standard: 5.NBT.B.7

2:40

Adding decimals: 9.087+15.31

Sal solves 9.087+15.31 using the "standard algorithm".

1:46

Adding decimals: 0.822+5.65

Sal solves 0.822+5.65 using "standard algorithm".

2:45

Adding three decimals

Sal adds 7.056+605.7+5.67 using the "standard algorithm".

Article

Adding decimals

Start with simple problems like 0.2 + 0.4 and build to more complex problems like 10.3 + 36.75.

Exercise

Add decimals 1

Add tenths like 0.7 + 0.5

Exercise

Add decimals 2

Add whole numbers and tenths like 4 + 5.7

Exercise

Add decimals 3

Add larger numbers with tenths like 40.1+7.6

Exercise

Add decimals 4

Add hundredths like 0.76+0.21

Exercise

Add decimals 5

Add whole numbers, tenths, and hundredths like 60+2.57 or 5.53+3.1

Exercise

Add decimals 6

Add more challenging whole numbers, tenths, and hundredths like 5.7+4.51 or 47.75+11.98

## Subtracting decimals

Anything you can do with whole numbers, you can do with decimals. Subtraction is no exception. In this tutorial, you'll get some good practice subtracting decimals up the hundredths place.

1:11

Subtracting decimals: 9.57-8.09

Sal subtracts 9.57-8.09 using "standard algorithm".

1:53

Subtracting decimals: 10.1-3.93

Sal subtracts 10.1-3.93 using "standard algorithm".

Article

Subtracting decimals

We'll start with simple problems like 0.9 - 0.8 and build to more complex problems like 12.6 - 8.89.

Exercise

Subtract decimals 1

Subtract tenths like 0.9-0.7

Exercise

Subtract decimals 2

Subtract small whole numbers and tenths like 1.6-0.3

Exercise

Subtract decimals 3

Subtract larger whole numbers and tenths like 78.4-3

Exercise

Subtract decimals 4

Subtract trickier numbers with tenths like 56.8-17.9

Exercise

Subtract decimals 5

Subtract hundredths like 0.75-0.56

Exercise

Subtract decimals 6

Subtract small whole numbers, tenths, and hundredths like 0.6-0.43 or 1.58-0.5

Exercise

Subtract decimals 7

Subtract larger whole numbers, tenths, and hundredths like 67.89-6 or 35.65-17.34

Exercise

Subtract decimals 8

More challenging subtraction problems with whole numbers, tenths, and hundredths like 15-7.45 or 12.19-7.68

## Multi-digit multiplication

Learn how to multiply multi-digit whole numbers like 345 times 892.

Exercise

Multiply by taking out factors of 10

Multiply numbers like 900 x 1000

10:27

Multiplying multiple digit numbers

Sal multiplies 2- and 3-digit numbers using "standard algorithm".

Exercise

Multi-digit multiplication

Multiply 2-3 digits by 3-4 digits with carrying.

## Multiplying decimals

The real world is seldom about whole numbers. If you precisely measure anything, you're likely to get a decimal. If you don't know how to multiply these decimals, then you won't be able to do all the powerful things that multiplication can do in the real world (figure out your commission as a robot possum salesperson, determining how much shag carpet you need for your secret lair, etc.).

3:50

Intro to multiplying decimals

Sal introduces multiplying decimals with problems like 9x0.6.

6:29

Multiplying decimals: place value

Sal uses an understanding of place value to multiply 2.91x3.2.

Article

Multiplying decimals (no standard algorithm)

We'll start with simple problems like 0.9 x 0.2 and build to more complex problems like 3.4 x 6.1.

Exercise

Multiply decimals 1

Multiply tenths like 0.6 x 0.4

Exercise

Multiply decimals 2

Multiply decimals and whole numbers like 8x0.2 or 0.56x4

Exercise

Multiply decimals 3

Multiply numbers with tenths and hundredths like 3.1x3.3 or 1.7x0.12

## Multi-digit division

We're taking division a step further and moving beyond single-number division. Let's learn to divide any whole number by a multiple-digit whole number! Common Core Standard: 5.NBT.B.6

Exercise

Divide by taking out factors of 10

Divide numbers like 2400÷30.

Exercise

Basic multi-digit division

Divide numbers like 105÷21 or 119÷17

5:09

Dividing by 2-digits: 9815÷65

Sal divides 9815÷65. There is no remainder.

2:49

Dividing by 2-digits: 7182÷42

Sal divides 7182÷42. There is no remainder.

Exercise

Division by 2-digits

Divide 3-digit and 4-digit numbers by a 2-digit number without remainders.

## Dividing decimals

In this tutorial, we'll extend our division skills to include decimals! We get into some pretty fun stuff here including dividing decimals by whole numbers, and dividing whole numbers by decimals. Finally...dividing decimals by decimals. Common Core Standard 5.NBT.B.7

2:37

Dividing whole numbers to get a decimal

Sal divides 63÷35.

Article

Dividing decimals

We'll start with simple problems like 3 / 2 and build to more complex problems like 4.5 / 0.15.

Exercise

Divide decimals 1

Dividing whole numbers to get a decimal quotient like 15÷6=2.5

Exercise

Divide decimals 2

Dividing larger whole numbers to get a decimal quotient like 63÷12=5.25

Exercise

Divide decimals 3

Dividing decimals by whole numbers like 2.5÷5 or 1.86÷2

Exercise

Divide decimals 4

Dividing decimals where we can factor a 10 out of the divisor like 9÷30

Exercise

Divide decimals 5

Dividing larger whole numbers by whole numbers to get a decimal like 80÷200

Exercise

Divide decimals 6

Dividing tenths by tenths like 0.6÷0.2.

Exercise

Divide decimals 7

Dividing numbers by 0.1 or 0.01 like 10÷0.1 or 5.3÷0.01

Exercise

Divide decimals 8

More challenging division with decimals like 14÷0.7 or 1.32÷0.12.