If you know how to add and subtract whole numbers, then you can add and subtract decimals!.

To add decimal numbers:1. Put the numbers in a vertical column, aligning the decimal points 2. Add each column of digits, starting on the right and working left. If the sum of a column is more than ten, "carry" digits to the next column on the left. 3. Place the decimal point in the answer directly below the decimal points in the terms.

To add these numbers, first arrange the terms vertically, aligning the decimal points in each term. Don't forget, for a whole number like the first term, the decimal point lies just to the right of the ones column. You can add zeroes to the right of the decimal point to make it easier to align the columns. Then add the columns working from the right to the left, positioning the decimal point in the answer directly under the decimal points in the terms.

To subtract decimal numbers:1. Put the numbers in a vertical column, aligning the decimal points. 2. Subtract each column, starting on the right and working left. If the digit being subtracted in a column is larger than the digit above it, "borrow" a digit from the next column to the left. 3. Place the decimal point in the answer directly below the decimal points in the terms. 4. Check your answer by adding the result to the number subtracted. The sum should equal the first number.

To subtract these numbers, first arrange the terms vertically, aligning the decimal points in each term. You can add zeroes to the right of the decimal point, to make it easier to align the columns. Then subtract the columns working from the right to the left, putting the decimal point in the answer directly underneath the decimal points in the terms. Check your answer by adding it to the second term and making sure it equals the first.

27.583- 0.200

27.383

To multiply decimal numbers:

1. Multiply the numbers just as if they were whole numbers.

Line up the numbers on the right - do not align the decimal points.

2. Place the decimal point in the answer by starting at the right and moving a number of places equal to the sum of the decimal places in both numbers multiplied

3.77x 2.8

3016+754

10556

2 decimal places1 decimal place

3 decimal places means move the decimal 3 places to the left,

Multiply 9.683 x6.1

To divide decimal numbers:

1. If the divisor is not a whole number, move decimal point to right to make it a whole number and move decimal point in dividend the same number of places.

2. Divide as usual. Keep dividing until the answer terminates or repeats.

3. Put decimal point directly above decimal point in the dividend.

4. Check your answer. Multiply quotient by divisor. Does it equal the dividend?

Like fractions are fractions with the same denominator. You can add and subtract like fractions easily - simply add or subtract the numerators and write the sum over the common denominator

Before you can add or subtract fractions with unlike denominators, you must first find equivalent fractions with the same denominator, like this:

1. Find the smallest multiple (LCM) of both numbers.

2. Rewrite the fractions as equivalent fractions with the LCM as the denominator.

Use your notes from Number sense I

€

34

+25

Add The LCM for 4 and 5 is 20

34

2

5

= 20

= 20

Convert each fraction to 20ths by using the backwards Z method.

Divide the denominator of the original fraction into the LCD

20

€

÷ 4 = 5 20

€

÷ 5 = 4Multiply by the numerator of the original fraction to get the new numerator

5 x 3 = 15

4 x 2 = 8

15

8

Then add or subtract

720

Add 45

+ 35

75

When adding fractions we sometimes get an improper fraction as the sum.

To change the improper fraction to a proper fraction divide the numerator by the denominator.

5 7

1

5

2

Whole number

numerator

Denominator remains the same.

2 5

= 1

Subtract 2 14

- 2 5

Convert to like fractions

2520

- 8 20

In this problem 1 whole = 20 20

If we borrow 1 we are going to add 20 to the numerator.

+ 20 20

1 2520

- 8 20

Then subtract

11720

1. Simplify the fractions if not in lowest terms.

2. Multiply the numerators of the fractions to get the new numerator.

3. Multiply the denominators of the fractions to get the new denominator.

Multiplying a mixed number by a whole number

Change the whole number to a fraction

Change mixed number to improper fraction

Multiply Simplify

9 5 x 3 8

To divide any number by a fraction:

First step: Find the reciprocal of the fraction.

Second step: Multiply the number by the reciprocal of the fraction.

Third step: Simplify the resulting fraction if possible.

Fourth step: Check your answer: Multiply the result you got by the divisor and be sure it equals the original dividend.

Reciprocal of 1 is 4 4

The Reciprocal of 3 is 4 4 3

Here are the steps for dividing mixed numbers.

1. Change each mixed number to an improper fraction.

2. Multiply by the reciprocal of the divisor, simplifying if possible.

3. Put answer in lowest terms.

4. Check to be sure the answer makes sense.

Solve 30 2 1 2

€

÷

1. Write the whole number and the mixed number as improper fractions.

2. Write the reciprocal of the divisor, 2/5, and multiply.

3. Simplify, if possible.

4. Perform the simple multiplication of the numerators and the denominators.

5. Put the answer in lowest terms, and check the answer.

Notice that we can simplify our problem at this step, to make our calculations easier. Five goes evenly into 30, so we can divide both 5 and 30 by 5, to give 1 and 6.

Place these numbers in order from least to greatest.

2.1, 0.49, 0.0999, 1, 2.09

There are 3 basic steps.

1. Identify which order is asked for , least to greatest, or greatest to least. ( Most people make a mistake here by not reading the directions)

2. Line up the numbers by the decimal point vertically.(Annex zeroes if needed)

2.10000.49000.09991.00002.0900

3. Start at the left and move to the right. If least to greatest write the largest number last.

2.10002.09001.00000.49000.0999

Place these fractions in order from Greatest to Least

1, 3, 2, 5, 7, 2 4 3 9 12

There are several methods to use here.These are 2 of the easiest when using a list.

1. Change each fraction to a decimal and then compare.0.5, 0.75, 0.66, 0.55, 0.583

2. Find the LCM (108) of each and make equivalent fractions and then compare.

54 81 36 60 63108 108 108 108 108

Place these numbers in order from Greatest to Least

1, 0.32, 3, 1, 0.782 5 8

There are 2 basic choices.

1. Change all to fractions. 2. Change all to decimals.

When comparing 2 fractions, cross products works well.

3 54 7

Multiply the denominator of one fraction to the numerator of the other.

Then compare products

2021

Since 21>20 that means 3 > 54 7

In the Language of Algebra, an equation is the basic number "sentence". An equation is a mathematical expression that contains an equals sign.

An equation can contain variables represented by letters

and constants (numbers).

Key words to look for

“of” means multiplication Ten dollars is two-thirds of the total money spent

A number n times 3 is equal to 120.

“is” means equal to

“times” is multiply 3n = 120

In these examples look for the key words, plus, more than, sum.

Other words like product, less than, decreased, separated into, quotient all give clues.

Another type of sentence used in algebra is called an inequality.

An inequality is used when we don't know exactly what an expression is equal to. Instead of an equals sign, we use one of these symbols:

> greater than < less than

< less than or equal to> greater than or equal to

Examples

A number minus 4 is greater than 2. n - 4 > 2

The sum of x and 5 is less than or equal to -2. x + 5 < -2

Look for the key words as you did for equations.