Frequency Table

Bar Graph

Quadrilateral

Data handling

Decimals

Fractions

Introduction to Ratio

Ratios

A ratio compares values.

A ratio says how much of one thing there is compared to another thing.

There are 3 blue squares to 1 yellow square

Ratios can be shown in different ways:

Using the ":" to separate the values:		3 : 1
Instead of the ":" we can use the word "to":		3 to 1
Or write it like a fraction:		31

A ratio can be scaled up:

Here the ratio is also 3 blue squares to 1 yellow square,
even though there are more squares.

Using Ratios

The trick with ratios is to always multiply or divide the numbers by the same value.

Example:

4 : 5 is the same as 4×2 : 5×2 = 8 : 10

Recipes

Example: A Recipe for pancakes uses 3 cups of flour and 2 cups of milk.

So the ratio of flour to milk is 3 : 2

To make pancakes for a LOT of people we might need 4 times the quantity, so we multiply the numbers by 4:

3×4 : 2×4 = 12 : 8

In other words, 12 cups of flour and 8 cups of milk.

The ratio is still the same, so the pancakes should be just as yummy.

"Part-to-Part" and "Part-to-Whole" Ratios

The examples so far have been "part-to-part" (comparing one part to another part).

But a ratio can also show a part compared to the whole lot.

Example: There are 5 pups, 2 are boys, and 3 are girls

Part-to-Part: The ratio of boys to girls is 2:3 or 2/3   The ratio of girls to boys is 3:2 or 3/2   Part-to-Whole: The ratio of boys to all pups is 2:5 or 2/5   The ratio of girls to all pups is 3:5 or 3/5

Try It Yourself

What is the ratio of oranges to strawberries?    :  

What is the ratio of strawberries to oranges?    :  

What is the ratio of oranges to total fruit?    :  

What is the ratio of strawberries to total fruit?    :  

© 2015 MathsIsFun.com v0.91

Scaling

We can use ratios to scale drawings up or down (by multiplying or dividing).

The height to width ratio of the Indian Flag is 2:3 So for every 2 (inches, meters, whatever) of height there should be 3 of width.
If we made the flag 20 inches high, it should be 30 inches wide. If we made the flag 40 cm high, it should be 60 cm wide (which is still in the ratio 2:3)

Linear equation

A linear equation is an equation for a straight line

These are all linear equations:

y = 2x + 1

5x = 6 + 3y

y/2 = 3 − x

Let us look more closely at one example:

Example: y = 2x + 1 is a linear equation:

The graph of y = 2x+1 is a straight line

• When x increases, y increases twice as fast, hence 2x
• When x is 0, y is already 1. Hence +1 is also needed
• So: y = 2x + 1

Here are some example values:

x	y = 2x + 1
-1	y = 2 × (-1) + 1 = -1
0	y = 2 × 0 + 1 = 1
1	y = 2 × 1 + 1 = 3
2	y = 2 × 2 + 1 = 5

Check for yourself that those points are part of the line above!

Different Forms

There are many ways of writing linear equations, but they usually have constants (like "2" or "c") and must have simple variables (like "x" or "y").

Examples: These are linear equations:

		y = 3x − 6
		y − 2 = 3(x + 1)
		y + 2x − 2 = 0
		5x = 6
		y/2 = 3

But the variables (like "x" or "y") in Linear Equations do NOT have:

• Exponents (like the 2 in x²)
• Square roots, cube roots, etc

Examples: These are NOT linear equations:

		y2 − 2 = 0
		3√x − y = 6
		x3/2 = 16

Fraction

Fractions

A fraction is a part of a whole

Slice a pizza, and we get fractions:

1/2	1/4	3/8
(One-Half)	(One-Quarter)	(Three-Eighths)

The top number says how many slices wehave. 
The bottom number says how many equal slices it was cut into.

Have a try yourself.

Thanks

Decimal

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Decimals

A Decimal Number (based on the number 10) contains a Decimal Point.

First, let's have an example:

Here is the number"forty-five and six-tenths"written as a decimal number:

The decimal point goes between Ones and Tenths.

45.6 has 4 Tens, 5 Ones and 6 Tenths, like this:

Now, let's discover how it all works ...

Place Value

It is all about Place Value !

When we write numbers, the position(or "place") of each digit
is important.

In the number 327:

• the "7" is in the Ones position, meaning 7 ones (which is 7),
• the "2" is in the Tens position meaning 2 tens (which is twenty),
• and the "3" is in the Hundreds position, meaning 3 hundreds.

"Three Hundred Twenty Seven"

	As we move left, each position is 10 times bigger!
	Tens are 10 times bigger than Ones Hundreds are 10 times bigger thanTens

... and ...

As we move right, each position is 10 times smaller.
From Hundreds, to Tens, to Ones

But what if we continue past Ones? What is 10 times smallerthan Ones? 110ths (Tenths) are!

But we must first put a decimal point, so we know exactly where the Ones position is:
"three hundred twenty seven and four tenths" but we usually just say "three hundred twenty seven point four"