Recipe Design

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[Addition/Subtraction]:Adding Fractions

Adding Fractions

There are 3 Simple Steps to add fractions:

Step 1: Make sure the bottom numbers (the denominators) are the same
Step 2: Add the top numbers (the numerators), put the answer over denominatorthe
Step 3: Simplify the fraction (if needed)

Example 1:

1	+	1
4		4

Step 1. The bottom numbers (the denominators) are already the same. Go straight to step 2.

Step 2. Add the top numbers and put the answer over the same denominator:

1	+	1	=	1 + 1	=	2
4		4		4		4

Step 3. Simplify the fraction:

2	=	1
4		2

In picture form it looks like this:

1/4	+	1/4	=	2/4	=	1/2

... and do you see how 2/4 is simpler as 1/2 ? (see Equivalent Fractions.)

  

Example 2:

1	+	1
3		6

Step 1: The bottom numbers are different. See how the slices are different sizes?

1/3	+	1/6	=	?

We need to make them the same before we can continue, because we can't add them like that.

The number "6" is twice as big as "3", so to make the bottom numbers the same we can multiply the top and bottom of the first fraction by 2, like this:

× 2

1	=	2
3		6

× 2

Important: you multiply both top and bottom by the same amount,
to keep the value of the fraction the same

Now the fractions have the same bottom number ("6"), and our question looks like this:

2/6	+	1/6

The bottom numbers are now the same, so we can go to step 2.

Step 2: Add the top numbers and put them over the same denominator:

2	+	1	=	2 + 1	=	3
6		6		6		6

In picture form it looks like this:

2/6	+	1/6	=	3/6

Step 3: Simplify the fraction:

3	=	1
6		2

In picture form the whole answer looks like this:

2/6	+	1/6	=	3/6	=	1/2

With Pen and Paper

And here is how to do it with a pen and paper (press the play button):

Play with it! Try the Adding Fractions Animation.

A Rhyme To Help You Remember

♫ "If adding or subtracting is your aim,
The bottom numbers must be the same!
♫ "Change the bottom using multiply or divide,
But the same to the top must be applied,
♫ "And don't forget to simplify,
Before its time to say good bye"

Example 3:

1	+	1
3		5

Again, the bottom numbers are different (the slices are different sizes)!

1/3	+	1/5	=	?

But let us try dividing them into smaller sizes that will each be the same:

5/15	+	3/15

The first fraction: by multiplying the top and bottom by 5 we ended up with 5/15 :

× 5

1	=	5
3		15

× 5

The second fraction: by multiplying the top and bottom by 3 we ended up with 3/15 :

× 3

1	=	3
5		15

× 3

The bottom numbers are now the same, so we can go ahead and add the top numbers:

5/15	+	3/15	=	8/15

The result is already as simple as it can be, so that is the answer: 8/15

Making the Denominators the Same

In the previous example how did we know to cut them into 1/15ths to make the denominators the same? Read how to do this using either one of these methods:

• Common Denominator Method, or the
• Least Common Denominator Method

They both work, use whichever you prefer!

Example: Cupcakes

You want to make and sell cupcakes:

• A friend can supply the ingredients, if you give them ¹/₃of sales
• And a market stall costs ¹/₄ of sales

How much is that altogether?

We need to add ¹/₃ and ¹/₄

1	+	1	=	?
3		4		?

First make the bottom numbers (the denominators) the same.

Multiply top and bottom of ¹/₃ by 4:

1 × 4	+	1	=	?
3 × 4		4		?

And multiply top and bottom of ¹/₄ by 3:

1 × 4	+	1 × 3	=	?
3 × 4		4 × 3		?

Now do the calculations:

4	+	3	=	4+3	=	7
12		12		12		12

Answer: ⁷/₁₂ of sales go in ingredients and market costs.

[Knowledge]:Ordering Numbers

Ordering Numbers

"Waiter, I would like a 7 and a 3, please..."
NO, not THAT type of ordering. I mean putting them in order ...

To put numbers in order, place them from lowest (first) to highest (last). This is called "Ascending Order" (think of ascending a mountain)

Example: Place 17, 5, 9 and 8 in ascending order. Answer: 5, 8, 9, 17

Sometimes you want the numbers to go the other way, from highest down to lowest, this is called "Descending Order" (think of a "steep descent")

Example: Place 17, 5, 9 and 8 in descending order. Answer: 17, 9, 8, 5

Practice by neatening up your friends. Measure their heights, then place them in ascending order of height. Try it again, but use their weights.

[Knowledge]:Rounding

Rounding

What is "Rounding" ?

Rounding means reducing the digits in a number while trying to keep its value similar. The result is less accurate, but easier to use. Example: 73 rounded to the nearest ten is 70, because 73 is closer to 70 than to 80.

Common Method

There are several different methods for rounding, but here we will only look at the common method, the one used by most people ...

How to Round Numbers

• Decide which is the last digit to keep
• Leave it the same if the next digit is less than 5 (this is called rounding down)
• But increase it by 1 if the next digit is 5 or more (this is called rounding up)

Example: Round 74 to the nearest 10

• We want to keep the "7" as it is in the 10s position
• The next digit is "4" which is less than 5, so no change is needed to "7"

Answer: 70

(74 gets "rounded down")

Example: Round 86 to the nearest 10

• We want to keep the "8"
• The next digit is "6" which is 5 or more, so increase the "8" by 1 to "9"

Answer: 90

(86 gets "rounded up")

So: when the first digit removed is 5 or more, increase the last digit remaining by 1.

Why does 5 go up ?

5 is in the middle ... so we could go up or down. But we need a method that everyone agrees to.

So think about sport: you should have the same number of players on each team, right?

0,1,2,3 and 4 are on team "down" 5,6,7,8 and 9 are on team "up"

And that is the "common" method of rounding. Read about other methods of rounding.

Rounding Decimals

First you need to know if you are rounding to tenths, or hundredths, etc. Or maybe to "so many decimal places". That tells you how much of the number will be left when you finish.

Examples	Because ...
3.1416 rounded to hundredths is 3.14	... the next digit (1) is less than 5
1.2635 rounded to tenths is 1.3	... the next digit (6) is 5 or more
1.2635 rounded to 3 decimal places is 1.264	... the next digit (5) is 5 or more

Rounding Whole Numbers

You may want to round to tens, hundreds, etc, In this case you replace the removed digits with zero.

Examples	Because ...
134.9 rounded to tens is 130	... the next digit (4) is less than 5
12,690 rounded to thousands is 13,000	... the next digit (6) is 5 or more
1.239 rounded to units is 1	... the next digit (2) is less than 5

Rounding to Significant Digits

To round to "so many" significant digits, count digits from left to right, and then round off from there.

Note: if there are leading zeros (such as 0.006), don't count them because they are only there to show how small the number is.

Examples	Because ...
1.239 rounded to 3 significant digits is 1.24	... the next digit (9) is 5 or more
134.9 rounded to 1 significant digit is 100	... the next digit (3) is less than 5
0.0165 rounded to 2 significant digits is 0.017	... the next digit (5) is 5 or more

Significant Digit Calculator

(Try increasing or decreasing the number of significant digits. Also try numbers with lots of zeros in front of them like 0.00314, 0.0000314 etc)