Various contexts and models are introduced to help students make sense of when multiplication is appropriate.In Problem 2.1 students develop an understanding of multiplication with simple fractions. Problems 2.2 and 2.3 focus on multiplication with fraction, mixed number, and whole-number combinations. Use your knowledge of fractions, equivalence of fractions, and properties of numbers to develop algorithms for adding, subtracting, multiplying, and dividing fractions Recognize when addition, subtraction, multiplication, or division is the appropriate operation to solve a problem.
Multiply the tops, multiply the bottoms.
There are 3 simple steps to multiply fractions
1. Multiply the top numbers (the numerators).
2. Multiply the bottom numbers (the denominators).
3. Simplify the fraction if needed.
Example:
Step 1. Multiply the top numbers:
12 × 25 = 1 × 2 = 2
Step 2. Multiply the bottom numbers:
12 × 25 = 1 × 22 × 5 = 210
Step 3. Simplify the fraction:
210 = 15
With Pizza
Here you can see it with pizza ...
Do you see that half of two-fifths is two-tenths?
Do you also see that two-tenths is simpler as one-fifth?
With Pen and Paper
And here is how to do it with a pen and paper (press the play button):
Another Example:
Step 1. Multiply the top numbers:
13 × 916 = 1 × 9 = 9
Step 2. Multiply the bottom numbers:
13 × 916 = 1 × 93 × 16 = 948
Step 3. Simplify the fraction:
948 = 316
(This time we simplified by dividing both top and bottom by 3)
The Rhyme
2.2 Multiply A Fraction By A Whole Numbermr. Mac's Page Sheet
♫ 'Multiplying fractions: no big problem,
Top times top over bottom times bottom.
'And don't forget to simplify,
Before it's time to say goodbye' ♫
Fractions and Whole Numbers
2.2 Multiply A Fraction By A Whole Numbermr. Mac's Page Printable
What about multiplying fractions and whole numbers?
Make the whole number a fraction, by putting it over 1.
Example: 5 is also 51
Then continue as before.
Example:
Make 5 into 51 :
23 × 51
Now just go ahead as normal.
Multiply tops and bottoms:
2.2 Multiply A Fraction By A Whole Numbermr. Mac's Page Number
23 × 51 = 2 × 53 × 1 = 103
The fraction is already as simple as it can be.
Answer = 103
With Pen and Paper
And here is how to do it with a pen and paper (press the play button):
Another Example:
Step 1. Multiply the top numbers:
13 × 916 = 1 × 9 = 9
Step 2. Multiply the bottom numbers:
13 × 916 = 1 × 93 × 16 = 948
Step 3. Simplify the fraction:
948 = 316
(This time we simplified by dividing both top and bottom by 3)
The Rhyme
2.2 Multiply A Fraction By A Whole Numbermr. Mac's Page Sheet
♫ 'Multiplying fractions: no big problem,
Top times top over bottom times bottom.
'And don't forget to simplify,
Before it's time to say goodbye' ♫
Fractions and Whole Numbers
2.2 Multiply A Fraction By A Whole Numbermr. Mac's Page Printable
What about multiplying fractions and whole numbers?
Make the whole number a fraction, by putting it over 1.
Example: 5 is also 51
Then continue as before.
Example:
Make 5 into 51 :
23 × 51
Now just go ahead as normal.
Multiply tops and bottoms:
2.2 Multiply A Fraction By A Whole Numbermr. Mac's Page Number
23 × 51 = 2 × 53 × 1 = 103
The fraction is already as simple as it can be.
Answer = 103
Or you can just think of the whole number as being a 'top' number:
Example:
Multiply tops and bottoms:
3 × 29 = 3 × 29 = 69
Simplify:
69 = 23
Mixed Fractions
You can also read how to multiply mixed fractions
