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Since the room is rectangular the area is the length times the width, so
the
amount of rug needed (or the area) is 12 1/2 * 10 3/4 feet.
This problem involves multiplying fractions, so let's spend a few minutes discussing multiplication.
Multiplying fractions in some ways is much easier than adding or subtracting fractions,
because you no longer need a common denominator.
However it does have something to do with dieting: what you have to do is reduce,reduce,reduce.
To multiply two fractions all you have to do is
multiply the
numerator by numerator, and
denominator by denominator,
just like you have been doing each time you changed a fraction to one with the
LCD.
However, then you have the arduous process of reducing the fraction to lowest terms.
Instead, we'll reduce the fractions as much as we can and then do the multiplication.
Okay how do we go about reducing the fractions as much as we can?
The answer is we are going to actually reduce the fractions four times.
Each of the fractions gets reduced to lowest terms just as before
and then
we're going to reduce the fractions along two diagonals
the numerator of the first fraction and the denominator of the second fraction
and
the denominator of the first fraction and the numerator of the second fraction
A few examples should make this clear.
6/15 * 30/32Okay this next one will be a little tougher, then it's you turn
Step 1: 6/15 = (3*2)/(3*5) = 2/5
Step 2: 30/32 = (2*15)/(2*16) = 15/16
So far 6/15 * 30/32 = 2/5 * 15/16
Step 3: Now let's examine the first diagonal: the numerator of the first fraction(2) and the denominator of the second fraction(16).
2/5 * 15/16 = (2*1)/5 * 15/(2*8) = 1/5 * 15/8
So far 6/15 * 30/32 = 1/5 * 15/8
Step 4: Now let's examine the second diagonal: the denominator of the first fraction(5) and the numerator of the second fraction(15).
1/5 * 15/8 = 1/(5*1) * (5*3)/8 = 1/1 * 3/8
So far 6/15 * 30/32 = 1/1 * 3/8
Step 5: Now we do the actual multiplication
1/1 * 3/8 = (1*3)/(1*8) = 3/8
6/15 * 30/32 = 3/8
8/18 * 15/28Okay are you ready to try your new wheels out?
Step 1: 8/18 = (4*2)/(9*2) = 4/9
Step 2: 15/28 is alread in lowest terms
So far 8/18 * 15/28 = 4/9 * 15/28
Step 3: Now let's examine the first diagonal: the numerator of the first fraction(8) and the denominator of the second fraction(28).
4/9 * 15/28 = (4*1)/9 * 15/(4*7) = 1/9 * 15/7
So far 8/18 * 15/28 = 1/9 * 15/7
Step 4: Now let's examine the second diagonal: the denominator of the first fraction(9) and the numerator of the second fraction(15).
1/9 * 15/7 = 1/(3*3) * (5*3)/7 = 1/3 * 5/7
So far 8/18 * 15/28 = 1/3 * 5/7
Step 5: Now we do the actual multiplication
1/3 * 5/7 = (1*5)/(3*7) = 5/21
8/18 * 15/28 = 5/21
You're doing fineExercise 1 2/3 * 12/10 Go to the Fraction home page
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Exercise 2 4/5 * 15/16 Go to the Fraction home page
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Exercise 3 9/14 * 16/27 Go to the Fraction home page
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Exercise 4 14/25 * 30/32 Go to the Fraction home page
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Exercise 5 10/16 * 4/3 Go to the Fraction home page
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3 3/5 * 2 1/8Okay, this next one is a little tricky, so pay attention
3 3/5 = 18/5
2 1/8 = 17/8
3 3/5 * 2 1/8 = 18/5 * 17/8
18/5 is is in lowest terms
17/8 is in lowest terms
18/5 * 17/8
the 18 and 8 are both divisible by 2 so 18/5 * 17/8 = 9/5 * 17/4
the 5 and 17 do not share any factors
3 3/5 * 2 1/8 = 9/5 * 17/4 = (9*17)/(5*4) = 153/20
153/20 = 7 13/20 which is already in lowest terms
3 3/5 * 2 1/8 = 7 13/20
25 * 2 1/5Now it's your turn again (isn't it fun sharing-we're taking turns)
first of all, think of 25 as 25/1
2 1/5 = 11/5
25 * 2 1/5 = 25/1 * 11/5 = (5*5)/1 * 11/(5*1) = 5/1 * 11/1 = (5*11)/(1*1) = 55/1 = 55.
25 * 2 1/5 = 55
Now back to our rugExercise 1 2/3 * 1 1/6 Go to the Fraction home page
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Exercise 2 2 4/12 * 9/14 Go to the Fraction home page
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Exercise 3 100 * 1 1/3
[HINT: Consider 100 as 100/1] Go to the Fraction home page
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Exercise 4 3 1/2 * 5 1/3 Go to the Fraction home page
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Exercise 4 2 1/3 * 1/5 Go to the Fraction home page
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You have a rectangular room in your house that you want to buy carpeting for
the measurements of the room are 12 1/2 by 10 2/5 feet.
How many square feet of rug do you need?
Since the room is rectangular the are is the length times the width, so the amount of rug needed (or the area) is 12 1/2 * 10 3/4 feet.
Answer1: It would be better to leave the room with the floorboards.
That way we don't have to worry about this problem at all
Answer2: 12 1/2 * 10 2/5 feet.
12 1/2 = 25/2
10 2/5 = 52/5
Both 25/2 and 52/5 are in lowest terms
25/2 * 52/5 = 5/2 * 52/1 = 5/1 * 26/1 = 130/1 = 130
You need 130 square feet of carpeting
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Basically we have to divide 3 3/4 by 1/4 to arrive at the answer.
We'll come back to this problem after examining how to divide fractions.
Remember when subtraction turned out to be just another form of addition?
Well division is multiplication with just one extra step.
(like you need an extra step-6 wasn't enough)
What is that step you may ask? (go ahead, ask)
The divsor is turned upside down and then it's a multiplication problem
so here goes
4/5 ¸ 2/3 = 4/5 * 3/2Mixed fractions work th same way, except first change the fractions to improper fractions and then flip the divisor
I took the divisor 2/3, turned it upside down to make it 3/2, and now it's a multiplication problem.
4/5 * 3/2 = 2/5 * 3/1 = 6/5 = 1 1/5
2 3/8 ¸ 1 1/2By now you should be ready to show off, so here's your chance
2 3/8 = 21/8
1 1/2 = 3/2
2 3/8 divided by 1 1/2 = 21/8 divided by 3/2
Flip the 3/2 to 2/3
2 3/8 ¸ 1 1/2 = 21/8 * 2/3
Both 21/8 and 2/3 are already in lowest terms
21 and 3 are both divisible by 3 21/8 * 2/3 = 7/8 * 2/1
8 and 2 are both divisible by 2 7/8 * 2/1 = 7/4 * 1/1 = 7/4
7/4 = 1 3/4 which is already in lowest terms
2 3/8 divided by 1 1/2 = 21/8 * 2/3 = 7/4 = 1 3/4
Exercise 1 8/9 ¸ 5/6 Go to the Fraction home page
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Exercise 2 6/7 ¸ 2 Go to the Fraction home page
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Exercise 3 9 3/4 ¸ 3 1/4 Go to the Fraction home page
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Exercise 4 2 5/8 ¸ 1 1/4 Go to the Fraction home page
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Exercise 5 22/24 ¸ 2 5/14 Go to the Fraction home page
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Exercise 6 3 1/8 ¸ 1 1/2 Go to the Fraction home page
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3 3/4 = 15/4
3 3/4 divided by 1/4 = 15/4 divided by 1/4 = 15/4 * 4/1
15/4 * 4/1 = 15/1 * 1/1 = 15
Answer: You'll make approximately 15 sandwiches
Now you only have one more section to go!
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