Download 1.02 Fractions Fact Sheet

1.02 Fractions Fact Sheet
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Fractions show parts of a whole.
The denominator (number on the bottom) shows how many pieces are in the whole thing.
The numerator (number on the top) shows how many pieces someone or something has.
For example:
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¾ or 3/4 of a candy bar
3 is the numerator, and you have 3 pieces of the candy bar
4 is the denominator and there are 4 pieces in the whole candy bar
A mixed number is a whole number and a fraction. It means you have a whole portion and
part of another portion.
For example:
3½ or 3 1/2 of a pizza
3 is the whole number and ½ is the fraction. You have 3 whole pizzas plus another half of a
pizza.
An improper fraction is a fraction where the numerator is larger than the denominator.
It can be changed into a mixed number.
For example:
7/4 of a pie
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There are 4 pieces in a whole pie. You have 7 pieces, so you have enough to
make one whole pie and have 3 pieces left over.
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You have
1¾ or 1 3/4 pies.
7/4 is the same as 1¾.
To add fractions, the fractions must have the same denominator. Add the numerators and
keep the denominator the same.
For example: 4/6 + 1/6 = 5/6
If the denominators are not the same, you must make them the same or find common
denominators. The easiest way to do this is to look at the highest of the denominators.
For example: 2/3 + 2/6 = _____
 6 is the highest denominator.
 To change the 3 (the other denominator) into a 6, you must multiply it by 2.
 If you multiply the denominator by a number, you must multiply the numerator by
the same number. So, multiply the numerator 2 by 2. (2 x 2 = 4)
 The fraction is now 4/6 and the denominators are the same.
 Add numerators, 4 + 2 = 6, and keep the denominators the same. 6/6 or 1 whole.
 Remember: You must multiply the numerator and denominator by the same number.
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To subtract fractions, the fractions must have the same denominator. Subtract the
numerators and keep the denominator the same.
For example: 4/6 - 1/6 = 3/6
If the denominators are not the same, you must make them the same or find common
denominators. The easiest way tot do this is to look at the highest of the denominators.
For example: 9/12 – 1/3 = _____
 12 is the highest denominator.
 To change the 3 to a 12 you must multiply it by 4.
 If you multiply the denominator by a number, you must multiply the numerator by
the same number. So, multiply the numerator 1 by 4. (1 x 4 = 4)
 The fraction is now 4/12 and the denominators are the same.
 Subtract numerators, 9 – 4 = 5. and keep the denominators the same, 5/12.
 Remember: You must multiply the numerator and denominator by the same
number.
Any fraction that has the same numerator and denominator is equal to 1 whole.
For example: 3/3 = 1 whole
7/7 = 1 whole
20/20 = 1 whole
To simplify a fraction, you make the numerator and denominator as small as possible by
dividing by the same number.
For example: 3/12
 Both the numerator and denominator can be divided by 3, so the fraction can be
reduced.
 3  3 = 1 (numerator) and 12  3 = 4 (denominator) so 3/12 can be reduced to ¼.
You can simplify any fraction that has an even number for both the numerator and
denominator. Divide each number by 2 and continue until it cannot be divided by 2 evenly.
For example: 10/16
 10  2 = 5 and 16  2 = 8, so 10/16 can be reduced to 5/8.
 Another example: 12/16
 12  2 = 6 and 16  2 = 8 to equal 6/8. Both numbers are still even, so they can be
divided by 2 again.
 6 2 = 3 and 8  2 = 4 to equal ¾. 3 is an odd number, so it cannot be reduced any
further.
You need to be able to make conversions between these fraction families:
 halves, fourths, and eights (1/2, 1/4, 1/8)
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thirds, sixths, and twelfths (1/3, 1/6, 1/12)
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fifths, tenths, hundredths, and thousandths (1/5, 1/10, 1/100, 1/1000)
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When converting a fraction to a decimal, divide the numerator by the denominator.
For example: ¾ = 3  4 = .75
When converting a decimal to a fraction, say the fraction aloud.
 If there is one number after the decimal, the denominator is 10.
 If there are two numbers after the decimal, the denominator is 100.
 If there are three numbers after the decimal, the denominator is 1,000.
 The numerator is the original number without any decimals.
For example: .72 is seventy-two hundredths
 the denominator is 100
 the numerator is 72
 the fraction is 72/100
Another example: .4 is four tenths
 the denominator is 10
 the numerator is 4
 the fraction is 4/10 ( and it can be reduced to 2/5 by dividing each number
by 2)
Another example: .395 is three hundred ninety five thousandths
 the denominator is 1000
 the numerator is 395
 the fraction is 395/1000
When comparing fractions, it is easiest to change them into decimals by dividing the
numerator by denominator. Fix the calculator to 2 places if you have a TI-15.
For example: Place the fractions in ascending order (smallest to largest)
1/2
3/12
5/6
3/8
12 = .50
312= .25
56= .83
38=.37
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Think about money when you compare the numbers with decimals.
The smallest amount is .25 or 25 cents, which is 3/12, so it is first.
The next smallest amount is .37 or 37 cents, which is 3/8.
The next smallest amount is .50 or 50 cents, which is 1/2.
The largest amount is .83 or 83 cents, which is 5/6.
In ascending order the fractions are 3/12, 3/8, 1/2, and 5/6.
To put the fractions in descending order (largest to smallest) you follow the same steps, but
put the largest numbers first and end with the smallest number,.
Hint: ascending starts with a, like the alphabet, so you start at the beginning and go up.
descending starts with d, so you start with the biggest number and go down
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To compare fractions without a calculator, think about halves and compare each fraction to a
half.
For example: Place the fractions is ascending order (smallest to largest)
2/8
half of eight would
be four, so 2/8 is
less than half
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1/2
this is exactly one
half
8/9
if there were nine
slices and I had
eight of them, I
would only be one
slice away from
having the whole
thing, so 8/9 is more
than half
4/7
half of seven would
be 3½ and I have 4
so I have just a little
bit more than half
Now I know that 2/8 is less than half, ½ is exactly half, 4/7 is just a little bit more
than half and 8/9 is almost the whole thing, so I can put the fractions in order.
ascending order would be 2/8, 1/2, 4/7, 8/9
You can also use the clock to help you compare fractions. Always start at 12 and go to the
center before you go to the next number.
 Draw a line from the 12 to the 3 and you have ¼ of the clock.
 Draw a line from 12 to 6 and you have ½ of the clock.
 Draw a line from the 12 to the 9 and you have ¾ of the clock.
 Draw a line from the 12 to the 4 and you have 1/3 of the clock.
 Draw a line from the 12 to the 8 and you have 2/3 of the clock.
 Draw a line from the 12 to the 2 and you have 1/6 of the clock.
 Draw a line from the 12 to the 4 and you have 2/6 or 1/3 of the clock.
 Draw a line from the 12 to the 6 and you have 3/6 or ½ of the clock.
 Draw a line from the 12 to the 8 and you have 4/6 or 2/3 of the clock.
 Draw a line from the 12 to the 10 and you have 5/6 of the clock.
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