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1 FRACTIONS
INSTRUCTION SHEET
CONVERSIONS
Changing a Mixed Number to an Improper Fraction
Mixed number 4 EMBED Equation.3 (contains a whole number and a fraction)
Improper fraction - EMBED Equation.3 (numerator is larger than denominator)
Step 1 Multiply the denominator and the whole number
Step 2 Add this answer to the numerator; this becomes the new numerator
Step 3 Carry the original denominator over
Example #1: 3 EMBED Equation.3 = 3 8 + 1 = 25
EMBED Equation.3
Example #2: 4 EMBED Equation.3 = 4 9 + 4 = 40
EMBED Equation.3
Changing an Improper Fraction to a Mixed Number
Step 1 Divide the numerator by the denominator
Step 2 The answer from step 1 becomes the whole number
Step 3 The remainder becomes the new numerator
Step 4 The original denominator carries over
Example #1: EMBED Equation.3 = 47 5 or 5 EMBED Equation.3 = 5 EMBED Equation.3 = 9 EMBED Equation.3
2
Example #2: EMBED Equation.3 = 2 EMBED Equation.3 = 2 EMBED Equation.3 = 4 EMBED Equation.3
Reducing Fractions
Step 1 Find a number that will divide into both the numerator and the
denominator
Step 2 Divide numerator and denominator by this number
Example #1: EMBED Equation.3 = EMBED Equation.3 (because both 10 and 15 are divisible by 5)
Example #2: EMBED Equation.3 = EMBED Equation.3 (because both 4 and 8 are divisible by 4)
Raising Fractions to Higher Terms When a New Denominator is Known
Step 1 Divide the new denominator by the old denominator
Step 2 Multiply the numerator by the answer from step 1 to find the new
numerator
*Note: If the original number is a mixed number, convert it to an improper
fraction before raising to higher terms (see Example #2)
Example #1: EMBED Equation.3 = EMBED Equation.3 becomes EMBED Equation.3 = EMBED Equation.3 because 12 3 = 4
and 2 4 = 8
Example #2: 2 EMBED Equation.3 = EMBED Equation.3 becomes EMBED Equation.3 = EMBED Equation.3 becomes EMBED Equation.3 = EMBED Equation.3
because 20 5 = 4 and 11 4 = 44
E. Converting fractions to decimals
Step 1 - Divide the numerator (the top number) by the denominator (the
bottom number) of the fraction.
Example: 5
8
8 EMBED Equation.3 ( Add as many zeros as needed.
48
20
16
40
40
0
F. Converting decimals to fractions
Step 1 - Determine the place value of the last number in the decimal; this
becomes the denominator.
Step 2 Make the decimal number your numerator.
Step 3 - Reduce your answer.
Example: .625 - the 5 is in the thousandths column, therefore,
.625 = EMBED Equation.3 = reduces to EMBED Equation.3
(Hint: Your denominator will have the same number of zeros as there are decimal
digits in the decimal number you started with - .625 has three decimal digits so the
denominator will have three zeros before reductions.)
G. Multiplying Simple Fractions
Step 1 Multiply the numerators
Step 2 Multiply the denominators
Step 3 Reduce the answer to lowest terms
Example: EMBED Equation.3 EMBED Equation.3 = EMBED Equation.3 which reduces to EMBED Equation.3
H. Multiplying Mixed Numbers
Step 1 Convert the mixed numbers to improper fractions first
Step 2 Multiply the numerators
Step 3 Multiply the denominators
Step 4 Reduce the answer to lowest terms
Example: 2 EMBED Equation.3 1 EMBED Equation.3 = EMBED Equation.3 EMBED Equation.3 = EMBED Equation.3 which then reduces to 3 EMBED Equation.3
*Note When opposing numerators and denominators are divisible by a common number, you may reduce the numerator and denominator before multiplying. In the above example, after converting the mixed numbers to improper fractions, you will see that the 3 in the numerator and the opposing 3 in the denominator could have been reduced by dividing both numbers by 3, resulting in the following reduced fraction:
EMBED Equation.3 EMBED Equation.3 = EMBED Equation.3 = 3 EMBED Equation.3
I. Dividing Simple Fractions
Step 1 Change division sign to multiplication
Step 2 Change the fraction following the multiplication sign to its
reciprocal (flip the fraction around so the old denominator is the
new numerator and the old numerator is the new denominator)
Step 3 - Multiply the numerators
Step 4 Multiply the denominators
Step 5 Change the answer to lowest terms
Example: EMBED Equation.3 EMBED Equation.3 = becomes EMBED Equation.3 EMBED Equation.3 which when solved is EMBED Equation.3
J. Dividing Mixed Numbers
Step 1 Convert the mixed number or numbers to improper fraction
Step 2 Change the division sign to multiplication
Step 3 Change the fraction following the multiplication sign to its
reciprocal (flip the fraction around so the old denominator is the
new numerator and the old numerator is the new denominator)
Step 4 - Multiply the numerators
Step 5 Multiply the denominators
Step 6 Change the answer to lowest terms
Example: 3 EMBED Equation.3 2 EMBED Equation.3 = becomes EMBED Equation.3 EMBED Equation.3 becomes EMBED Equation.3 EMBED Equation.3 =
which when solved is EMBED Equation.3 EMBED Equation.3 = EMBED Equation.3 which simplifies to 1 EMBED Equation.3
K. Adding and Subtracting Fractions
Step 1 Find a common denominator (a number that both denominators
will go into)
Step 2 Raise each fraction to higher terms as needed
Step 3 Add or subtract the numerators only as shown
Step 4 Carry denominator over
Step 5 Change the answer to lowest terms
Example #1: EMBED Equation.3 + EMBED Equation.3 = Common denominator is 8 because both 2 and
8 will go into 8
EMBED Equation.3 = EMBED Equation.3
+ EMBED Equation.3 = EMBED Equation.3
EMBED Equation.3 which simplifies to 1 EMBED Equation.3
Example #2: 4 EMBED Equation.3 EMBED Equation.3 = Common denominator is 20 because both 4
and 5 will go into 20
4 EMBED Equation.3 = 4 EMBED Equation.3
EMBED Equation.3 = EMBED Equation.3
4 EMBED Equation.3
Example #3: 2 EMBED Equation.3 = 2 EMBED Equation.3 = 12 EMBED Equation.3 + EMBED Equation.3 = 1 EMBED Equation.3
1 EMBED Equation.3 = 1 EMBED Equation.3 = 1 EMBED Equation.3 = 1 EMBED Equation.3
EMBED Equation.3 **
**Note In this problem you must borrow from the whole number to adjust your fraction so that you can subtract. However, you may do this problem another way. Simply change the mixed number to improper form before finding the common denominator to prevent having to borrow.
2 EMBED Equation.3 = EMBED Equation.3 = EMBED Equation.3
1 EMBED Equation.3 = EMBED Equation.3 = EMBED Equation.3
EMBED Equation.3
FRACTIONS
PRACTICE SHEET
Write as an improper fraction.
1 EMBED Equation.3 2. 4 EMBED Equation.3 3. 1 EMBED Equation.3 4. 2 EMBED Equation.3
5. 2 EMBED Equation.3 6. 2 EMBED Equation.3 7. 1 EMBED Equation.3 8. 3 EMBED Equation.3
9. 7 EMBED Equation.3 10. 5 EMBED Equation.3 11. 3 EMBED Equation.3 12. 6 EMBED Equation.3
Write as a mixed number.
1. EMBED Equation.3 2. EMBED Equation.3 3. EMBED Equation.3 4. EMBED Equation.3
5. EMBED Equation.3 6. EMBED Equation.3 7. EMBED Equation.3 8. EMBED Equation.3
9. EMBED Equation.3 10. EMBED Equation.3 11. EMBED Equation.3 12. EMBED Equation.3
Write in lowest terms.
1. EMBED Equation.3 2. EMBED Equation.3 3. EMBED Equation.3 4. EMBED Equation.3
5. EMBED Equation.3 6. EMBED Equation.3 7. EMBED Equation.3 8. EMBED Equation.3
5. 1 EMBED Equation.3 10. 2 EMBED Equation.3 11. 5 EMBED Equation.3 12. 3 EMBED Equation.3
Find the missing numerator by raising the fraction to higher terms.
1. EMBED Equation.3 = EMBED Equation.3 2. EMBED Equation.3 = EMBED Equation.3 3. EMBED Equation.3 = EMBED Equation.3 4. EMBED Equation.3 = EMBED Equation.3
5. 5 EMBED Equation.3 = EMBED Equation.3 6. 1 EMBED Equation.3 = EMBED Equation.3 7. 1 EMBED Equation.3 = EMBED Equation.3 8. 2 EMBED Equation.3 = EMBED Equation.3
Convert the following fractions into decimals.
1. EMBED Equation.3 2. EMBED Equation.3 3. EMBED Equation.3 4. EMBED Equation.3 5. EMBED Equation.3 6. EMBED Equation.3
Convert the following decimals to fractions.
1. .225 2. .375 3. .0175 4. .95 5. .5 6. .45
Multiply.
1. EMBED Equation.3 EMBED Equation.3 = 2. EMBED Equation.3 EMBED Equation.3 = 3. EMBED Equation.3 EMBED Equation.3 = 4. EMBED Equation.3 EMBED Equation.3 =
5. EMBED Equation.3 EMBED Equation.3 = 6. EMBED Equation.3 EMBED Equation.3 = 7. EMBED Equation.3 EMBED Equation.3 = 8. EMBED Equation.3 EMBED Equation.3 =
9. EMBED Equation.3 10 = 10. 1 EMBED Equation.3 EMBED Equation.3 = 11. EMBED Equation.3 EMBED Equation.3 = 12. 14 EMBED Equation.3 =
13. EMBED Equation.3 1 EMBED Equation.3 = 14. 3 EMBED Equation.3 EMBED Equation.3 = 15. 18 1 EMBED Equation.3 = 16. 16 2 EMBED Equation.3 =
17. 6 EMBED Equation.3 1 EMBED Equation.3 = 18. 2 EMBED Equation.3 4 EMBED Equation.3 = 19. 4 EMBED Equation.3 4 EMBED Equation.3 = 20. 3 EMBED Equation.3 2 EMBED Equation.3 =
Divide as shown.
1. EMBED Equation.3 EMBED Equation.3 = 2. EMBED Equation.3 EMBED Equation.3 = 3. EMBED Equation.3 EMBED Equation.3 = 4. EMBED Equation.3 EMBED Equation.3 =
5. 4 EMBED Equation.3 = 6. 8 EMBED Equation.3 = 7. 9 EMBED Equation.3 = 8. EMBED Equation.3 EMBED Equation.3 =
9. EMBED Equation.3 EMBED Equation.3 = 10. EMBED Equation.3 EMBED Equation.3 = 11. EMBED Equation.3 4 = 12. 14 EMBED Equation.3 =
13. 15 EMBED Equation.3 = 14. 8 EMBED Equation.3 = 15. 1 EMBED Equation.3 1 EMBED Equation.3 = 16. 3 EMBED Equation.3 5 =
17. 6 EMBED Equation.3 2 EMBED Equation.3 18. 5 EMBED Equation.3 2 EMBED Equation.3 = 19. 2 EMBED Equation.3 1 EMBED Equation.3 = 20. 3 EMBED Equation.3 1 EMBED Equation.3 =
Add or subtract as shown.
1. EMBED Equation.3 + EMBED Equation.3 = 2. EMBED Equation.3 + EMBED Equation.3 = 3. EMBED Equation.3 + EMBED Equation.3 = 4. EMBED Equation.3 + EMBED Equation.3 =
5. EMBED Equation.3 + EMBED Equation.3 = 6. EMBED Equation.3 + 1 EMBED Equation.3 = 7. EMBED Equation.3 + EMBED Equation.3 = 8. 2 EMBED Equation.3 + 1 EMBED Equation.3 =
9. 1 EMBED Equation.3 + EMBED Equation.3 = 10. 2 EMBED Equation.3 + EMBED Equation.3 = 11. EMBED Equation.3 EMBED Equation.3 = 12. EMBED Equation.3 EMBED Equation.3 =
13. EMBED Equation.3 EMBED Equation.3 = 14. EMBED Equation.3 EMBED Equation.3 = 15. EMBED Equation.3 EMBED Equation.3 = 16. 1 EMBED Equation.3 EMBED Equation.3 =
17. 5 EMBED Equation.3 2 EMBED Equation.3 = 18. 3 EMBED Equation.3 1 EMBED Equation.3 = 19. 2 EMBED Equation.3 EMBED Equation.3 = 20. 4 EMBED Equation.3 1 EMBED Equation.3 =
Solve the word problems below using fractions.
The Cooper family decided to hike to Hillside Lake, approximat e l y 8 ]! m i l e s a w a y . A f t e r a n h o u r t h e l a k e w a s s t i l l 5 S! m i l e s a w a y . H o w f a r d i d t h e g r o u p h i k e s o f a r ?
W h i l e r i d i n g h e r b i k e , S u s a n b u r n s 4 5 0 c a l o r i e s e v e r y h o u r . B a s e d o n t h i s r a t e , h o w m a n y c a l o r i e s w i l l S u s a n b u r n i f s h e r i d e s t h e b i k e f o r 1?
Last Friday Tony worked for 7 hours. Express this time as a fraction of the day.
When an oil tank is EMBED Equation.3 full, it contains 5 gallons. How many gallons does it hold when full?
How many pieces of 10 EMBED Equation.3 inch bar can be cut from a stock 20 foot bar?
Byron purchased a box of candy at the store. On his way home he ate of the candy in the box. At dinner with friends later that night he served of what was left. If there are 6 chocolates now left in the box, how many did the box contain to start with?
Seth earns $560 per week. He has EMBED Equation.3 of his income withheld for federal taxes, EMBED Equation.3 of his income withheld for state taxes, and EMBED Equation.3 of his income withheld for medical coverage. How much income is left each week after those deductions?
A bolt extends through thick plywood, a wa s h e r t h a t i s [! t h i c k , a n d a n u t t h a t i s E M B E D E q u a t i o n . 3 t h i c k . T h e b o l t s h o u l d b e ]! l o n g e r t h a n t h e s u m o f t h e t h i c k n e s s o f t h e p l y w o o d , w a s h e r a n d n u t . W h a t i s t h e m i n i m u m l e n g t h o f t h e b o l t ?
A r e c i p e f o r F r e n c h t o a s t t h a t s e r v e s 6 c a l l s f o r c u p g r a n u l a t e d s u g a r , 1 c u p o f e v a p o r a t e d m i l k , S! t e a s p o o n o f v a n i l l a , a n d 1 2 t h i c k s l i c e s o f F r e n c h b r e a d . H o w m u c h o f e a c h i n g r e d i e n t i s n e e d e d t o s e r v e o n l y t h r e e ?
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C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 _ 1 1 4 9 6 0 7 9 0 0 F GnjGnj O l e
P
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F Microsoft Equation 3.0 DS Equation Equation.3 9q ( 4i
? 7 2 C o m p O b j f O b j I n f o E q u a t i o n N a t i v e : _ 1 1 4 9 6 0 7 9 4 6 F GnjGnj O l e
C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6
F Microsoft Equation 3.0 DS Equation Equation.3 9q p Դ
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F Microsoft Equation 3.0 DS Equation Equation.3 9q
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C o m p O b j f O b j I n f o E q u a t i o n N a t i v e : _ 1 1 4 9 6 0 8 0 4 2 F GnjGnj O l e
C o m p O b j f
? 1 2
F Microsoft Equation 3.0 DS Equation Equation.3 9q : Ԇ
4 5
F Microsoft Equation 3.0 DS Eq O b j I n f o E q u a t i o n N a t i v e 6 _ 1 1 4 9 6 0 8 0 2 7 F GnjGnj O l e
C o m p O b j f O b j I n f o E q u a t i o n N a t i v e : _ 1 1 4 9 6 0 8 9 8 0 F Gnj nj uation Equation.3 9q 0
? 1 0
F Microsoft Equation 3.0 DS Equation Equation.3 9q ( |
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C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 _ 1 1 4 9 6 0 8 9 3 7 F nj nj O l e
C o m p O b j f O b j I n f o
F Microsoft Equation 3.0 DS Equation Equation.3 9q 9
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F Microsoft Equation 3.0 DS Equation Equation.3 9q E q u a t i o n N a t i v e : _ 1 1 4 9 6 0 8 9 6 7 F nj nj O l e
C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 _ 1 1 4 9 6 0 9 0 0 4 F nj nj O l e
P:
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F Microsoft Equation 3.0 DS Equation Equation.3 9q 8w
? 1 0 C o m p O b j f O b j I n f o E q u a t i o n N a t i v e : _ 1 1 4 9 6 1 0 5 2 5 e F nj nj O l e
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F Microsoft Equation 3.0 DS Equation Equation.3 9q
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F Microsoft Equation 3.0 DS Equation Equation.3 9q _ 1 1 4 9 6 1 0 5 5 1 F nj nj O l e
C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 _ 1 1 4 9 6 1 0 5 7 0 F nj nj O l e
C o m p O b j f 0
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C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 _ 1 1 4 9 6 1 0 6 4 8 F nj nj uation Equation.3 9q
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F Microsoft Equation 3.0 DS Equation Equation.3 9q E q u a t i o n N a t i v e : _ 1 1 4 9 6 0 9 1 4 6 F nj nj O l e
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1 2 C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 _ 1 1 4 9 6 0 9 2 1 2 F nj nj O l e
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F Microsoft Equation 3.0 DS Equation Equation.3 9q P
7 1 0
F Microsoft Equation 3.0 DS Equation Equation.3 9q _ 1 1 4 9 6 0 9 2 5 1 F nj nj O l e
C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 _ 1 1 4 9 6 0 9 2 8 1 ) F nj nj O l e
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C o m p O b j f O b j I n f o
E q u a t i o n N a t i v e
: _ 1 1 4 9 6 0 9 4 2 9
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3 4 O l e
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C o m p O b j f O b j I n f o
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2 3
F Microsoft Equation 3.0 DS Equation Equation.3 9q E q u a t i o n N a t i v e 6 _ 1 1 4 9 6 0 9 4 9 4 F nj nj O l e
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Z
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4 3 C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 _ 1 1 4 9 6 0 9 5 5 5 $ ! F nj nj O l e
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F Microsoft Equation 3.0 DS Eq O b j I n f o - , E q u a t i o n N a t i v e - 6 _ 1 1 4 9 6 0 9 6 3 6 0 F nj nj O l e
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3 4 O l e
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B t
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G C o m p O b j H J H f O b j I n f o K J E q u a t i o n N a t i v e K :
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F Microsoft Equation 3.0 DS Equation Equation.3 9q _ 1 1 4 9 6 0 9 8 2 5 N F s"njs"nj O l e
L C o m p O b j M O M f O b j I n f o P O E q u a t i o n N a t i v e P 6 _ 1 1 4 9 6 0 9 9 3 8 S F s"njs"nj O l e
Q C o m p O b j R T R f س t
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F Microsoft Equation 3.0 DS Eq O b j I n f o U T E q u a t i o n N a t i v e U 6 _ 1 1 4 9 6 0 9 9 6 8 X F s"njs"nj O l e
V C o m p O b j W Y W f O b j I n f o Z Y E q u a t i o n N a t i v e Z 6 _ 1 1 4 9 6 0 9 9 9 8 V ` ] F s"njs"nj uation Equation.3 9q Ȍ 0
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1 1 6 O l e
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` C o m p O b j a c a f O b j I n f o d c
F Microsoft Equation 3.0 DS Equation Equation.3 9q
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F Microsoft Equation 3.0 DS Equation Equation.3 9q E q u a t i o n N a t i v e d 6 _ 1 1 4 9 6 1 0 1 6 1 [ y g F s"njs"nj O l e
e C o m p O b j f h f f O b j I n f o i h E q u a t i o n N a t i v e i 6 _ 1 1 4 9 6 1 0 2 0 0 l F s"njs"nj O l e
j Ȍ
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1 8 C o m p O b j k m k f O b j I n f o n m E q u a t i o n N a t i v e n 6 _ 1 1 4 9 6 1 0 2 5 7 j t q F s"njs"nj O l e
o C o m p O b j p r p f O b j I n f o s r E q u a t i o n N a t i v e s 6
F Microsoft Equation 3.0 DS Equation Equation.3 9q 0w 1
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F Microsoft Equation 3.0 DS Equation Equation.3 9q _ 1 1 4 9 6 1 0 2 7 9 v F s"njs"nj O l e
t C o m p O b j u w u f O b j I n f o x w E q u a t i o n N a t i v e x 6 _ 1 1 4 9 6 1 0 3 0 9 o { F s"njp$nj O l e
y C o m p O b j z | z f 9 S
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F Microsoft Equation 3.0 DS Equation Equation.3 9q 4
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F Microsoft Equation 3.0 DS Eq O b j I n f o } | E q u a t i o n N a t i v e } 6 _ 1 1 4 9 6 1 0 3 3 5 F p$njp$nj O l e
~ C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 _ 1 1 4 9 6 1 0 3 6 0 ~ F p$njp$nj uation Equation.3 9q h
3 8
F Microsoft Equation 3.0 DS Equation Equation.3 9q W
4 9 O l e
C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 _ 1 1 4 9 6 1 0 3 9 0 F p$njp$nj O l e
C o m p O b j f O b j I n f o
F Microsoft Equation 3.0 DS Equation Equation.3 9q ; :
2 4
F Microsoft Equation 3.0 DS Equation Equation.3 9q E q u a t i o n N a t i v e 6 _ 1 1 4 9 6 1 0 4 1 3 F p$njp$nj O l e
C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 _ 1 1 4 9 6 1 0 4 3 6 F p$njp$nj O l e
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F Microsoft Equation 3.0 DS Equation Equation.3 9q
2 5 C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 _ 1 1 4 9 6 1 1 2 8 7 F p$njp$nj O l e
C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6
F Microsoft Equation 3.0 DS Equation Equation.3 9q
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F Microsoft Equation 3.0 DS Equation Equation.3 9q _ 1 1 4 9 6 1 1 3 0 9 F p$njp$nj O l e
C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 _ 1 1 4 9 6 1 1 4 3 1 F p$njp$nj O l e
C o m p O b j f
1 4
F Microsoft Equation 3.0 DS Equation Equation.3 9q P
2 5
F Microsoft Equation 3.0 DS Eq O b j I n f o E q u a t i o n N a t i v e 6 _ 1 1 4 9 6 1 1 4 3 0 F p$njp$nj O l e
C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 _ 1 1 5 0 1 7 7 9 7 9 F p$njp$nj uation Equation.3 9q Ȏ t
1 2
F Microsoft Equation 3.0 DS Equation Equation.3 9q
؆ l
8 3 O l e
C o m p O b j f O b j I n f o E q u a t i o n N a t i v e 6 _ 1 1 5 0 1 7 8 0 1 6 F p$njp$nj O l e
C o m p O b j f O b j I n f o
F Microsoft Equation 3.0 DS Equation Equation.3 9q
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2 3
F Microsoft Equation 3.0 DS Equation Equation.3 9q E q u a t i o n N a t i v e 6 _ 1 1 5 0 1 7 8 0 7 0 F p.'njp.'nj O l e
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