SAUSD CAHSEE Math Problem of the Day -- Week 10
Lowest Common Denominator
Day 1
(CAHSEE Math Released Item #23 )
This week you will be working with fractions.
When adding fractions you must make sure all of 23. Which of the following is the prime
the denominators (number on the bottom of the
factored form of the lowest common
fraction) are the same. To do this you must first
denominator of
find the Lowest Common Denominator or
LCD. The LCD is the lowest number that both of
the denominators can be divided into without a
remainder.
Steps to find the Lowest Common
Denominator:
1. Factor each of the denominators into
primes. (Prime factors are those numbers
that can only be divided by 1 or
themselves)
2. Count the number of times each prime
number appears in each of the
factorizations
3. For each prime number, take the largest
of these counts.
4. Write down that prime number as many
times as you counted for it in step #3
5. The lowest common denominator is the
product of all the prime numbers written
down.
In today’s problem you will be doing steps one
through four:
A
5x1
B
2x3x5
C
2x5x3x5
D
10 x 15
Additional Practice:
Which of the following is the prime factored
form of the lowest common denominator of
Example:
What is the prime factored form of the lowest
common denominator of
The prime factors of 8 are _____ _____ _____
A
3x7
B
3x3x7
C
7x9
D
21 x 9
The prime factors of 12 are _____ ____ _____
The factored form of the Lowest Common
Denominator are _____ ______ ______ _____
Laura Westermeier, Ed.D.
Educational Services, SAUSD
Fall, 2007
Week 10 – Student - Page 1 of 5
SAUSD CAHSEE Math Problem of the Day -- Week 10
Day 2
Parts of a fraction:
(CAHSEE Math Released Item # 22)
numerator (top)
1
denominator (bottom)
3
Steps for adding fractions:
1. Change the fractions so they each have
the lowest common denominator (steps 15 of Day 1) (Note: Remember to multiply
the numerator of each fraction by the
same number that you used to multiply
the denominator)
2. Add the numerators to find the answer.
(Do not add the denominators)
3. Reduce the fraction to lowest terms by
finding an equivalent fraction in which the
numerator and denominator are as small
as possible.
22. Which fraction is equivalent to
?
A
B
C
D
Example: What is
The Lowest Common Denominator is ______
To change
to the LCD multiply the
Additional Practice
Which fraction is equivalent to
numerator and denominator both by ______.
A
Does
have the LCD? ________
Rewrite the fractions with the LCD and add to
find the answer:
+
B
=
Can the answer be reduced? ________
C
To reduce the fraction divide both the numerator
and denominator by _____
Write the reduced fraction _______
Laura Westermeier, Ed.D.
Educational Services, SAUSD
D
Fall, 2007
Week 10 – Student - Page 2 of 5
SAUSD CAHSEE Math Problem of the Day -- Week 10
Day 3
Steps for subtracting fractions:
The steps for subtracting and adding fractions
are the same except you subtract on step 2.
1. Change the fractions so they each have
the lowest common denominator (steps 15 of Day 1) (Note: Remember to multiply
the numerator of each fraction by the
same number that you used to multiply the
denominator)
2. Subtract the numerators. (Do not subtract
the denominators)
3. Reduce the fraction to lowest terms by
finding an equivalent fraction in which the
numerator and denominator are as small
as possible. To do this divide the
numerator and denominator by the same
number.
Example: What is
(CAHSEE Math Released Item # 24 )
24. What is
A
B
C
D
?
The Lowest Common Denominator is ______
To change
to the LCD multiply the
numerator and denominator both by ______.
Does
have the LCD? ________
Rewrite the fractions with the LCD and subtract
to find the answer:
-
=
Can the answer be reduced? ________
The numerator and denominator each needs to be
divided by ______.
Write the reduced fraction _______
Laura Westermeier, Ed.D.
Educational Services, SAUSD
Fall, 2007
Week 10 – Student - Page 3 of 5
SAUSD CAHSEE Math Problem of the Day -- Week 10
Day 4
Steps for fraction problems with
(CAHSEE Math Released Item # 4 )
parentheses:
1. Do the parts of the problem inside the
parentheses first.
2. Once the answer is found for each part
inside the parentheses then finish finding
the answer for the problem.
Example:
( )+( ) =
First find the answer for each part inside the
parentheses:
=
_________
=
_________
Now write the fraction for each parentheses:
+
What is the Lowest Common Denominator? ____
Rewrite the problem with the Lowest Common
Denominator and then find the answer:
+
=
Can the answer be reduced? _________
Laura Westermeier, Ed.D.
Educational Services, SAUSD
Fall, 2007
Week 10 – Student - Page 4 of 5
SAUSD CAHSEE Math Problem of the Day -- Week 10
Day 5
Mixed numbers:
An improper fraction is a fraction that has a
numerator larger than or equal to its denominator.
A proper fraction is a fraction with the numerator
smaller than the denominator.
A mixed number consists of an integer followed
by a proper fraction.
Changing an improper fraction to a mixed
number: The improper fraction 8/5 can be
changed to the mixed number 1 3/5 by dividing
the numerator (8) by the denominator (5). This
gives a quotient of 1 and a remainder of 3. The
remainder is placed over the divisor (5).
Changing a mixed number to an improper
fraction: The mixed number 1 3/5 can be
changed to the improper fraction 8/5 by
multiplying the integer (1) by the denominator (5)
and adding that to the numerator.
(CAHSEE Math Released Item #7)
7. John uses ⅔ of a cup of oats per serving to
make oatmeal. How many cups of oats
does he need to make 6 servings?
A
2⅔
B
4
C
5⅓
D
9
Steps for multiplying fractions:
1. Change any integers or mixed numbers
back to improper fractions.
2. Multiply the numerators and multiply the
denominators.
3. Reduce the answer to lowest terms and, if
possible, change back to a mixed number.
Example:
Mary uses 1 ½ cups of sugar to make a gallon
of lemonade. How may cups of sugar does she
need to make 2 gallons of lemonade?
Write the equation to solve the problem:
x
= cups of sugar needed
Change 1 ½ back to the mixed number: _______
Change the integer to an improper fraction: ____
Rewrite the equation and find the answer:
x
=
Change the improper fraction to an integer or
mixed number:
Laura Westermeier, Ed.D.
Educational Services, SAUSD
Fall, 2007
Week 10 – Student - Page 5 of 5