CAHSEE Math Problem of the Day -- Week 10

CAHSEE Math Problem of the Day -- Week 10 

Teacher Notes & Answers 

Week & Day Week 10 – Day 1 

Concept/Skill Lowest Common Denominator 

Standard 7 NS: 2.2 Add and subtract fractions by using factoring to find common 

denominators. 

Materials CAHSEE Math Released Item # 23 

Overview for Week 

This week students will be adding, subtracting and multiplying fractions. They need to 

know how to find the lowest common denominator, change mixed numbers to improper 

fractions, and reduce fractions to lowest terms. On Day 5 they will be writing an 

equation to find the answer to a word problem that uses fractions. 

• Review the Lowest Common Denominator, also known as the Least Common 

Denominator. When adding fractions students must make sure all of the denominators 

(number on the bottom of the fraction) are the same. To do this they must first 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. 

• Have students review the 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. 

• Have students do the guided practice on Day 1 of the student CAHSEE Math 

Problem of the Day -- Week 10 worksheet. 

In today’s problem students will be doing steps one through four: 

Example: 

What is the prime factored form of the lowest common denominator of 

The prime factors of 8 are _____ 2 _____ 2 _____ 2 

The prime factors of 12 are _____ 2 ____ 2 _____ 3 

The factored form of the Lowest Common Denominator are _____ 

2 2 

______ ______ 

2 

_____ 

3 

Day 1 is continued on next page. 

Laura Westermeier, Ed.D. Fall 2007 

SAUSD, Educational Services Week 10 – Teacher - Page 1 of 10



• You may choose to have students do an additional practice problem for Day 1. 

Additional Practice: 

Which of the following is the prime factored form of the lowest common denominator of 

A 3 x 7 

B 3 x 3 x 7 

C 7 x 9 

D 21 x 9 

The factors of 21 are: 3 x 7 

The factors of 9 are: 3 x 3 

The factors in the Lowest Common Denominator are 3 x 3 x 7 

Since 9 is not a prime number answer C can not 

be the correct answer. 

• Have students do the CAHSEE released test item on Day 1 of the student CAHSEE 

Math Problem of the Day -- Week 10 worksheet. 

23. Which of the following is the prime factored form of the lowest common 

denominator of 

A 5 x 1 

B 2 x 3 x 5 

C 2 x 5 x 3 x 5 

D 10 x 15 

The prime factors of 10 are 2 x 5 

The prime factors of 15 are 3 x 5 

The Lowest Common Denominator is 2 x 3 x 5 





Week Week 10 – Day 2 

Concept/Skill Adding fractions 


denominators. 


• Review the parts of a fraction: 

numerator (top) 1 

denominator (bottom) 3 

• Have students review the steps for adding fractions: 

1. Change the fractions so they each have the lowest common denominator (steps 1-5 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. 



Example: What is 

The Lowest Common Denominator is ______ 6 

To change 

to the LCD multiply the numerator and denominator both by ______. 3 

Does 

have the LCD ________ Yes 

Rewrite the fractions with the LCD and add to find the answer: 

3 1 4 

+ = 

6 6 6 Remind students not to add the denominator. 

Can the answer be reduced ________ Yes 

To reduce the fraction divide both the numerator and denominator by _____ 2 

Write the reduced fraction _______ 2 

3 

Day 2 continued on next page. 





• You may choose to have students do an additional practice problem for Day 2. 

Additional Practice 

Which fraction is equivalent to 

A 

B 

The Lowest Common Denominator for 4 and 10 is 20. 

Change 1/4 to 5/20. 

Change 2/10 to 4/20. 

C 

D 



22. Which fraction is equivalent to 

A 

B 

The Lowest Common Denominator for 6 and 8 is 24. 

Change 5/6 to 20/24. 

Change 7/8 to 21/24. 

C 

D 

Note: This is an improper fraction, however, students 

do not need to change it to a mixed number. 






Concept/Skill Subtracting fractions 


denominators. 


Have students review the Steps for subtracting fractions: 

Note: The steps for subtracting and adding fractions are the same except students 

subtract on step 2. 

1. Change the fractions so they each have the lowest common denominator (steps 1- 

5 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 

The Lowest Common Denominator is ______ 36 

12 = 2 x 2 x 3 

36 = 2 x 2 x 3 x 3 

LCD = 2 x 2 x 3 x 3 

To change 

to the LCD multiply the numerator and denominator both by ______. 3 

Does have the LCD ________ Yes 

Rewrite the fractions with the LCD and subtract to find the answer: 

15 - 5 = 

10 

36 36 36 Remind students not to subtract the denominator. 

Can the answer be reduced ________ Yes 

The numerator and denominator each needs to be divided by ______. 2 

Write the reduced fraction _______ 5 

18 








24. What is 

A 

B 

C 

The Lowest Common Denominator for 4 and 6 is 12. 



D 






Concept/Skill Adding and subtracting fractions in problems with parentheses 

Standard 7 NS: 1.2 Add, subtract, multiply, and divide rational numbers (integers, 

fractions, and terminating decimals) and take positive rational numbers 

to whole-number powers. 


• Orally quiz the students to see if they can remember what to do when a problem has 

parentheses. They should know to find the answer to the part inside the parentheses 

and then use that number to complete the calculation. 

• Review the steps for fraction problems with 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. 

• Have students do the guided practice test item on Day 4 of the student CAHSEE 


Example: ( )+( ) = 

First find the answer for each part inside the parentheses: 

= 

= 

_________ 

_________ 

Now write the fraction for each parentheses: 

1 

4 

+ 

What is the Lowest Common Denominator ____ 12 

Rewrite the problem with the Lowest Common Denominator and then find the answer: 

3 

2 

3 

+ = 

8 11 

12 12 12 

Can the answer be reduced _________ No 








First find the answer of the problem inside 

the parentheses: ⅓ + ¼ = 4/12 + 3/12 = 7/12 

Next find the answer for 11/12 – 7/12 which 

is 4/12 

Reduce 4/12 to its lowest terms which is ⅓ 






Concept/Skill Multiplying fractions 

Standard 7 NS: 1.2 Add, subtract, multiply, and divide rational numbers (integers, 

fractions, and terminating decimals) and take positive rational numbers 

to whole-number powers. 


• Review the definitions of improper fractions and 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. 

• Review 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). 

• Review 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. 

• Review the 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 it back to a mixed 

number. 

• Have students do the guided practice test item on Day 5 of the student CAHSEE 


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: 1 1/2 x 2 = cups of sugar needed 

Change 1 ½ back to the mixed number: ______ 

Change the integer to an improper fraction: ____ 

3 2 

Rewrite the equation and find the answer: x = 

2 1 

Change the improper fraction to an integer or mixed number: 

3 

6 

2 







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 x = 

B 4 

C 5⅓ = 4 

D 9 

• At the end of the week remind students to keep the student CAHSEE Math 

Problem of the Day -- Week 10 worksheet to use as a study guide as they continue 

to prepare for the CAHSEE. 


SAUSD, Educational Services Week 10 – Teacher - Page 10 of 10

CAHSEE Math Problem of the Day -- Week 10

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?