Addition & Subtraction
Add: 1/2 + 2/3
11/6
Define numerator.
The top number showing how many parts are counted.
Multiply: 2/3 × 3/4
Answer: 1/2
Find three equivalent fractions for 3/4
6/8, 9/12, 12/16.
Identify the error: 1/2 + 1/4 = 2/6
Student added numerators and denominators separately. Correct: 1/2 + 1/4 = 2/4 + 1/4 = 3/4
Subtract: 13/8 – 1/2
7/8
Define denominator.
The bottom number showing how many equal parts make a whole.
Divide: 5/8 ÷ 1/4
Answer: 21/2
Find missing numerator: ?/20 = 3/5
12
True or false? 3/5 – 1/2 = 2/10. Explain.
False; find common denominator: 3/5 – 1/2 = 6/10 – 5/10 = 1/10
Combine: 21/4 + 1/6 - 11/2
11/12
What is a mixed number?
A number made of a whole number and a fraction.
Multiply: 11/2 × 4/5
Answer: 11/5
Find missing denominator: 2/3 = 8/?
12
Student says: 11/2 + 1/3 + 1/4 = 21/8. Check & correct.
Answer: Incorrect. Correct answer: 2 1/12.
Subtract: 42/3 - 15/6
2 5/6
Why must fractions have common denominators to add/subtract?
Fractions must refer to same-sized parts to combine accurately.
Divide: 23/4 ÷ 7/8
Answer: 3 1/14
1.) Simplify 42/56.
2.) Convert 43/11 to an improper fraction.
3.) Convert 88/6 to a mixed number in simplest form.
1.) GFC of 42 & 56 is 14. So, reduce 42/56 by a factor of 14. Result: 3/4
2.) Convert 4 wholes to 11ths & add to numerator (11*4+3). Result: 47/11
3.) Divide 88 by 6. Get 14 remainder 4/6. Keep 14 & reduce 4/6 by common factor of 2. Result: 142/3
Explain & correct the mistake: 4/5 ÷ 2/3 = 2/15
Incorrect. The student divided numerators and multiplied denominators. Instead, divide fractions by multiplying by reciprocal: 4/5 ÷ 2/3 = 4/5 × 3/2 = 12/10 = 1 1/5
🌅 Wilma’s Lemonade Routine — Concise Version
On a hot late summer afternoon, Wilma sat on her porch with a pitcher of lemonade and a tall glass. She poured a cup into her glass and sipped 3/4 of a cup while enjoying the golden rays.
As she continued to relax, she repeated this routine twice more:
She poured 2/3 of a cup back into her glass.
She drank 3/4 of a cup while the afternoon stretched to evening.
At this time the sun had just finished setting. So, she took her pitcher and glass inside.
How much lemonade was left in her glass?
1.) Wilma pours 1 cup of lemonade into her glass.
2.) She drinks 3/4 of a cup → 1 − 3/4 = 1/4
3.) She pours 2/3 of a cup more → 1/4 + 2/3 = 11/12
4.) She drinks 3/4 of a cup → 11/12 − 3/4 → 11/12 − 9/12 → 2/12 = 1/6
5.) She pours 2/3 of a cup more → 1/6 + 2/3 → 1/6 + 4/6 = 5/6
6.) She drinks a final 3/4 of a cup → 5/6 − 3/4 → 10/12 − 9/12 = 1/12
Final Answer: 1/12 of a cup of lemonade is left.
Multi-step: 3/4 of the students in a homeroom are in choir. Of those, 1/3 are also in band. 1/7 of the class is only in band. If there are 28 students total, then:
1.) How many take choir?
2.) How many take both choir and band?
3.) How many take band?
4.) How many do not take either choir or band?
Choir: 3/4 * 28/1 = 21 students in choir.
Band & Choir: 1/3 * 21/1 = 7 students in band & choir.
Band only: 7 + 1/7(28-21) = 7 + 1/7(7/1) = 7 + 1 = 8 students in band.
Neither: 28 students in the class - (21 students in choir + 1 student in band) = 28 - 22 = 6 students are in neither band nor chorus.
A baker makes 1 batch, 1/2 batch, and 1/4 batch of cookies.
Each batch uses 2/3 cup of sugar.
How much sugar total?
Answer: 11/6 cups sugar for the 1 3/4 batches cookies.
Multi-step: A baker uses 3/5 of a bag of flour for cookies and 2/3 of the remainder for muffins. If the bag has 15 cups flour, how much is used for muffins?
Flour for cookies: 3/5 × 15 = 9 cups.
Remaining: 15 – 9 = 6 cups.
Muffins: 2/3 × 6 = 4 cups.
Student says: 31/4 - 15/6 = 27/12. Find the mistake and provide a correct answer.
Mistake: student subtracted the fraction part of the numbers incorrectly, specifically 3/12 from 10/12 instead of vice versa.
Correction steps:
1.) Convert to a common denominator: 31/4 = 33/12 & 15/6 = 110/12.
2.) Regroup 33/12 to 215/12 and subtract 110/12, yielding 15/12.
3.) Final Answer: 15/12.