Basic math problems form the foundation of all higher mathematics. Whether your child is in elementary school, middle school, or just needs to refresh core skills, mastering these fundamental question types builds confidence and prevents gaps that make algebra, geometry, and beyond much harder. Below you’ll find the most common categories of basic math problems that appear year after year in school homework, placement tests, state assessments, and everyday life — together with step-by-step solutions, common mistakes to avoid, and quick tips for faster understanding.
A Clear & Detailed Guide for Students & Parents
These are some basic math problems and solutions to practice at home. Parents can get help here:
1. Addition & Subtraction Word Problems (Ages 6–9)
Problem 1 Mia had 48 stickers. She gave 17 stickers to her friend and then bought 29 more. How many stickers does Mia have now?
Step-by-step solution 48 − 17 = 31 31 + 29 = 60
Answer: 60 stickers
Quick tip Teach children to underline the key numbers and circle the action words (gave = subtract, bought = add). Many mistakes happen when students add everything or subtract everything.
2. Multiplication & Division Basics (Ages 8–11)
Problem 2 A bakery packs 9 cookies into each box. If they fill 7 full boxes and have 5 cookies left over, how many cookies did they bake in total?
Solution 9 cookies/box × 7 boxes = 63 cookies 63 + 5 leftover = 68 cookies
Answer: 68 cookies
Common mistake Students forget to add the remainder. Remind them: “The remainder is part of the total.”
Problem 3 A ribbon that is 84 cm long is cut into 6 equal pieces. How long is each piece?
Solution 84 ÷ 6 = 14
Answer: 14 cm
Tip Use the “fact family” method: if 6 × 14 = 84, then 84 ÷ 6 = 14.
3. Fractions – The Most Misunderstood Basics
Problem 4 What is 3/4 of 24?
Solution 24 ÷ 4 = 6 6 × 3 = 18
Answer: 18
Alternative quick method 24 × 3 ÷ 4 = 72 ÷ 4 = 18
Problem 5 Sarah ate 2/5 of a pizza and her brother ate 1/5. What fraction of the pizza is left?
Solution 2/5 + 1/5 = 3/5 eaten 1 − 3/5 = 2/5 left
Answer: 2/5
Tip Always draw a quick rectangle divided into equal parts and shade what is eaten. Visuals reduce fraction fear by 70–80% in early learners.
4. Decimals & Money Problems
Problem 6 A book costs $12.95. Sales tax is $0.91. How much change will you get from a $20 bill?
Solution 12.95 + 0.91 = 13.86 20.00 − 13.86 = 6.14
Answer: $6.14
Tip Line up the decimal points when adding and subtracting money — a very frequent careless error.
5. Basic Percentages (Introduced around ages 10–12)
Problem 7 A shirt originally priced at $40 is on sale for 25% off. What is the sale price?
Solution 25% of 40 = 0.25 × 40 = 10 40 − 10 = 30
Answer: $30
Faster mental math shortcut 25% off = pay 75% → 75% of 40 = 0.75 × 40 = 30
6. Simple Area & Perimeter (Geometry Basics)
Problem 8 A rectangular garden is 12 m long and 5 m wide. What is its perimeter and area?
Perimeter 2 × (12 + 5) = 2 × 17 = 34 m
Area 12 × 5 = 60 m²
Answer: Perimeter = 34 meters, Area = 60 square meters
Tip Perimeter = “around” → add all sides Area = “inside” → multiply length × width
7. Order of Operations (PEMDAS/BODMAS)
Problem 9 Calculate: 18 ÷ 3 + 4 × 5 − 2
Solution (follow PEMDAS: Parentheses → Exponents → Multiplication & Division → Addition & Subtraction)
18 ÷ 3 = 6 4 × 5 = 20 6 + 20 = 26 26 − 2 = 24
Answer: 24
Common mistake Doing left to right without respecting multiplication/division before addition/subtraction.
Bonus: Mixed Bag – Real-World Problem
Problem 10 A movie ticket costs $11.50 for children and $14.75 for adults. A family buys 3 child tickets and 2 adult tickets. How much do they spend in total?
Solution 3 × 11.50 = 34.50 2 × 14.75 = 29.50 34.50 + 29.50 = 64.00
Answer: $64.00
Final Tips for Parents & Students
- Practice 10–15 minutes daily instead of cramming once a week.
- Always write down the question and show every step (even simple ones) — this catches 80% of careless mistakes.
- Use real-life objects (coins, food portions, measuring tape) to make concepts concrete.
- Celebrate small wins — confidence grows faster than skill.
If your child struggles with any of these basic math areas, consistent short one-on-one sessions with a patient online tutor can close gaps very quickly.
Many families see noticeable improvement in understanding and attitude after just 8–12 focused sessions. Would you like personalized help with these foundational topics? Math Make Smart offers a free trial lesson with expert online Math tutors who specialize in building strong basic math skills.