Basic Math Problems and Their Solutions (Step by Step)
Why Basic Math Problems Matter
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
Here are ten basic math problems with solutions to practice at home.
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? You might also like Finding the Area of the Shaded Region Step by Step (With Examples).
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 the part eaten. Visuals make fractions much less scary for young 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 most 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.
Conclusion
Basic math is a set of building blocks: addition and subtraction lead to multiplication and division, which lead to fractions, decimals and percentages. When one block is shaky, everything above it feels harder. Working through problems step by step, writing out each stage and checking answers is the most reliable way to build strong foundations.
Practice a few problems from each section regularly, and focus on the topics that cause the most mistakes. If your child is still stuck on a particular skill, a short session with a tutor can often clear it up quickly.
Frequently Asked Questions
What are basic math problems?
Basic math problems cover the core skills taught in elementary and early middle school: addition, subtraction, multiplication, division, fractions, decimals, percentages, simple geometry and the order of operations.
What is PEMDAS?
PEMDAS sets the order of operations: Parentheses, Exponents, Multiplication and Division (left to right), then Addition and Subtraction (left to right). In the UK and some other countries the same rule is called BODMAS.
How can my child get better at word problems?
Read the problem twice, underline the numbers and key words, decide which operation is needed, and write the steps out. Drawing a quick picture or diagram often makes the problem much clearer.
Why do kids find fractions so hard?
Fractions ask children to think about parts of a whole, which is a new idea compared with whole numbers. Visual models such as pie charts, fraction bars and number lines make the concept much easier to grasp.
How much math practice should kids do each day?
Ten to twenty minutes of focused daily practice works better than one long session a week. Short, regular practice keeps skills fresh and builds confidence.