What is the difference between GCF and LCM problems?

GCF or Greatest Common Factor is used for problems about dividing equally into the largest number of groups, signalled by keywords such as divided equally, same amount, or the most. LCM or Least Common Multiple is used for repeating events that coincide, signalled by keywords such as together again, at the same time, or light up together. Both are best solved using prime factorisation.

When do you use pi as 22/7 and when 3.14?

Use pi equal to 22/7 when the radius or diameter is a multiple of 7, such as 7, 14, or 21, because the calculation becomes whole and easier. Use pi equal to 3.14 for numbers that are not multiples of 7, such as 10 or 5. Choosing the right value of pi makes calculating the area and circumference of circles faster and reduces mistakes.

How many math practice problems per day are ideal for a grade 6 child?

Ideally a grade 6 child should do 3 to 5 quality problems every day on a regular basis, rather than cramming dozens of problems the night before an exam. Regular practice in small portions is more effective for memory. More important than the number of problems is discussing the ones answered wrong and asking the child to explain their steps, because the ability to explain signals genuine understanding.

Math Education

10 min

Grade 6 Math Problems + Solutions: Complete Practice (2026)

Published: 22.07.2026·Updated: 22.07.2026

Putri Anggraini

Head of Math Program, Algonova

Grade 6 Math Problems + Solutions: Complete Practice (2026)

Grade 6 primary math problems cover six core topics: fraction operations, GCF & LCM, solid geometry, the area & circumference of circles, discharge rate, and data presentation. This page contains more than 15 complete example problems with step-by-step solutions, written for parents and grade 6 students preparing for daily tests, mid-terms, final exams, or school exams. Every problem uses numbers and formats aligned with the Merdeka Curriculum.

Grade 6 Math Topics at a Glance

Before the practice, here is a map of the topics that appear most often in grade 6 math problems, with an example of each:

Topic	What is tested	Example problem type
Fraction operations	Adding, subtracting, multiplying, dividing fractions	"Find 2/3 + 1/4 = ..."
GCF & LCM	Prime factorisation, schedule & sharing word problems	"The LCM of 12 and 18 is ..."
Solid geometry	Volume & surface area of cubes, cuboids, cylinders	"Volume of a cylinder with radius 7 cm ..."
Circles	Area and circumference of circles	"Circumference of a circle with diameter 14 cm ..."
Discharge rate	Relationship of volume, time, and rate	"Water discharge of 5 litres/second ..."
Data presentation	Mean, median, mode	"The average test score ..."

Have your child try each example first, then check it against the solution. This is far more effective than reading the answer straight away without attempting it.

Grade 6 Fraction Problems + Solutions

Fraction operations trip up grade 6 students the most, especially when denominators differ. The key is simple: match the denominators first for addition and subtraction, then for multiplication just multiply numerator by numerator and denominator by denominator.

$Illustration of the fraction concept for grade 6 math problems$

Problem 1 — Adding fractions with different denominators Calculate: 2/3 + 1/4

Solution:

Match the denominators. The LCM of 3 and 4 is 12.
Convert: 2/3 = 8/12 and 1/4 = 3/12.
Add the numerators: 8/12 + 3/12 = 11/12.

Answer: 11/12

Problem 2 — Subtracting mixed fractions Calculate: 3 1/2 − 1 3/4

Solution:

Convert to improper fractions: 3 1/2 = 7/2 and 1 3/4 = 7/4.
Match denominators (LCM of 2 and 4 = 4): 7/2 = 14/4.
Subtract: 14/4 − 7/4 = 7/4 = 1 3/4.

Answer: 1 3/4

Problem 3 — Multiplying and dividing fractions Calculate: 4/5 × 10/3, then divide the result by 2/3.

Solution:

Multiply: 4/5 × 10/3 = 40/15 = 8/3.
Dividing fractions means multiplying by the reciprocal: 8/3 ÷ 2/3 = 8/3 × 3/2 = 24/6 = 4.

Answer: 4

Parent tip: ask your child to explain why the denominators must match, not just memorise the steps. Understanding the concept makes fraction word problems far easier. Try a free math class to see how a teacher explains it.

Grade 6 GCF and LCM Problems + Solutions

GCF (Greatest Common Factor) and LCM (Least Common Multiple) almost always appear as word problems. The trick is to use prime factorisation: the GCF is found by multiplying the shared prime factors with the smallest powers, while the LCM is found by multiplying all prime factors with the largest powers.

Problem 4 — Finding GCF and LCM Find the GCF and LCM of 12 and 18.

Solution:

Prime factorisation: 12 = 2² × 3 and 18 = 2 × 3².
GCF = shared factors with smallest powers = 2 × 3 = 6.
LCM = all factors with largest powers = 2² × 3² = 4 × 9 = 36.

Answer: GCF = 6, LCM = 36

Problem 5 — LCM word problem (schedule) A red light flashes every 4 seconds and a green light flashes every 6 seconds. If both flash together now, after how many seconds will they flash together again?

Solution:

The keyword "flash together again" signals an LCM problem for 4 and 6.
4 = 2² and 6 = 2 × 3, so LCM = 2² × 3 = 12.

Answer: every 12 seconds

Problem 6 — GCF word problem (equal sharing) A mother has 24 cakes and 36 candies. All are shared equally into several bags with no leftovers. What is the largest number of bags she can make?

Solution:

The keywords "shared equally" and "largest" with no leftovers signal a GCF problem for 24 and 36.
24 = 2³ × 3 and 36 = 2² × 3², so GCF = 2² × 3 = 12.

Answer: 12 bags (each bag has 2 cakes and 3 candies)

A child who truly understands does not memorise whether a problem is GCF or LCM. They read the keywords: “together again” means LCM, “shared equally into the most groups” means GCF.

Putri Anggraini, Head of Math Program, Algonova

Grade 6 Solid Geometry and Circle Problems + Solutions

Geometry in grade 6 requires children to memorise formulas and understand when to use them. Use pi = 22/7 when the radius or diameter is a multiple of 7, and pi = 3.14 for other numbers.

Illustration of solid shapes cube, cylinder, and cone for grade 6 math problems

Problem 7 — Volume of a cylinder A cylinder has a radius of 7 cm and a height of 10 cm. Find its volume. (pi = 22/7)

Solution:

Cylinder volume formula: V = pi × r² × h.
V = 22/7 × 7 × 7 × 10 = 22 × 7 × 10 = 1,540.

Answer: 1,540 cm³

Problem 8 — Volume of a cube A cube has an edge length of 8 cm. Find its volume.

Solution:

Cube volume formula: V = s × s × s = s³.
V = 8 × 8 × 8 = 512.

Answer: 512 cm³

Problem 9 — Circumference and area of a circle A circle has a diameter of 14 cm. Find its circumference and area. (pi = 22/7)

Solution:

Radius r = diameter ÷ 2 = 7 cm.
Circumference = pi × diameter = 22/7 × 14 = 44 cm.
Area = pi × r² = 22/7 × 7 × 7 = 154 cm².

Answer: circumference 44 cm, area 154 cm²

Remember: the most common mistake on circle problems is confusing radius and diameter. Always write down the value of r before calculating. See how a teacher explains geometry.

Grade 6 geometry is not about memorising as many formulas as possible, but knowing when to use pi = 22/7 and when 3.14. This small habit saves a lot of exam marks.

Dewi Lestari, Mathematics Specialist, Algonova

Discharge Rate, Scale, and Data Problems + Solutions

These three topics round out grade 6 math problems and often appear in final and school exams. The key is getting the unit conversions right.

Problem 10 — Discharge rate A tap pours 5 litres of water every second. How much water is collected over 2 minutes?

Solution:

Formula: volume = discharge rate × time.
Match the time units: 2 minutes = 120 seconds.
Volume = 5 × 120 = 600 litres.

Answer: 600 litres

Problem 11 — Scale The distance between two cities on a map is 4 cm. The map scale is 1 : 500,000. What is the real distance?

Solution:

Real distance = map distance × scale = 4 × 500,000 = 2,000,000 cm.
Convert to kilometres: 2,000,000 cm = 20 km.

Answer: 20 km

Problem 12 — Mean Test scores of 5 children: 70, 80, 90, 60, and 100. What is the average?

Solution:

Add all the scores: 70 + 80 + 90 + 60 + 100 = 400.
Divide by the number of values: 400 ÷ 5 = 80.

Answer: 80

Problem 13 — Median and mode Score data: 7, 8, 8, 9, 6. Find the median and mode.

Solution:

Order the data: 6, 7, 8, 8, 9. Median = middle value = 8.
Mode = the most frequent value = 8.

Answer: median 8, mode 8

The Best Way to Practise Grade 6 Math Problems

Practice only helps when a child understands why a step is used, not just copies the answer. A few approaches that reliably work:

Do 3–5 problems a day regularly; don't cram everything the night before an exam.
Ask your child to explain the steps out loud — if they can explain it, they truly understand it.
Discuss the problems answered wrong, not only the ones answered right.
Mix in math games for kids so practice never feels dull.

At Algonova, more than 600,000 students worldwide and 13,000+ in Indonesia learn math through small-group live classes with certified teachers, backed by an AI-based ability diagnostic from day one — so practice targets exactly where each child is weak.

Want your child to feel more confident with problems? Try a free math class at Algonova — one trial session, no cost.

How Should a Grade 6 Child Practise Maths Problems?

The core grade 6 maths material covers integer and fraction operations, GCF and LCM, solid shapes, basic statistics, and scale and ratio. Mastering these five areas is the main preparation for the final exams.

What is an effective way to practise? Work through a few problems each day and review the wrong ones until the concept is clear, rather than chasing quantity.

How do you help a child stop fearing word problems? Train the child to translate a word problem into logical steps, the same skill used in coding. To build this reasoning further, see Algonova's coding classes for ages 5–17, or try a free coding class.

Frequently Asked Questions about Grade 6 Math Problems

What topics are covered in grade 6 math problems?

Grade 6 primary math problems cover fraction operations, GCF and LCM, integers, solid geometry such as the volume and surface area of cubes, cuboids, and cylinders, the area and circumference of circles, discharge rate, scale and ratio, and data presentation such as mean, median, and mode. These topics follow the Merdeka Curriculum and appear most often in daily tests, mid-term exams, final exams, and school exams for grade 6.

How do you solve fraction problems with different denominators?

To add or subtract fractions with different denominators, first make the denominators equal by finding the LCM of both denominators, convert each fraction to the common denominator, then add or subtract the numerators. Example: 2/3 + 1/4, the LCM of 3 and 4 is 12, so it becomes 8/12 + 3/12 = 11/12. For multiplication, multiply numerator by numerator and denominator by denominator without matching denominators.

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Grade 6 Math Problems + Solutions: Complete Practice (2026)

Grade 6 Math Topics at a Glance

Grade 6 Fraction Problems + Solutions

Grade 6 GCF and LCM Problems + Solutions

Grade 6 Solid Geometry and Circle Problems + Solutions

Discharge Rate, Scale, and Data Problems + Solutions

The Best Way to Practise Grade 6 Math Problems

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