TL;DR: GMDAS stands for Grouping symbols, Multiplication, Division, Addition, Subtraction. Grouping first, then multiplication and division together as one left-to-right step, then addition and subtraction together as one left-to-right step. It is the Grade 5 form of the order of operations in the Philippine curriculum, sitting between MDAS in Grade 4 and GEMDAS once exponents arrive by the end of Grade 6, and the Grade 5 stage under the MATATAG curriculum applies it to fractions and decimals as well as whole numbers. DepEd material often writes PMDAS or GMDAS together: P covers only parentheses, G covers all grouping symbols including the fraction bar. Almost every wrong answer comes from one of two mistakes, doing multiplication before an earlier division, or doing addition before an earlier subtraction.
If you searched for a GMDAS example, you probably do not need the theory. You need to see solutions written out, at the level the rule is actually taught, with the fractions and decimals that make Grade 5 items harder than the whole-number examples in most explainers.
That is what this guide is. Twelve worked examples, the wrong answers each one produces if you break the rule, and a short note on where the rule sits in the curriculum. If you need the version with exponents, our GEMDAS guide covers that and the arguments about ambiguous expressions.
The Rule in Four Lines
| Step | What you do | Direction |
|---|---|---|
| G | Everything inside grouping symbols, innermost first | Apply the whole rule again inside |
| M and D | Multiplication and division, one stage | Left to right |
| A and S | Addition and subtraction, one stage | Left to right |
| Check | Rewrite the expression after each stage | Do not skip lines |
Grouping symbols are more than round brackets. They include:
- parentheses ( )
- square brackets [ ]
- braces { }
- the fraction bar, which groups the whole numerator and the whole denominator separately
- the radical sign and absolute value bars, which appear later
That last group is the entire reason DepEd material writes PMDAS or GMDAS. P names only the parentheses; G names all of them. On an item that uses only round brackets, the two acronyms give the same answer.
Where GMDAS Sits in the Curriculum
The Philippine curriculum builds the rule in stages rather than teaching the full acronym at once, which is why the name on a worksheet depends on the grade level.
| Level | What is expected | Name used |
|---|---|---|
| Grade 4 | Two or more different operations on whole numbers | MDAS |
| Grade 5 | A series of operations with grouping symbols, extended to fractions and decimals | PMDAS or GMDAS |
| End of Grade 6 | Exponential form, including calculation using the rules | GEMDAS |
| Grade 7 | Numerical expressions involving integers | GEMDAS |
The current curriculum is the MATATAG curriculum, rolled out under DepEd Order No. 010, s. 2024, Policy Guidelines on the Implementation of the MATATAG Curriculum. Its Grade 5 mathematics content standard has learners applying the GMDAS rule to expressions involving fractions and decimals, and DepEd's own learning resource portal carries Grade 5 material titled for simplifying a series of operations using PMDAS or GMDAS. Our MATATAG curriculum guide covers the rollout, and the DepEd mathematics curriculum guide covers how the maths strand is organised across grades.
Twelve Worked Examples
The expressions and word problems below are illustrative. They were written for this guide to match the Grade 5 level and are not taken from any DepEd examination or official reviewer.
Disclaimer: this is a study guide, not an official DepEd reviewer. Notation, the acronym your school uses, and the way solutions are expected to be laid out can differ between teachers and divisions. Follow your teacher's marking scheme where it differs from the presentation here.
Whole numbers
Example 1. One grouping symbol
(18 − 6) ÷ 4 + 7 × 2
- Grouping: 18 − 6 = 12
- Multiplication and division, left to right: 12 ÷ 4 = 3, then 7 × 2 = 14
- Addition: 3 + 14 = 17
Answer: 17.
Example 2. Division comes before multiplication here
48 ÷ 6 × 2 + 5
- Equal rank, so left to right: 48 ÷ 6 = 8, then 8 × 2 = 16
- Addition: 16 + 5 = 21
Answer: 21. Doing the multiplication first gives 6 × 2 = 12, then 48 ÷ 12 = 4, then 9. That is the single most common GMDAS error.
Example 3. Nested grouping
2 × [30 − (5 + 4 × 3)]
- Innermost grouping, applying the whole rule inside it: 4 × 3 = 12, then 5 + 12 = 17
- Outer grouping: 30 − 17 = 13
- Multiplication: 2 × 13 = 26
Answer: 26. Working left to right inside the bracket would give 5 + 4 = 9, then 9 × 3 = 27, and the whole answer collapses.
Fractions
Example 4. Grouping with like fractions
(3/4 + 1/4) × 8 − 3
- Grouping first: 3/4 + 1/4 = 1
- Multiplication: 1 × 8 = 8
- Subtraction: 8 − 3 = 5
Answer: 5.
Example 5. Multiplication before addition
1/2 + 2/3 × 3/4
- Multiplication first: 2/3 × 3/4 = 6/12 = 1/2
- Addition: 1/2 + 1/2 = 1
Answer: 1. Adding first gives 1/2 + 2/3 = 7/6, then 7/6 × 3/4 = 7/8. Two plausible-looking answers, one rule apart.
Example 6. Dividing by a fraction
5/6 ÷ 1/3 + 1/2
- Division first, so invert and multiply: 5/6 × 3/1 = 15/6 = 5/2
- Addition: 5/2 + 1/2 = 6/2 = 3
Answer: 3.
Example 7. Mixed numbers with two groupings
(2 1/2 + 1 1/2) × (10 − 6)
- Both groupings, in any order since neither depends on the other: 2 1/2 + 1 1/2 = 4, and 10 − 6 = 4
- Multiplication: 4 × 4 = 16
Answer: 16.
Decimals
Example 8. Multiplication and division, then subtraction
2.5 × 4 − 6.4 ÷ 2
- Multiplication and division, left to right: 2.5 × 4 = 10, then 6.4 ÷ 2 = 3.2
- Subtraction: 10 − 3.2 = 6.8
Answer: 6.8.
Example 9. Grouping, then dividing by a decimal
(7.2 − 3.2) ÷ 0.5 + 1.5
- Grouping: 7.2 − 3.2 = 4
- Division: 4 ÷ 0.5 = 8
- Addition: 8 + 1.5 = 9.5
Answer: 9.5. Dividing by 0.5 doubles the number. Learners who expect division always to make things smaller stop and second-guess a correct step here.
Example 10. The fraction bar as a grouping symbol
(4.5 + 1.5) written over (3 × 0.5), as a single fraction
- The bar groups numerator and denominator separately, so finish both: 4.5 + 1.5 = 6, and 3 × 0.5 = 1.5
- Divide: 6 ÷ 1.5 = 4
Answer: 4. If you rewrite this on one line you must add brackets. Typed as 4.5 + 1.5 ÷ 3 × 0.5, it is a different expression with a different value.
Word problems
Example 11. Money
A pupil buys 3 notebooks at 24.50 pesos each and pays with a 100-peso bill. The change is shared equally between 2 younger siblings. How much does each receive?
- Write the expression with grouping that shows what must happen first: (100 − 3 × 24.50) ÷ 2
- Inside the grouping, multiplication before subtraction: 3 × 24.50 = 73.50, then 100 − 73.50 = 26.50
- Division: 26.50 ÷ 2 = 13.25
Answer: 13.25 pesos each.
Example 12. Measurement with a fraction
A ribbon is 12 metres long. One quarter of it is cut off, and the remainder is divided into 3 equal pieces. How long is each piece?
- Expression: (12 − 12 × 1/4) ÷ 3
- Inside the grouping: 12 × 1/4 = 3, then 12 − 3 = 9
- Division: 9 ÷ 3 = 3
Answer: 3 metres. Without the grouping symbols, 12 − 12 × 1/4 ÷ 3 says something the problem never said.
Where the Wrong Answers Come From
Nearly all of them are one of six mistakes, and five of the six are about order rather than arithmetic.
| Mistake | What it looks like | Fix |
|---|---|---|
| Treating M as before D | 48 ÷ 6 × 2 read as 48 ÷ 12 | MD is one stage, left to right |
| Treating A as before S | 20 − 8 + 5 read as 20 − 13 | AS is one stage, left to right |
| Working left to right inside a bracket | (5 + 4 × 3) read as 9 × 3 | The whole rule applies inside too |
| Dropping the fraction bar when retyping | Numerator or denominator loses its grouping | Add brackets when you flatten a fraction |
| Doing the outer bracket before the inner one | Innermost pair left unfinished | Start innermost and work outward |
| Arithmetic slips on fractions and decimals | Order correct, value wrong | Check the order and the computation separately |
That last row is worth taking seriously at Grade 5. Once fractions and decimals enter, a correct GMDAS solution can still land on a wrong number because of a common denominator or a misplaced decimal point. Marking the two things separately, first the order, then the arithmetic, tells you which one actually needs practice.
How to Write a Solution That Gets Full Marks
- Rewrite the whole expression after each stage. Do not compute in the margin and jump to the answer. Teachers mark the line, not the head.
- Do both operations of a stage in the same line when they do not interfere with each other, then rewrite. That is what makes the left-to-right rule visible.
- Name the step. Writing "grouping" or "MD" beside a line costs nothing and makes an error easy to find.
- Keep fractions in one form through the solution, either all improper or all mixed, and convert at the end.
- Check the answer against the wording in a word problem. If the number is impossible in the story, the expression was written wrongly before the rule was ever applied.
If the arithmetic itself is the problem rather than the order, a board game built for exactly this is worth a look; our Damath guide covers the Philippine maths board game and the operations each version drills.
Ready to find the right school? Browse schools or explore more study guides for Filipino learners on SchoolFinderPH.
Sources
- DepEd — DO 010, s. 2024, Policy Guidelines on the Implementation of the MATATAG Curriculum
- DepEd — MATATAG Mathematics Curriculum Guide, Grades 1 to 4 and 7 (official PDF)
- DepEd Learning Resource Portal — Simplifying a Series of Operations using PMDAS or GMDAS, Grade 5
- DepEd Learning Resource Portal — Grade 5 Mathematics, Order of Operations
- SchoolFinderPH — GEMDAS: Order of Operations, With Worked Examples
- SchoolFinderPH — DepEd Mathematics Curriculum Guide
