DMAS — Order of
Operations
DMAS is the rule that tells you exactly which mathematical operation to do first. Without it, the same expression can give different answers. By the end of this course you will solve any expression correctly — every time.
÷ and × first (left to right), then + and − (left to right). Brackets ( ) override everything.
What is DMAS?
When an expression has more than one operation, DMAS tells you the exact order to follow. Get the order wrong and the answer is always wrong. DMAS is used in Arabic-speaking countries and corresponds to BODMAS / PEMDAS internationally.
Without rules: left to right gives 5×4=20. With DMAS: 3×4=12 first, then 2+12=14. The answer is always 14.
Multiplication and Division are always done before Addition and Subtraction. They have equal priority — resolve left to right.
Addition and Subtraction come last. They also have equal priority — resolve left to right after all × and ÷ are done.
When two operations have equal priority, work left to right. 12÷4=3 first (leftmost), then 3×3=9. Never do 4×3 first.
2 × 32 × 3 = 610 − 6 = 4415 ÷ 3 = 55 + 5 = 10103 × 2 = 64 + 6 − 14 + 6 = 1010 − 1 = 99Division (D ÷) — The First Letter
The D in DMAS stands for Division. Division shares the top priority with Multiplication. When you see ÷ anywhere in an expression (with no brackets), it must be resolved before any + or −.
Splitting into equal groups. 12 items split into 4 groups = 3 per group. The symbol ÷ and / both mean "divided by".
Always complete the division before touching any + or − sign in the expression.
Do the leftmost ÷ or × first. 8÷4=2, then 2×2=4. If you did 4×2=8 first: 8÷8=1 — wrong!
Dividing by 1 gives the same number. Useful shortcut when you spot it in an expression.
20 ÷ 4 = 55 + 3 = 8818 ÷ 3 = 66 − 2 = 4412 ÷ 4 = 33 × 3 = 99 (NOT 1)30 ÷ 5 = 62 + 6 − 32 + 6 = 8, then 8 − 3 = 55Multiplication (A ×) — Second Letter
The A in DMAS stands for الضرب — Multiplication. It shares the top priority with Division. Multiplication must be done before any + or −.
All three mean the same thing. In algebra, placing letters together (3x) implies multiplication.
Never add before multiplying. The multiplication 4×2 must happen first no matter where it appears.
Any number times 0 is always 0. Useful shortcut: if you see ×0 in an expression, that whole product becomes 0.
When there are two separate multiplication groups, compute both first, then add/subtract the results.
3 × 4 = 122 + 12 = 1414 (not 20)3 × 0 = 05 + 0 = 553 × 4 = 122 × 5 = 1012 + 10 = 22222 × 3 = 610 − 6 + 410 − 6 = 4, then 4 + 4 = 88Addition (M +) — Third Letter
The M stands for الجمع — Addition. Addition is a lower-priority operation. It is always performed after all × and ÷ have been resolved. Addition and Subtraction share equal priority.
No matter where the + sign appears in the expression, it must wait until all × and ÷ are done.
You can add numbers in any order and get the same result: 3+5=5+3=8. This is the commutative property.
Adding 0 to any number gives the same number. Quick simplification when you spot +0.
When + and − appear together (after all × ÷ done), work strictly left to right. Never do all additions first.
4×3=12 and 2×5=1012 + 10 = 222210 + 5 = 1515 − 3 = 12122×3=6. Expression: 8+4−68+4=12, then 12−6=66Subtraction (S −) — Last Letter
The S stands for الطرح — Subtraction. It shares the lowest priority with Addition. After all × and ÷ are done, work through + and − from left to right.
Unlike addition, you cannot swap the numbers in a subtraction. 8−3=5 but 3−8=−5. Order always matters.
10−3=7 first, then 7−2=5. If you did 3−2=1 first, then 10−1=9 — WRONG! Always left to right.
Even if − appears first in the expression left to right, if a × or ÷ appears later, do those first.
At beginner level we mainly use positive results, but know that subtraction can give a negative number if the second number is larger.
10 − 3 = 77 − 2 = 55 (NOT 9)5×3=1515−6=992×4=8 and 12÷3=415−8+4−115−8=7, 7+4=11, 11−1=1010Brackets ( ) — The Priority Override
Brackets are not a letter in DMAS, but they are the most important rule. Whatever is inside brackets is always evaluated first, using DMAS rules inside them. Brackets let you change the natural priority order.
Without brackets: 2+3×4=14. With brackets: (2+3)=5 first, then 5×4=20. Brackets completely change the answer.
Inside a bracket, DMAS still governs. 2×4=8 first (inside the bracket), then 3+8=11.
If two separate brackets exist: solve each one, then use the results in the rest of the expression.
When brackets are inside other brackets, solve the innermost first, then work outward.
(3 + 5) = 88 × 2 = 1616(2+3)=520÷5=44(5+3)=8 and (4−2)=28×2=16164×2=8 first10−8=2. Bracket resolved.3×2=66(10−4)=6. Expression: 2+6÷3×2−16÷3=2, then 2×2=4. Expression: 2+4−12+4=6, then 6−1=551️⃣ Are there brackets? → Solve them first (innermost first)
2️⃣ Are there × or ÷? → Solve left to right
3️⃣ Are there + or −? → Solve left to right
4️⃣ Write your final answer.
Practice Exams
Three exams — each 20 questions. Complete each exam before checking your score. Use the 💡 hint on any question if you get stuck.