Download Chapter 1 : Worsheet 1 : PEMDAS

LLG
Paris – Abu Dhabi
Advanced Math and Science Pilot Class
Mathematics, Grade 10
2014 – 2015
Chapter 1 : Worsheet 1 : PEMDAS
1. Priority of operations
There are 4 different operations on numbers (basically only two, since
subtracting by a number is equivalent to adding the opposite of this number
and dividing by a number is equivalent to multiply by its reciprocal). Inside an
expression these operations should not be computed in any order.
The rule that gives the priorities of the operations is called PEMDAS, which
stands for (from the highest to the lowest priority) :
P……………………………………………………………………….
E…………………………………………………………………….…
M………………………………………………………………………
D……………………………………………………………………….
A………………………………………………………………….……
S…………………………………………………………………….….
Remarks :
o When two operations have the same priority in an expression, we
apply them from left to right.
o When there are different levels of brackets inside an expression, the
priority goes to the most interior.
Example : (3 + 2) × 7 ≠ 3 + 2 × 7
Exercises :
1. Find where to put one pair of brackets in each expression below to
obtain a true equality :
2+3×5−5+4 = 6
2 + 3 × 5 − 5 + 4 = 16
2 + 3 × 5 − 5 + 4 = 24
2+3×5−5+4 = 8
2 + 3 × 5 − 5 + 4 = 14
2. Calculate, then check with your calculator :
𝐴=5×3+
6
+
7−5
3
𝐵 = 5 × (3 +
6
)+
7−5
3
𝐶=
2−3−(5−7)×(−2)
−3−(−3)+6
𝐷 = [8 (8 + 8 − (−8)) − 8 (−8)] + 8 − (−2 × (−3) − 4)
2. How to distinguish a sum and a product
Definitions :
• A sum is an expression where the operation with the lowest priority (the last
to be performed) is addition or subtraction. A sum is made of terms.
• A product is an expression where the operation with the lowest priority (the
last to be performed) is multiplication or division. A product is made of factors.
Example : 2 (5𝑦 − 2) is a product (of two factors), while 3 × 𝐴 × 𝐵 + 1 is a
sum of two terms.
Draw the tree diagrams of these two expressions.
Remark : In a tree diagram the operation with the lowest priority, which
decides whether it is a sum or a product, is the one situated at the top of the
tree.
For the next expressions, draw their tree diagram then decide if it’s a sum or a
product.
 7𝑦 + 6
 2𝑎 × 𝑏 − 𝑎𝑏
 4 × 𝑌 + 3(𝑋 + 2)
 (𝑦 + 6)(𝑦 + 6)
3𝑥−2
 𝑦+2
8
𝑏

6+

2𝐴 + ( 7 ) × 7
(2 + 3𝑥)2

2−𝑌