Operations

Question 1

Order of operations (BEMA)

Answer 1

1. Brackets
2. Exponentiation
3. Multiplication/division
4. Addition/subtraction

Question 2

Fractions:
adding / subtracting fractions with the same denominator

Answer 2

Just add or subtract the numerators:

1/9 + 2/9 = (1+2)/9 = 3/9 = 1/3
7/8 - 1/8 = (7-1)/8 = 6/8 = 3/4

Question 3

Fractions:
adding / subtracting fractions with different denominators

Answer 3

Work out the LCM of the denominators, then add/subtract the numerators:

3/8 + 1/4 = 3/8 + 2/8 = (3+2)/8 = 5/8 [LCM = 8]
5/6 - 1/2 = 5/6 - 3/6 = 2/6 = 1/3 [LCM = 6]

1) draw slanted line over fraction and write a number to multiply by
2) draw a long horizontal line, write LCM in the denominator, calculation in the numerator
3) underline similar terms in the new numerator
4) simplify the result as much as possible

Question 4

Fractions:
multiplying fractions

Answer 4

multiply the numerators, then multiply the denominators, then simplify the resulting fraction:

1/2 x 2/5 = (1 x 2) / (2 x 5) = 2/10 = 1/5

Question 5

Fractions:
dividing fractions

Answer 5

multiply the 1st fraction by a reciprocal of the 2nd fraction (if the second number is integer, multiply by 1divided by this integer):

1/3 divided by 9/16 = 1/3 x 16/9 = (1x16) / (3x9) = 16/27

1/7 divided by 5 = 1/7 x 1/5 = (1x1) / (7x5) = 1/35

Question 6

Fractions:
mixed fraction

Answer 6

Improper fraction: 11/8
Proper fraction: 3/8
Mixed fraction: 1+ ⅜ = 1⅜

Always simplify a fraction and then convert it to a mixed fraction

Question 7

Operations: Distributive property
(give to all elements in brackets)

Answer 7

A x (B + C) = A x B + A x C

• The distributive property is a process of opening the brackets.
• Factoring is a reverse process: we look for a common multiplier (also called “factor”) and we put it outside the brackets.

Question 8

Operations: Transitive property

Answer 8

If A = B and B = C, then A = C

Addition, Subtraction, Multiplication and Division are ALL transitive

• We use this property when solving a system of two equations.
• We can add/subtract or multiply/divide the left-hand sides of these equations and do the same with their right-hand sides.

Question 9

Operations: Associative property

Answer 9

(A + B) + C = A + (B + C) = (A + C) + B

(A x B) x C = A x (B x C) = (A x C) x B

• Addition and Multiplication are associative.
• Subtraction and Division are NOT associative.

Question 10

Operations: Commutative property
(commuters travel back and forth)

Answer 10

A + B = B + A
A x B = B x A

• Addition and Multiplication are commutative.
• Subtraction and Division are NOT commutative.