AR · 8 cards

Whole-Number Operations and Order of Operations flashcards

8 cards with the formulas, rules and traps from this lesson. Answer in your head, then flip to check.

Rule · 1/8
What is the order of operations?
Grouping symbols, then exponents, then multiplication and division from left to right, then addition and subtraction from left to right.
Common trap · 2/8
Evaluate $18 \div 3 \times 2$ .
12. Multiplication and division share one level, so go left to right: $18 \div 3 = 6$ , then $6 \times 2 = 12$ . Multiplying first (giving 3) is the PEMDAS trap.
Rule · 3/8
How do you evaluate nested grouping such as $4 [6 + 3 (8 - 5)]$ ?
Work from the innermost group outward: $8 - 5 = 3$ , then $6 + 3 \times 3 = 15$ , then $4 \times 15 = 60$ . A number written next to a bracket means multiply.
Common trap · 4/8
347 trainees ride vans seating 8. Full vans, vans needed, people left over?
$347 \div 8 = 43$ remainder 3: 43 full vans, 44 vans needed so nobody is left behind, and 3 trainees left over. The question decides which number to report.
Rule · 5/8
What are the divisibility tests for 3, 9, 4 and 6?
3: the digit sum is a multiple of 3. 9: the digit sum is a multiple of 9. 4: the last two digits form a multiple of 4. 6: the number passes both the 2 test and the 3 test.
Strategy · 6/8
Mental shortcuts for multiplying by 5, 25 and 99?
By 5: times 10, then halve ( $68 \times 5 = 340$ ). By 25: times 100, then divide by 4 ( $64 \times 25 = 1600$ ). By 99: times 100, minus the number ( $37 \times 99 = 3663$ ).
Strategy · 7/8
How do you multiply a two-digit number by 11 in your head?
Place the sum of its digits between the digits, carrying 1 into the left digit when the sum is 10 or more: $43 \times 11 = 473$ and $78 \times 11 = 858$ .
Strategy · 8/8
How do you check a division answer that has a remainder?
Multiply the quotient by the divisor and add the remainder; you should get the dividend back. For $380 \div 32 = 11$ R 28: $11 \times 32 + 28 = 380$ .

← Turning Words into Math Fractions and Mixed Numbers →