Multiplicative Comparisons
What does it mean when we say “15 is 5 times as many as 3”?
3 × 5 = 15
Start with 0. Use the rule add 6. Write the first four numbers.
0, 6, 12, 18
What is a factor?
number that divides evenly into another number.
What makes a number prime?
It has exactly two factors — 1 and itself.
Tickets cost $6 each. How much for 3 tickets?
$18
Write an equation to show that 54 is 6 times as many as 9.
54 = 6 × 9
Start with 24. Use the rule divide by 2. Write the next three numbers.
12, 6, 3
List all factor pairs of 12.
(1,12), (2,6), (3,4)
Is 9 prime or composite? Explain.
Composite — 9 has more than two factors (1, 3, 9).
Nia makes 28 pancakes, burns 6, freezes 10, and shares the rest on 4 plates.
How many pancakes per plate?
(28 − 6 − 10) ÷ 4 = 3 pancakes per plate
A model shows that 3 × 5 = 15. Describe the comparison in words.
15 is 5 times as many as 3.
A pattern goes: pentagon, rectangle, pentagon, rectangle...
What shape is in the 10th position?
Pentagon
List all factor pairs of 63.
(1,63), (3,21), (7,9)
Is 17 prime or composite?
Prime
Aditya buys 4 bags of 8 lemons each. He uses 6 lemons per pitcher.
How many full pitchers can he make?
(4 × 8) ÷ 6 = 5 full pitchers
Michelle checks out 4 books. Her sister checks out 5 times as many.
How many books do they check out altogether?
4 + (4 × 5) = 24 books
The pattern starts at 8 and follows add 8.
What is the 40th number in the pattern?
8 + (39 × 8) = 320
A number has only the factors 1, 2, 4, 8, and 16. What is the number?
16
Which number is composite: 19 or 33?
33 — it has factors 1, 3, 11, and 33.
A farmer collects 55 eggs and 28 eggs, and puts 6 in each carton.
How many cartons are needed?
(55 + 28) ÷ 6 = 13 remainder 5 → 14 cartons total
A farmer says the total number of eggs is 7 times as many as 6.
Write an equation and solve.
7 × 6 = 42
A shape pattern alternates between 4-sided and 5-sided shapes.
Which numbered positions have pentagons?
Odd-numbered positions
Find all factor pairs of 36.
(1,36), (2,18), (3,12), (4,9), (6,6)
How can a factor tree show if a number is prime or composite?
If the number breaks down into more than one factor pair, it’s composite.
Gabriel sells drinks for $3, hot dogs for $5, and shirts for $15.
He makes $60 from each type.
How many of each did he sell?
20 drinks, 12 hot dogs, 4 shirts