Comparison stories come in two kinds. Some say "more than" (an amount added on). Others say "times as many" (copies of an amount), which you met in Times as Many. The words tell you which operation to use.
Key idea
"$d$ more than" compares by adding or subtracting. "$k$ times as many" compares by multiplying or dividing. To find the smaller amount from the larger one, undo the comparison.
Why it works
Picture two tapes. With "6 more," the longer tape is the shorter tape plus an extra piece of 6. With "3 times as long," the longer tape is 3 copies of the shorter tape. Different pictures, different math.
Worked example: Times as many
A blue ribbon is 6 cm long. A red ribbon is 3 times as long. How long is the red ribbon?
- "3 times as long" means 3 copies of 6 cm.
- $3 \times 6 = 18$.
Answer: 18 cm
Worked example: More than
A blue ribbon is 18 cm long. A red ribbon is 6 cm longer. How long is the red ribbon?
- "6 cm longer" means the blue length plus 6 more.
- $18 + 6 = 24$.
Answer: 24 cm
Worked example: Find the smaller amount
A dog weighs 45 pounds. That is 5 times as much as a cat. How much does the cat weigh?
- 45 is 5 copies of the cat's weight.
- Split 45 into 5 equal parts: $45 \div 5 = 9$.
- Check: $5 \times 9 = 45$.
Answer: 9 pounds
Common mistake
Grabbing the numbers and multiplying no matter what the story says. Read the comparison words first: "more" or "less" means add or subtract; "times as" means multiply or divide.