Math Core

You already know that $3 \times 4$ means 3 groups of 4. Multiplication can also compare two amounts. When someone says a whale is 5 times as long as a boat, they are using multiplication to compare.

"Times as many"

Nora has 4 books. Ben has 3 times as many books as Nora. How many books does Ben have?

"3 times as many" means Ben has Nora's amount, 3 times over. Each jump below is one copy of Nora's 4 books.

Three jumps of 4 land on 12. Ben has 3 times as many books as Nora.

So Ben has $3 \times 4 = 12$ books.

Multiplying to compare

" $a$ is $n$ times as many as $b$ " means $a = n \times b$ .

For example, "12 is 3 times as many as 4" means $12 = 3 \times 4$ .

One equation, two comparisons

Look at $12 = 3 \times 4$ again. You can read it two ways:

12 is 3 times as many as 4.
12 is 4 times as many as 3.

Both are true, because $3 \times 4$ and $4 \times 3$ are both 12.

Worked example: Write the equation

Write an equation for "42 is 6 times as many as 7." Then say the comparison another way.

"42 is" means $42 =$ . "6 times as many as 7" means $6 \times 7$ . The equation is

42 = 6 \times 7.

Another way to say it: 42 is 7 times as many as 6.

Worked example: Finding the bigger amount

A cat weighs 8 pounds. A dog weighs 5 times as much as the cat. How much does the dog weigh?

The dog is the bigger amount. Multiply the cat's weight by 5:

5 \times 8 = 40.

The dog weighs 40 pounds.

Finding the smaller amount

Sometimes you know the bigger amount and need the smaller one. Then you are looking for a missing factor, so you can divide.

Worked example: A missing factor

A pumpkin weighs 36 pounds. That is 4 times as much as a melon weighs. How much does the melon weigh?

Write the comparison: $36 = 4 \times ?$ . Ask yourself, "4 times what is 36?" Since $4 \times 9 = 36$ , the melon weighs 9 pounds. You could also divide: $36 \div 4 = 9$ .

"Times as many" or "more than"?

These two phrases sound alike, but they mean very different things.

Worked example: Two kinds of comparing

Eli has 5 shells. Rosa has 3 more shells than Eli. Jack has 3 times as many shells as Eli. How many do Rosa and Jack have?

"3 more than" means add: Rosa has $5 + 3 = 8$ shells.
"3 times as many" means multiply: Jack has $3 \times 5 = 15$ shells.

Common mistake

Read the comparison words carefully. "More than" tells you to add. "Times as many" (or "times as long," "times as heavy") tells you to multiply. Mixing them up is the most common mistake in comparison problems.

Tip

Draw a quick bar picture. Draw one bar for the smaller amount. Then draw the bigger amount as several of those bars in a row. The number of bars is the "times."

Practice

Practice 1

Maya has 6 stickers. Leo has 3 times as many stickers as Maya. How many stickers does Leo have?

Type a number.

Practice 2

Which equation means "32 is 4 times as many as 8"?

Practice 3

A cat weighs 9 pounds. A dog weighs 7 times as much as the cat. How many pounds does the dog weigh?

Type a number.

Practice 4

Sam has 8 marbles. Ava has 24 marbles. Ava has how many times as many marbles as Sam?

Type a number.

Practice 5

A red ribbon is 45 inches long. It is 5 times as long as a blue ribbon. How long is the blue ribbon, in inches?

Type a number.

Practice 6

A tree is 6 feet tall. A building is 8 times as tall as the tree. How many feet taller is the building than the tree?

Type a number.

Practice 7

Tom has 5 cards. Jen has 4 more cards than Tom. Kai has 4 times as many cards as Tom. How many more cards does Kai have than Jen?

Type a number.