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R.2 Multiply by multiples of ten: up to two digits

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What is a multiple of ten?

A multiple of ten is any number you get when you multiply ten by a whole number. These numbers end in a zero.

Examples:
  • 10, 20, 30, 40, 50
  • 60, 70, 80, 90, 100
Note

You can easily spot a multiple of ten because it always has at least one zero in the ones place.

The pattern of multiplying by a multiple of ten

When you multiply a number by a multiple of ten, you first multiply the non-zero parts. Then, you add the total number of zeros from both factors to the end of the product.

Steps:
  • Look at the problem: 14 × 30
  • First, multiply the basic fact: 14 × 3 = 42
  • Then, add the zero from the multiple of ten: 42 → 420
Note

Think of it as "how many groups of tens" you have. For example, 14 × 30 is like 14 groups of 30, or 14 × 3 groups of 10.

Multiply a two-digit number by a multiple of ten

When both numbers have two digits, and one is a multiple of ten, use place value. Break the problem into simpler multiplication facts you already know.

Example breakdown:
  • Solve: 60 × 25
  • Think: 60 is 6 tens
  • Calculate: 6 × 25 = 150
  • Remember the ten: 150 is 15 tens, so add a zero: 1,500
  • Final answer: 60 × 25 = 1,500
Note

You can also reverse the factors. For example, 25 × 60 will give you the same answer because multiplication is commutative.

Solve problems with different combinations

You can use the same strategy no matter which number is the multiple of ten. The key is to focus on the basic fact first, then count and add the zeros.

More examples:
  • 32 × 40 = ? → 32 × 4 = 128 → Add one zero → 1,280
  • 50 × 18 = ? → 5 × 18 = 90 → Add one zero → 900
  • 70 × 60 = ? → 7 × 6 = 42 → Add two zeros → 4,200
Note

Always check your final answer. Does it have the correct number of zeros? Does the number of digits make sense for the size of the numbers you multiplied?

Apply the skill in different situations

Multiplying by multiples of ten is a useful skill for solving real-world problems, like calculating total items in multiple packages or finding distances.

Word problem example:
  • "There are 20 pencils in one box. A school orders 35 boxes. How many pencils are there in total?"
  • This is: 20 × 35
  • Solve: 2 × 35 = 70 → Add one zero → 700 pencils.
Note

When you see a problem with a number ending in zero, it’s a signal that this efficient strategy can be used.