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R.4 Multiply one-digit numbers by two-digit numbers: word problems

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What is multiplication with one-digit and two-digit numbers?

Multiplication is combining equal groups to find a total amount. When we multiply a two-digit number by a one-digit number, we are adding the two-digit number multiple times.

Example:

If you have 4 boxes with 25 crayons in each box, you multiply to find the total:

25
× 4
100
Note

Remember: 25 × 4 means 25 + 25 + 25 + 25. Both expressions equal 100.

Breaking down the multiplication process

We solve these problems by multiplying the ones place first, then the tens place. This method is called partial products.

Steps for 36 × 7:
  1. Multiply the ones: 6 ones × 7 = 42 ones (write 2, carry 4 tens)
  2. Multiply the tens: 3 tens × 7 = 21 tens
  3. Add the carried tens: 21 tens + 4 tens = 25 tens
36
× 7
252
Note

Always start multiplying from the rightmost digit (ones place) and move left to the tens place.

Solving word problems step by step

Word problems describe real situations where you need to find a total by multiplication. Read carefully to identify the numbers and what operation to use.

Example problem:

A farmer plants 8 rows of corn. Each row has 14 corn plants. How many corn plants are there in total?

  1. Identify the numbers: 8 rows (one-digit) and 14 plants per row (two-digit)
  2. Set up the multiplication: 14 × 8
  3. Solve: 4 × 8 = 32 (write 2, carry 3), then 1 × 8 = 8, plus 3 = 11
14
× 8
112

Answer: There are 112 corn plants in total.

Note

Look for clue words like "each," "per," "every," or "total" to know when to multiply.

Checking your multiplication

After solving a multiplication problem, you should verify your answer to make sure it is reasonable and correct.

How to check 23 × 6 = 138:
  • Estimate first: 23 is close to 20, so 20 × 6 = 120. Our answer 138 is close to 120, so it's reasonable.
  • Use addition: 23 + 23 + 23 + 23 + 23 + 23 = 138 (six groups of 23).
  • Check place value: 6 × 3 ones = 18 ones (8 ones, 1 ten carried), 6 × 2 tens = 12 tens plus 1 ten carried = 13 tens (130). 130 + 8 = 138.
23
× 6
138
Note

Estimating helps you catch major errors. If you multiply 23 × 6 and get 98, you know it's wrong because 20 × 6 alone is 120.

Different types of multiplication word problems

Multiplication word problems can appear in various situations. Understanding the context helps you choose the correct numbers to multiply.

Common situations:
  • Equal groups: "There are 9 classrooms. Each has 28 students." (28 × 9)
  • Arrays: "A parking lot has 7 rows with 15 cars in each row." (15 × 7)
  • Repeated addition: "A runner ran 12 miles each day for 6 days." (12 × 6)
  • Comparison: "A novel has 45 pages. A short story has 3 times as many pages." (45 × 3)
45
× 3
135

The short story has 135 pages.

Note

Sometimes word problems include extra information you don't need. Identify only the numbers necessary to solve the problem.

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