Multiplication Magic: 2-Digit Times 1-Digit

Words to Know

Multiply

Adding the same number over and over — a fast way to count groups

47 × 8 means 8 groups of 47!

Distributive property

Splitting a number into parts, multiplying each part, then adding them back together

47 × 8 = (40 × 8) + (7 × 8)

Partial products

The answers you get when you multiply each part separately

320 and 56 are the partial products of 47 × 8

Place value

What a digit is worth based on where it sits in a number — tens, ones, hundreds

In 47, the 4 is worth 40 (tens place)

Tens

The digit in the tens place — worth 10 times its face value

In 47, the tens part is 40

Ones

The digit in the ones place — worth its face value

In 47, the ones part is 7

Check What You Learned

Fun Facts

• The distributive property states that a × (b + c) = (a × b) + (a × c)

  Source: Common Core Math Standards, 4th Grade, CCSS.MATH.CONTENT.4.NBT.B.5

• Breaking 47 into 40 + 7, then multiplying each by 8: (40 × 8) + (7 × 8) = 320 + 56 = 376

  Source: standard arithmetic

• The "5, 6, 7, 8" memory trick for 7 × 8 = 56 works because the digits 5, 6, 7, 8 appear in sequence

  Source: math education mnemonic, widely used in elementary curricula

• The partial products method (breaking by place value) is the standard 4th-grade approach before introducing the standard algorithm

  Source: CCSS.MATH.CONTENT.4.NBT.B.5

• Mental math research shows breaking numbers into place-value parts improves number sense and fluency

  Source: Boaler, J., 2016, "Mathematical Mindsets"