Grade 4 (age 9-10)

grade 4 Multi-digit Multiplication

Multi-digit Multiplication

Multi-digit multiplication splits a large number by place value and multiplies piece by piece. Break 234 into 200, 30, and 4, multiply each piece, then add, and a hard-looking product becomes easy. You use it to find the total price of several items or to measure an area. Change the numbers with the sliders and the area model and the vertical algorithm gather the partial products into the answer.

How to multiply big numbers?

🏗️ Split it up to multiply easily!

①Split 234 into 200 + 30 + 4

②Multiply each part, then add them up

③This is called the area model

Understand with the Area Model

Big number (a)234

Multiplier (b)16

💡 Principle of the Area Model

①Split the big number into hundreds, tens, ones

②Multiply each part separately (partial products)

③Sum all partial products = final answer

④If a place product is 10 or more, add 1 to the next place (carry)

⑤The vertical form below uses the two slider numbers above

Calculate with Long Multiplication

📝 Long Multiplication Order

①Start with the ones place

②Tens-place product shifts one column left

③Line up and add → answer

Summary

Distributive Law

234 × 16 = 234 × 10 + 234 × 6

Split the multiplier, multiply each, then add

Area Model

(200+30+4) × (10+6) = sum of partial products

Visualize multiplication as a rectangle's area

Long Multiplication

Ones-product + Tens-product (×10) = answer

Align by place, multiply, then add in turn

🎯 Key Points

①Calculate big multiplications by splitting

②Distributive law: split, multiply, combine

③Long multiplication: aligning places matters

④Carry to the next place when needed

⑤The area model reduces mistakes

Examples and Unit Test

Example 1

Use the distributive law to calculate 234 × 16.

Split the multiplier 16 into 10 and 6: 234 × 10 + 234 × 6.

234 × 10 = 2340, 234 × 6 = 1404. 2340 + 1404 = 3744.

▸ 3744

Big multiplication is easy: split the multiplier, multiply each part, then add.

Example 2

Use the area model to calculate 23 × 14.

Split 23 into 20 and 3, and 14 into 10 and 4, to get four partial products.

20×10 + 20×4 + 3×10 + 3×4 = 200 + 80 + 30 + 12 = 322.

▸ 322

The area model adds up the partial products made by splitting both numbers.

Unit Test

What is the value of 123 × 3?

①339

②369

③366

④393

▸ ② 369

Split 123 into 100, 20, 3: 100×3 + 20×3 + 3×3.

300 + 60 + 9 = 369.

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Large Numbers

Fraction Addition & Subtraction