Break Apart Strategy

Calculate $14 \times 6$ mentally

Break 14 into friendly parts: $14 = 10 + 4$ = Two easier multiplications

Multiply each part by 6: $10 \times 6 = 60$ and $4 \times 6 = 24$ = 60 and 24

Add the results: $60 + 24 = 84$ = $14 \times 6 = 84$

Answer: $14 \times 6 = 84$

Multiply by 5 Trick

Calculate $18 \times 5$ mentally

Use the trick: multiply by 10, then halve: Multiplying by 5 = multiplying by 10 and dividing by 2 = Two-step shortcut

Multiply by 10: $18 \times 10 = 180$ = 180

Divide by 2: $180 \div 2 = 90$ = $18 \times 5 = 90$

Answer: $18 \times 5 = 90$

Doubling and Halving

Calculate $25 \times 16$ mentally

Double one factor, halve the other: Double 25 to get 50, halve 16 to get 8 = $25 \times 16 = 50 \times 8$

Repeat if helpful: Double 50 to get 100, halve 8 to get 4 = $50 \times 8 = 100 \times 4$

Calculate the easy multiplication: $100 \times 4 = 400$ = $25 \times 16 = 400$

Answer: $25 \times 16 = 400$

Multiply by 9 Trick

Calculate $9 \times 7$ mentally

Use the trick: multiply by 10, then subtract: $9 = 10 - 1$, so $9 \times 7 = 10 \times 7 - 7$ = Subtract once

Multiply by 10: $10 \times 7 = 70$ = 70

Subtract the original number: $70 - 7 = 63$ = $9 \times 7 = 63$

Answer: $9 \times 7 = 63$

Near Squares Strategy

Calculate $21 \times 19$ mentally

Notice these are close to 20: $21 = 20 + 1$ and $19 = 20 - 1$ = Both near 20

Use the difference of squares: $(20 + 1)(20 - 1) = 20^2 - 1^2$ = $400 - 1$

Calculate: $400 - 1 = 399$ = $21 \times 19 = 399$

Answer: $21 \times 19 = 399$

Mistake: Forgetting to add all parts when breaking apart

Why: When using the break apart strategy, every part must be multiplied and then added together.

Correct: For $14 \times 6$: Calculate BOTH $10 \times 6 = 60$ AND $4 \times 6 = 24$, then add: $60 + 24 = 84$

Mistake: Doubling both factors instead of doubling one and halving the other

Why: Doubling both would quadruple the answer! The strategy keeps the product the same.

Correct: For $25 \times 8$: Double 25 to 50, BUT halve 8 to 4. Answer: $50 \times 4 = 200$

Mistake: Using the multiply-by-9 trick but adding instead of subtracting

Why: $9 = 10 - 1$, not $10 + 1$. You need to subtract to get the correct answer.

Correct: For $9 \times 6$: Calculate $10 \times 6 = 60$, then SUBTRACT 6: $60 - 6 = 54$

Shopping and Budgeting

Calculate total costs quickly when buying multiple items.

8 notebooks at 3 dollars each: $8 \times 3 = 24$ dollars total.

Time Calculations

Convert between hours and minutes or calculate durations.

A 7-hour flight is $7 \times 60 = 420$ minutes. Using the trick: $7 \times 6 = 42$, then add a zero: 420.

Cooking and Recipes

Scale recipes by multiplying ingredient amounts.

A recipe calls for 4 eggs and serves 6. To serve 12 (double), you need $4 \times 2 = 8$ eggs.

Q: Which strategy should I use?

A: It depends on the numbers! For multiplying by 5, use the halving trick. For numbers close to 10, use the break apart method. With practice, you'll naturally choose the best strategy.

Q: Why does doubling and halving work?

A: When you double one factor and halve the other, the product stays the same because $2 \times \frac{1}{2} = 1$. For example: $4 \times 8 = 32$ and $8 \times 4 = 32$ - same answer!

Q: Can I combine strategies?

A: Absolutely! For example, to calculate $45 \times 6$, you could break 45 into $40 + 5$, then use the multiply-by-5 trick for the second part.