**Here’s the third in my series of multiplication tricks. The first was a trick for multiplying by 5. The second a trick for multiplying by 15, and now this one, a trick for multiplying by 25. Anyone see a pattern?**

**TRICK #3:**

**WHAT THE TRICK LETS YOU DO:** Quickly multiply numbers by 25.

**HOW YOU DO IT:** The key to multiplying by 25 is to think about quarters, as in “nickels, dimes, and quarters.”

Since four quarters make a dollar, and a dollar is worth 100 cents, the concept of quarters helps children see that 4 x 25 = 100.

Since four quarters make one dollar, children can see that twice that many quarters, 8, must make two dollars (200 cents). And from that fact children can see that 8 x 25 = 200.

Following this pattern, children can see that twelve quarters make three dollars (300 cents). So 12 x 25 = 300. And so on.

Fine. But how does all of this lead to a multiplication trick?

The trick is this. To multiply a number by 25, divide the number by 4 and then tack two 0s at the end, which is the same as multiplying by 100.

A few more examples:

16 x 25. Divide 16 by 4 to get **4**, so the answer is **4**00. [In money terms, 16 quarters make $**4** = **4**00 cents.]

24 x 25. Divide 24 by 4 to get** 6, **so the answer is **6**00. [In money terms, 24 quarters make $**6** = **6**00 cents.]

48 x 25. Divide 48 by 4 to get **12**, so the answer is **12**00. [In money terms, 48 quarters make $**12** = **12**00 cents.]

**Try these for practice:**

20 x 25

32 x 25

36 x 25

16 x 25

24 x 25

44 x 25

52 x 25

76 x 25

**Answers:**

20 x 25 = 500

32 x 25 = 800

36 x 25 = 900

16 x 25 = 400

24 x 25 = 600

44 x 25 = 1100

52 x 25 = 1300

76 x 25 = 1900

But wait, you protest … what about all of the numbers that are not divisible by 4? Good question! But it turns out that there’s a workaround. You still divide by 4, but now you pay attention to the remainder.

If the remainder is 1, that’s like having 1 extra quarter, an additional 25 cents, so you add 25 to the answer.

Example: 17 x 25. Since 17 ÷ 4 = **4** remainder 1, the answer is **4**00 + 25 = 425.

If the remainder is 2, that’s like having 2 extra quarters, an additional 50 cents, so you add 50 to the answer.

Example: 26 x 25. Since 26 ÷ 4 = **6** remainder 2, the answer is **6**00 + 50 = 650.

If the remainder is 3, that’s like having 3 extra quarters, an additional 75 cents, so you add 75 to the answer.

Example: 51 x 25. Since 51 ÷ 4 = **12** remainder 3, the answer is **1200** + 75 = 1275.

**Now try these for practice:**

9 x 25

11 x 25

14 x 25

19 x 25

22 x 25

25 x 25

34 x 25

49 x 25

**Answers:**

9 x 25 = 225

11 x 25 = 275

14 x 25 = 350

19 x 25 = 475

22 x 25 = 550

25 x 25 = 625

34 x 25 = 850

49 x 25 = 1225

Happy teaching!

— Josh

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