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Multiplying Above & Below the Reference Number 33 Mathematically, we would say: when we multiply two positive (plus) numbers ...

= x 0 1 2 3 4 5 6 7 8 9 ( ) % < > + - = x 0 1 2 3 4 5 6 7 8 9 ( ) % < > + - = x 0 1 2 3 4 5 6 7 8 9 ( ) % < &g ...

Checking Your Answers 35 Mathematicians have known this method of checking answers for about 1,000 years, although I have made a ...

36 Speed Math for Kids Five is our substitute for 14. We now do the same calculation (multiplication) using the substitute numbe ...

Checking Your Answers 37 +2 +4 10 12 × 14 = 160 3 5 + 8 168 6 If we have the right answer in our calculation, the digits in the ...

38 Speed Math for Kids +4 +4 10 14 × 14 = 180 5 5 + 16 196 7 A shortcut Th ere is another shortcut to this procedure. If we fi n ...

Checking Your Answers 39 calculators can’t handle the number of digits in the answer, so most would show the fi rst digits of th ...

40 Speed Math for Kids I write the substitute numbers in pencil above or below the actual numbers in the problem. It might look ...

Checking Your Answers 41 Th is method won’t fi nd all mistakes. For instance, say we had 3,789,360 for our last answer; by mista ...

42 Speed Math for Kids Eleven nines are 99. Nine plus 9 equals 18. Wrong answer? No, not yet. Eighteen is a two-digit number, so ...

43 = x 0 1 2 3 4 5 6 7 8 9 ( ) % < > + - = x 0 1 2 3 4 5 6 7 8 9 ( ) % < > + - = x 0 1 2 3 4 5 6 7 8 9 ( ) % < ...

44 Speed Math for Kids then multiply the answer by 10, or, you could say, you double the number and add a 0. For instance, to mu ...

Multiplication Using Any Reference Number 45 3 × 1 = 3 480 + 3 = 483 Th e problem now looks like this: +3 +1 20 23 × 21 = 24 480 ...

46 Speed Math for Kids We put 3 and 11 above 23 and 31: +3 +11 20 23 × 31 = Th ey are 3 and 11 above the reference number, 20. A ...

Multiplication Using Any Reference Number 47 23 × 31 = 713 5 4 11 2 Multiply our substitute numbers and then add the digits in t ...

48 Speed Math for Kids Using 20 as a reference number, we get: 20 18 × 17 = –2 –3 Subtract diagonally: 17 – 2 = 15 Multiply by 2 ...

Multiplication Using Any Reference Number 49 18 + 7 = 25 10 × 25 = 250 Multiply the numbers in the circles and add this to the s ...

50 Speed Math for Kids We now multiply the numbers in the circles: 2 × 14 = 28 It is actually –2 times 14 so our answer is –28. ...

Multiplication Using Any Reference Number 51 Let’s try it: 50 47 × 45 = –3 –5 Subtract diagonally: 45 – 3 = 42 Multiply 42 by 10 ...

52 Speed Math for Kids We divide by 2 to get 3,000. We then multiply the numbers in the circles and add the result to 3,000: 3 × ...