Math Homework: Multiplication and Division using Doubling/Halving

This assignment focuses on the application of doubling and halving as a method to simplify multiplication and division problems, particularly those involving larger numbers. The solution demonstrates how to solve equations by halving one number and doubling the other to arrive at an equivalent, simpler equation. It provides step-by-step examples for multiplying and dividing by 4, along with specific steps for multiplying by 20, 25, and 9, utilizing doubling, halving, and multiplying by powers of 10. The assignment includes detailed calculations for various problems, illustrating the practical application of these techniques. References are provided for further reading on speed mathematics and active learning in number and algebra.

Use Doubling and halving to multiply and divide by 4.
Doubling and halving is used to solve equations that have large numbers by minimizing
them to smaller doable equations as shown in below in the following question.
7. 4 x 56 = 2 x 112 = 224 (First half the four to make 2, then double the 56 to make 112.
now we have 2x 112 that gives us 224.)
8. 72 ÷ 4 = 36 ÷ 2 = 18 (First half the 72, then half 4. You get 36 and 2, so 36 divide by 2 is
18)
9. 153 x 4 = 306 x 2 = 612 (First double the 153 to make 306, then half the 4 to make 2.
Now we have 306 x 2 that gives us 612.)
10. 268 ÷ 4 = 134 ÷ 2 = 67 (First half the 268, then half 4. You get 134 and 2, so 134 divide
by 2 is 67)
Solve the multiplications using these Steps.
Multiplications steps to success
x20 start number by x2, then x10
x25 start number by x100, then ÷4
x9 start number x10, then x9
11. 20 x 57 = 57 x 2 = 114 x 10 = 1140 (First multiply 57 by 2, we get the result to be 114,
then multiply 114 by 10 to get 1140 as the answer. )
12. 20 x 34 = 34 x 2 = 68 x 10 = 680 (First multiply 34 by 2 to get 68, then multiply 68 by
10 to get 680 which is the answer )
13. 25 x 48 = 48 x 100 = 4800 ÷ 4 = 1200 (First multiply 48 by 100 to get 4800, then divide
4800 by 4 to get 1200 which is the answer)
14. 25 x 88 = 88 x 100 = 8800 ÷ 4 = 2200 (First multiply 88 by 100 to get 8800, then divide
8800 by 4 to get 2200 which is the answer.)
15. 9 x 25 = 25 x 10 =250 x 9 = 2250 (First multiply 25 by 10, to get 250 then multiply the
result 250 by 9 to get 2250 which is the answer)
16. 45 x 9 = 45 x 10 = 450 x 9 = 4050 (First multiply 45 by 10 to get 450, then multiply the
result 450 by 9 to get 4050 which is the correct answer)
17. 65 x 20 = 65 x 2 = 130 x 10 = 1300 (First multiply 65 by 2 to get 130 then multiply the
result 130 by 10 to get 1300 which is the correct answer)
18. 140 x 25 = 140 x 100 =14000 ÷ 4 = 3500 (First multiply 140 by 100 to get 14000, then
divide the result by 4 to get 3500 which is the correct answer )
References
Bill, H. (2011). Speed Mathematics: secret skills for quick calculation. New York: Wiley.
Ian, L. (2007). Active Learning in number and algebra: copiable math’s worksheets for years.
Brunswick: Vic