Question

Show three ways to estimate 3/5 times 9 1/2 identify each method you use

Answer 1

3/5 * 9 1/2

1st way. Distributive property of multiplication.

3/5 * 9 = 3*9 / 5*1 = 27/5
3/5 * 1/2 = 3*1 / 5*2 = 3/10

Add the products:
27/5 + 3/10 = (27/5 * 2/2) + 3/10 = 54/10 + 3/10 = 57/10 

Simplify: 57/10 into a mixed fraction 5 7/10 

2nd way:
Converting the mixed fraction into an improper fraction and multiply.

9 1/2 = ((9*2)+1)/ 2 = 19/2

3/5 x 19/2 = 3*19 / 5*2 = 57/10 

57/10 = 5 7/10

3rd way: We can use rounding of fractions to estimate the products.

3/5 * 9 1/2

9 1/2 can be rounded off to 10.

3/5 * 10 = 3*10 / 5
30 / 5 = 6 is the estimated product of rounding.