Explanation:
a mixed fraction number like x a/b is always a short form for
x + a/b
so,
1 ¼ = 1 + ¼
now you multiply it like any other sum :
(a + b) × c = ac + bc
(1 + ¼) × 8 = 1×8 + ¼×8 = 8 + 8/4
what you see is that 8/4 is actually more than 1. so, we simplify
8 + 8/4 = 8 + 2 = 10
another way is to consider that every whole number (or general integer number) is also a fraction :
x = x/1
so,
1 ¼ = 1/1 + 1/4
8 = 8/1
now we bring the fractions in the first sum to the same denominator (4) and get
4/4 + 1/4 = 5/4
and the multiplication is
5/4 × 8/1 = (5×8)/(4×1) = 40/4 = 10