Answer: 9/25 of a mile
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Step-by-step explanation:
Multiply the fractions 9/10 and 2/5 to get
(9/10)*(2/5)
(9*2)/(10*5)
18/50
9/25
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Here's a visual way to see what's going on. Start by drawing a rectangle of any size or shape. Cut the rectangle vertically into 10 equal slices. Then shade 9 of those slices to represent the fraction 9/10, which is how far (in miles) Lewis walked. See the diagram below. Specifically, refer to figure 1.
The friend walked 2/5 of this shaded amount. Draw 4 horizontal lines to split each vertical bar into 5 equal pieces. So we'll be forming a grid of smaller rectangles. For any given column, you'll shade exactly 2 smaller rectangles out of the 5 total. Hence the 2/5. This is shown in yellow in figure 2. The yellow region is 2 units tall by 9 units across, so we have 2*9 = 18 yellow rectangles in all. This is out of 5*10 = 50 smaller rectangles overall.
That's how we get to the fraction 18/50 which reduces to 9/25 when you divide both parts by the GCF 2.