Answer: 4 & 1/4
Note: your teacher may want you to leave out the & symbol. If so then you would type in 4 1/4
This mixed number is equivalent to the improper fraction 17/4
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Step-by-step explanation:
The number 10 & 5/8 is a mixed number in the format of a & b/c
a = whole part
b/c = fractional part
Let's convert that mixed number to an improper fraction using this formula.
a & b/c = (a*c + b)/c
10 & 5/8 = (10*8 + 5)/8
10 & 5/8 = (80 + 5)/8
10 & 5/8 = 85/8
So,
(2/5) * (10 & 5/8) = (2/5)*(85/8) = (2*85)/(5*8) = 170/40 = 17/4 is the answer as an improper fraction
Then we'll convert that result to a mixed number
17/4 = (16 + 1)/4
17/4 = 16/4 + 1/4
17/4 = 4 + 1/4
17/4 = 4 & 1/4 is the answer as a mixed number
You can think of it like this: You have 17 cookies and 4 friends to give them to. Each friend gets the same amount of cookies.
Each friend gets 17/4 = 4.25 = 4 whole cookies (quotient), which means 4*4 = 16 cookies are eaten so far.
That means there is 17 - 16 = 1 cookie left over (remainder).
Quotient = 4, remainder = 1, so 17/4 = 4 remainder 1 = 4 & 1/4
Or you could note that 17/4 = 4.25 and 4 & 1/4 = 4 + 1/4 = 4 + 0.25 = 4.25, so 17/4 must be equal to 4 & 1/4.