Answer: 4 & 2/3
Whole part = 4
Fractional part = 2/3
The mixed number 4 & 2/3 converts to the improper fraction 14/3.
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Explanation
Before multiplication can happen, we need to convert each mixed number to an improper fraction.
The formula to memorize is: a & b/c = (a*c + b)/c
Let's use the formula on the first mixed number.
a & b/c = (a*c + b)/c
2 & 5/8 = (2*8 + 5)/8
2 & 5/8 = 21/8
The mixed number 2 & 5/8 converts to the improper fraction 21/8.
Do the same for the other mixed number.
a & b/c = (a*c + b)/c
1 & 7/9 = (1*9 + 7)/9
1 & 7/9 = 16/9
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The original problem (2 & 5/8) * (1 & 7/9) is equivalent to (21/8)*(16/9)
Multiply the numerators straight across: 21*16 = 336
Do the same for the denominators: 8*9 = 72
It means (21/8)*(16/9) = 336/72
Reduce that fraction by dividing both parts by the GCF 24.
336/24 = 14
72/24 = 3
Therefore 336/72 = 14/3
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The last thing to do is to convert to a mixed number.
Use long division to find that 14/3 = 4 remainder 2
The quotient 4 forms the whole part, while the remainder 2 is the numerator of the fractional part.
14/3 = 4 & 2/3
Or you could use a calculator to see that 14/3 = 4.6666... where the 6s go on forever. Then notice that 2/3 = 0.66666... to see that 2/3 is the fractional part.