Question

5 7\10 × 7 4\16=????? I'm trash with multypliing ​

Answer 1

9514 1404 393

Answer:

41 13/40

Explanation:

Generally, you're told to multiply mixed numbers by converting each to an improper fraction:

5 7/10 = (5·10 +7)/10 = 57/10

7 4/16 = (7·16 +4)/16 = 116/16

The fractions are multiplied by multiplying their numerators to get the numerator of the result, and multiplying their denominators to get the denominator of the result.

`(5(7)/(10))(7(4)/(16))=(57)/(10)\cdot(116)/(16)=(57\cdot116)/(10\cdot16)=(6612)/(160)\\\\=41+(52)/(160)=\boxed{41(13)/(40)}`

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You don't have to mess with reducing the fraction of the result if you reduce the fraction 4/16 to 1/4 to begin with. Then the product is (57/10)(29/4).

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Alternate solution

You can also treat this as the product of two sums. The distributive property is handy for this.

(5 + 7/10)(7 + 1/4) = (5)(7) +(5)(1/4) +(7/10)(7) +(7/10)(1/4)

= 35 +5/4 +49/10 +7/40

= 35 +1 +1/4 + 4 + 9/10 + 7/40 . . . . take out the integer parts

= 40 +10/40 +36/40 +7/40 . . . . . . use 40 as a common denominator

= 40 +53/40 = 41 13/40