Question

How do you multiply `2\frac { 5} { 8} \times 3\frac { 1} { 7}`?

Answer 1

See a solution process below:

Explanation:

First, we need to convert the two mixed numbers into improper fractions:

`2 5/8 xx 3 1/7 => (2 + 5/8) xx (3 + 1/7) =>`

`([8/8 xx 2] + 5/8) xx ([7/7 xx 3] + 1/7) =>`

`(16/8 + 5/8) xx (21/7 + 1/7) => 21/8 xx 22/7`

Next, to multiply the two fractions we will multiply the numerators over the denominators multiplied:

`21/8 xx 22/7 => (21 xx 22)/(8 xx 7) => 462/56`

Now, if necessary we can convert the improper fraction into a mixed number:

`462/56 => 448/56 + 14/56 => 8 + (14 xx 1)/(14 xx 4) => 8 + (color(red)(cancel(color(black)(14))) xx 1)/(color(red)(cancel(color(black)(14))) xx 4) =>`

`8 + 1/4 = 8 1/4`

Answer 2

The answer is `33/4` or `8 1/4`.

Refer to the explanation for the process.

Explanation:

Multiply:

`2 5/8xx3 1/7`

Convert each mixed fraction to an improper fraction by multiplying the denominator by the whole number and adding the numerator, and putting the result over the denominator: `a b/c=((cxxa+b))/c`.

`2 5/8=((8xx2+5))/8=((16+5))/8=21/8`

`3 1/7=((7xx3+1))/7=((21+1))/7=22/7`

Now multiply the numerators of both fractions and the denominators of both fractions.

`21/8xx22/7=462/56`

Simplify by dividing the numerator and denominator by `14`. I determined this partially by trial and error.

`(462-:14)/(56-:14)=33/4`

Convert the improper fraction to a mixed number by dividing the numerator by the denominator to get the whole number, then take the remainder and place it over the denominator.

`33-:4=8` R 1

The mixed number is `8 1/4`.