Question

Multiply. Write in simplest form. How do I solve this in steps?
1/2*5 1/4

Answer 1

We'll start with the question \[\frac{ 1 }{ 2 } \times 5 \frac{ 1 }{ 4 }\] The best way to start this is to turn your mixed number into an improper fraction. To do this, multiply the whole number by the denominator, add the numerator, and put your new number over the original denominator, like this: \[5\frac{ 1 }{ 4 } = \frac{ 21 }{ 4 }\] Because 5 * 4 + 1 = 21, and the original denominator was 4.
From here, we just multiply the numbers straight across: \[\frac{ 1 }{ 2 } \times \frac{ 21 }{ 4 } = \frac{ 21 }{ 8 }\] As you can see, beyond converting the mixed number to an improper fraction is really the only "trick". If they want you to reduce this to a mixed number, you basically do the opposite of what you did to the 5 1/4 at the beginning.

See how many times 21 goes into 8 by doing simple division:

You'll use the remainder to determine the fraction part of your mixed number.
We see that the remainder is 5, and the original denominator was 8.
Our whole number will be 2 (you can think of it like this: "8 went into 21 2 whole times with some left over"), and our "some left over" will be 5/8. When all is said and done, your equation should look something like this:\[\frac{ 1 }{ 2 } \times 5 \frac{ 1 }{ 4 } = \frac{ 1 }{ 2 } \times \frac{ 21 }{ 4 } = \frac{ 21 }{ 8 } = 2\frac{ 5 }{ 8 }\]
I hope this helps!