How To Add Fractions And Simplify

- here's another exampleof simplifying expression that involves signed fractions. here we have the quantity2/3 + 1/4 x -2/3. so it's important to recognize these are connected hereby multiplication.

How To Add Fractions And Simplify, so using the orderof operations, the first step is going to be to simplifyinside the parentheses because we need to findthis sum here first.

now even though additionis listed last on the order of operations, because it's insidethe parentheses, it must be performed first. in order to add 2/3 and 1/4, we do want to find the leastcommon denominator of 3 and 4, which would be 12. 12 is the smallest numberthat's divisible by both 3 and 4 and it's also the leastcommon multiple of 3 and 4.

so we want to write 2/3 and 1/4as equivalent fractions with a denominator of 12. so for 2/3 we'll multiplyboth the denominator and the numerator by 4, and for 1/4,we'll multiply the denominator and the numerator by 3. notice how both fractionsnow have the denominator of 12. so now we'd have8/12 + 3/12 x -2/3. now that we havea common denominator,

we can add these fractions. so this sum hereis going to be 11/12. so this simplifiesto 11/12 x -2/3. and before wedetermine this product we do want to simplifylooking for any common factors between the numeratorsand denominators, and notice that the 2 and 12have a common factor of 2, and i prefer to showthe common factor, so i'm going to write thisas 11 all over 6 x 2 x -2/3.

so this 2 over 2simplifies to 1, and now we can multiply, knowing this productwill be in simplest form. notice we havea positive fraction times a negative fraction so the product will be negative. the numerator isgoing to be 11, and the denominatoris going to be 18. so we have -11/18.

another way to remind ourselvesthis fraction is negative is we could think ofthe numerator as +11 x -1, which would be -11. and whether the fraction hasa negative sign out in front or in the numeratorthe fractions are equivalent.