Post 2c: Are You Ready? Rational Number Operations: Adding and Subtracting Fractions

(by Chris B. with help from Sage the intrepid student dog)

Now that you and Sage reviewed Common Denominators in the previous post, it is time to review adding and subtracting fractions. Let's see how Sage solves the Addition and Subtraction challenge to clear the chasm.

Adding and Subtracting Fractions with the same Denominator

Adding and subtracting fractions is easy, so long as the two fractions have the same denominator. Simply add or subtract terms in the numerator and then leave the denominator alone.

Click here for an example

For instance, 1/5 and 2/5 have the same denominator. Because the two fractions have 5 as the denominator, it is easy to convert 1/5+2/5 to 3/5. Simply add the numerators over the same denominator.

The same goes for subtraction: 5/6-1/6 = 4/6. Simply take 1 from 5 and put it over the same Denominator.

"I get it. I get 3/4 cups at breakfast and 3/4 cups at dinner!" pipes in Sage, " That means I get to eat 6/4 cups in a day"

Of course, we've already established that Sage is food motivated when it comes to math!

"Sage, once we reduce that fraction do you know what we get?"

"More food?" Sage asks hopefully.

"Well, maybe a treat, but the reduced fraction is 1 and 1/2 cups in a day". We'll refresh on how that works at the end.

Adding and Subtracting Fractions without a common denominator

If your addition and subtraction involves fractions with different denominators, simply apply tricks from the previous post. Once you have a common denominator, you can add or subtract just like we discussed above. Just add the numerators and put them over the same denominator. Finish by reducing the fraction by pulling out common factors from the numerator and denominator.

The touchscreen TV flashes and a new scratchpad appears, showing how to perform the addition and subtraction. See the scratchpad from together.science below for examples on adding and subtracting rational numbers. There's also a workspace at the bottom so Sage can give it a try. Simply click on the "..." and replace it with your answer.

This time, Sage goes to the stack of blocks, but no equation appears.

"Is that it?" wonders Sage. He goes back to the board and see a new lesson on the scratchpad. Remember when we said that Sage's 6/4 cups of food in a day was not the final reduced fraction? Now we need to review how to reduce that fraction to the 1 and 1/2 cups.

Sage gets it! It's time to get that last problem! Sage runs back to the last stack. This time the equation pops up.

7/8 + 5/6

Sage is ready and runs back to the touchscreen TV. Sure enough, the scratchpad is prepopulated with this problem. Do you think you've got what it takes to complete this one? Let's give it a try!

Want some help? Click here to reveal the solution.

Sage returns to the blocks and notices they look much different. There's 12/14, 82/48, 12/48, 1/4, 35/48 and 1+17/24. Sage worked through the problem but stalled out part way through. Sage tentatively mouths his first guess which was 82/48. But there's no tingle or buzz. Sage works through some more steps and remembered to fully reduce the fraction. With confidence, Sage noses the 1+17/24 and feels a tingle.

"Ahhhh-Chooo!" Sage sneezes from his tingly nose. Sage grabs the block in his mouth and puts it on the plate. Whoosh! The final blocks turn into tiles that complete the floor. Sage catches the eye of one the kids. He notices the expression of the kid seems to have softened. The kid motions to the others to follow Sage. They cross the bridge and find a door with all covered with knobs and dials. Sage pushes it open.

Click here for the next post

Catch your algebra mistakes before they cost you

The scratchpad in this guide runs on moment.of.math — a free Chrome extension that checks your algebra line by line, on any problem. It can generate new variations problems, so you can get as much practice as you need. On many homework sites, it automatically detects the math on the page, so you don't have to copy anything over. Try it on tonight's homework.

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