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Math 7 · Unit 4, Lesson 5: Fraction and Decimal Coefficients · Tile 1 of 3

Fraction Coefficients

Common denominators, then count

Common denominators, then count

To combine like terms with fraction coefficients, add the fractions the way you always do. If the denominators are different, find a common denominator first. The variable just comes along for the ride.

12 x + 13 x36 x + 26 x common denominator 656 x
A half and a third make five sixthsThree bars, each split into six equal parts: one half shades three parts, one third shades two parts, and together they shade five of the six parts.1 half = 3 sixths1 third = 2 sixths5 sixths
A half is three sixths and a third is two sixths, so together they make five sixths.

A reminder from Lesson 1, Tile 3: x3 means 13 x.

Elle and Finn

ElleMath-speak

To combine like terms with rational coefficients, add the coefficients and keep the variable part.

FinnPlain English

Same as before. Add the numbers in front, and keep the letter. The numbers are just fractions now.

Elle and Finn talk it over

Finn

12 x + 13 x is 25 x. Add the tops, add the bottoms.

Elle

Would half a pizza plus a third of a pizza be less than half a pizza?

Finn

That's less pizza. That can't be right.

Elle

It isn't. Common denominator first. It's 56 x.

Finn

Five sixths of a pizza. Much better.

Two fifths is less than one half, so adding the tops and bottoms gives an answer that is too small. Always find a common denominator.

Watch it work

34 y − 16 y34 y + −16 y adding the opposite912 y + −212 y common denominator 12712 y
23 a + 5 − a + 1223 a + 5 + −1a + 12 adding the opposite, invisible 1(23 a + −33 a) + (5 + 12) move like terms together−13 a + 112

112 can also be written 5 12.

Let me try a few

NC standards: NC.7.EE.1, NC.7.NS.1.

Where to go next

Let me try a few6 problems on fraction coefficients. Next: Tile 2, Decimal CoefficientsLine up the decimals and keep the signs All tilesAll 3 parts of this lesson. Tell us what you thought about this tileA few quick questions about just this tile. It takes a few minutes, and opens in a new tab so you keep your place.