Math 7 · Unit 3, Lesson 3: Signed Fractions and Decimals · Tile 1 of 3

Pick One Form

Fractions or decimals, not both

Pick one form

Some problems mix fractions and decimals, like 5 12 + (⁻3.25). Before you do anything else, change every number into the same form. Then use the steps you already know from Lesson 1, Tile 4.

Which form to pick

Pick decimals when every fraction has a bottom (denominator) of 2, 4, 5, 8, or 10. These turn into decimals that stop, like money.
Pick fractions when you see a third, a sixth, or a ninth. 13 = 0.333..., and the 3s never stop. Fractions keep it exact. (Lesson 6 shows why some decimals go on forever.)

Fraction	Decimal
12	0.5
14	0.25
34	0.75
15	0.2
18	0.125
110	0.1

ElleMath-speak

Convert all the numbers to one form, fractions or decimals, before you compute.

FinnPlain English

Make every number speak the same language first. Then add.

Elle and Finn talk it over

Finn

Can't I just do half of it in fractions and half in decimals?

Elle

You can. You can also wear one sneaker and one flip-flop. You'll get there, just slower, and with more falling down.

Finn

Fine. Two sneakers.

Watch it work

5 12 + (⁻3.25)5.5 + ⁻3.25 One form: decimals2.25 Add

⁻2 34 − 0.5⁻2.75 − 0.5 One form⁻2.75 + ⁻0.5 Change⁻3.25 Add

⁻13 + 0.5⁻13 + 12 One form: fractions, because of the third⁻26 + 36 Common denominator16 Add

Let me try a few

NC standard: NC.7.NS.1.

Where to go next

Let me try a few6 problems on pick one form. Next: Tile 2, Move It AroundOnce it's all adding, the order is up to you 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.