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Math 7 · Unit 3, Lesson 7: Rational Number Problems · Tile 1 of 4

Order of Operations

Groups first, then times and divide, then add

Do the steps in order

When a problem has more than one operation, the order matters. First, work inside any grouping: parentheses, and the top and bottom of a fraction bar. Next, multiply and divide, left to right. Last, add and subtract, left to right. The sign rules don't change. Just do the steps in order.

  1. GroupsParentheses, and the top and bottom of a fraction bar.
  2. Multiply and divideLeft to right.
  3. Add and subtractLeft to right. Change each subtraction to adding the opposite, the same way as Lesson 2.

The hidden parentheses

A fraction bar groups its top and its bottom, even with no parentheses. In 4 + 56, add 4 + 5 first, then divide: 96 = 1 12.

A fraction whose top or bottom is itself a fraction is called a complex fraction. It is just a division problem: −3412 = −34 ÷ 12 = −1 12.

ElleMath-speak

Evaluate grouping symbols first, including the numerator and denominator of a fraction, then multiplication and division from left to right, then addition and subtraction from left to right.

FinnPlain English

Groups first. Then times and divide. Then plus and minus. A fraction bar is a group, even when you can't see the parentheses.

Elle and Finn talk it over

Finn

Can't I just go left to right? That's how I read.

Elle

Sure. You can also put your shoes on before your socks. It's an order. It's just the wrong one.

Finn

My feet would be so confused.

Watch it work

−3 + 4 × (−2)−3 + −8 Times first−11 Add

Warning: going left to right gives 1 × (−2) = −2, which is wrong.

−8 − 4−3 + 6−123 Groups: top and bottom−4 Divide
−2(5 − 9) + 7−2(−4) + 7 Groups8 + 7 Times15 Add

Let me try a few

NC standard: NC.7.NS.3.

Where to go next

Let me try a few8 problems on order of operations. Next: Tile 2, Plan It OutWrite one expression, estimate, then solve All tilesAll 4 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.