When operations meet: grouping and order
Distinguish the convention for operation order from grouping shown by parentheses.
Begin with the activity ↓Do 2+3×4 and (2+3)×4 tell the same story?
Multiplication and division precede addition and subtraction. Equal-priority operations go left to right; parentheses group a calculation first.
You have two loose beads and four bags of three beads. Write 2+3×4: the bags hold twelve, and the two loose beads make fourteen.
Now each bag contains two red and three blue beads, and you have four such bags. Write (2+3)×4. Parentheses tell us to treat the sum as one group first.
We agree on an order so that the same expression is not read differently. Without parentheses, multiplication and division precede addition and subtraction. This is a notation convention, not a claim that addition is unimportant.
Multiplication does not automatically come before division. Read 24÷3×2 from left to right: 8×2=16. The grouped expression 24÷(3×2)=4 is different.
Addition and subtraction also share priority. Thus 10−3+2 is 7+2=9. Adding 3 and 2 first would create the different expression 10−(3+2).
The convention is unchanged for decimals or fractions. In 0.5+0.2×3, combine three 0.2 amounts before adding 0.5 to get 1.1. Rewrite just the part you calculated at each step.
Listen one paragraph at a time
Hold on to this distinction
Explain why a step comes first, then rewrite one line at a time. Remember that multiplication and division share priority.
Change it and check
Choose an expression and click the part to calculate first. An incorrect choice explains how it would change the grouping.
2 + 3 × 4
2 + 3 × 4
Multiplication precedes addition.
This lesson covers parentheses and the four basic operations. Exponents belong to a later lesson.
Try with paper and objects
Draw two loose beads plus four bags of three, then four bags of five. Match each picture to its expression.
Check and explain another example
Check your idea 1
Check your idea 2
Apply it in a new setting
Connect the answer to its unit
Return to the explanationCompare with a solution
1.4 · number only
Multiply 0.4×2=0.8 first, then add 0.6.
Does your explanation include these ideas?
Explain aloud or in a drawing, then check your ideas. Different wording can express the same meaning.
Continue, or pause here
Connect mm, cm, m and km as different representations of the same length.