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C2.2 · Evaluate expressions with whole numbers and decimal tenths

Learn to evaluate expressions with whole numbers and decimal tenths through clear examples and targeted practice.

Ontario Grade 6 Mathematics

Algebra

Use the order of operations to find the value of an expression.

An expression is a group of numbers and operation signs, such as 8+3×28+3\times2. To evaluate an expression means to find its value. The same numbers can give different answers if the operations are done in a different order. In this lesson, you will use a shared set of steps so that an expression has one clear value. First, remember that addition combines amounts, subtraction finds a difference, multiplication makes equal groups, and division splits into equal groups. A decimal tenths number has one digit to the right of the decimal point, such as 2.42.4.

What you will learn

  • Explain what it means to evaluate an expression.
  • Use the order of operations to evaluate expressions with whole numbers and decimal tenths.
  • Check an answer by estimating or reviewing the calculation.

Make sense of the order

Imagine 4+3×24+3\times2 as four counters, plus three groups of two counters. The three groups contain six counters. Add the four counters to get ten. This picture shows why multiplication must be done before the addition: the groups of two belong together.
Use these steps when an expression has more than one operation: first calculate inside brackets, if there are any. Next, do multiplication and division, moving from left to right. Last, do addition and subtraction, moving from left to right. Brackets are curved marks that show which part to calculate first.
When two operations have the same priority, work from left to right. For example, in 18÷3×218\div3\times2, divide first because division appears first as you read from left to right. Then multiply the result by two.
A decimal tenths number has one digit after the decimal point. In 3.63.6, the digit six means six tenths. Read the decimal point carefully when adding or subtracting. Keep the decimal points lined up so tenths are combined with tenths.
  • Brackets first.
  • Then multiplication and division from left to right.
  • Then addition and subtraction from left to right.
  • Keep decimal points lined up when adding or subtracting.

Use a steady routine

Before calculating, scan the whole expression. Look for brackets and operation signs. Do not assume that the operation written first is always the one to do first.
Work through one part at a time. Write each new line so it shows the value of the previous line. This makes it easier to spot a missed bracket or an operation done in the wrong order.
For a decimal calculation, think about the place value as well as the operation. For example, 1.2+0.51.2+0.5 means twelve tenths plus five tenths, which is seventeen tenths, or 1.71.7. For multiplication or division, use the same order-of-operations steps; do not change the order just because a decimal appears.
A quick estimate is an answer that is close to the exact value. It helps you notice an answer that is far too large or too small. You can also check by repeating the steps and checking each operation.
  • Read all the operations before starting.
  • Show each calculation in order.
  • Use place value when working with decimal tenths.
  • Check whether the answer is reasonable.

Practice the routine

For each expression, name the operation that comes next before you calculate it. If there are brackets, begin inside them. Otherwise, look for multiplication or division. When only addition and subtraction remain, continue from left to right.
Try these for practice: 7+2×57+2\times5, (7+2)×5(7+2)\times5, and 9.4−2.1+19.4-2.1+1. For the first, multiplication comes before addition. For the second, the brackets change which part comes first. For the third, there is no multiplication or division, so work from left to right and keep the decimal points lined up.
After you find each value, check the steps. Did you follow the order? Did you copy the numbers correctly? Does the size of your answer make sense? These checks are part of evaluating carefully.
  • Brackets can change which operation comes first.
  • Multiplication comes before addition unless brackets say otherwise.
  • When addition and subtraction are together, work from left to right.

Worked example

Multiplication before addition

Evaluate 6+4×36+4\times3.
  1. Find the first operation
    There are no brackets. Multiplication comes before addition, so calculate four times three first.
    4×3=124\times3=12
  2. Add
    Now add six to the product. The expression has become an addition problem.
    6+12=186+12=18
Answer: The value is 1818.
Check: The product 4×34\times3 is 1212. Adding six gives a number a little larger than twelve, so 1818 is reasonable.

Worked example

Brackets and a decimal tenths number

Evaluate (5+1.4)×2(5+1.4)\times2.
  1. Calculate inside the brackets
    The brackets tell us to add five and one and four tenths first. Line up the decimal points. Five is the same amount as 5.05.0.
    5.0+1.4=6.45.0+1.4=6.4
  2. Multiply
    The brackets are now replaced by their value, 6.46.4. Multiply that value by two.
    6.4×2=12.86.4\times2=12.8
Answer: The value is 12.812.8.
Check: Twice 6.46.4 is a little more than twice six, which is twelve. The answer 12.812.8 is reasonable.

Worked example

Same-priority operations from left to right

Evaluate 20−6÷3+220-6\div3+2.
  1. Do division first
    There are no brackets. Division comes before subtraction and addition, so divide six by three.
    6÷3=26\div3=2
  2. Work from left to right
    The expression is now 20−2+220-2+2. Subtraction and addition have the same priority, so subtract first because it is farther left.
    20−2=1820-2=18
  3. Finish the addition
    Add the final two to eighteen.
    18+2=2018+2=20
Answer: The value is 2020.
Check: The division gives two. The remaining subtraction and addition cancel each other, so the value returns to twenty.

Common mistakes and how to avoid them

Adding before multiplying in 6+4×36+4\times3 because addition appears first.
Correction: Multiply first. Then add. The value is 1818.
Ignoring brackets and multiplying before adding in (5+1.4)×2(5+1.4)\times2.
Correction: Calculate inside the brackets first. The value is 12.812.8.
Always doing addition before subtraction, or division before multiplication, even when the other operation is farther left.
Correction: For operations with the same priority, work from left to right.
Not lining up decimal points in an addition or subtraction calculation.
Correction: Write the decimal points directly beneath one another so tenths stay in the tenths place.

Lesson summary

  • Evaluating means finding the value of an expression.
  • Calculate inside brackets first.
  • Then multiply or divide from left to right.
  • Then add or subtract from left to right.
  • Line up decimal points when adding or subtracting, and check that the answer makes sense.

Check your understanding

Question 1

What is the value of 8+3×48+3\times4?
  1. 2020
  2. 4444
  3. 2424
  4. 3232
Show answer and explanation
2020
Multiply first: 3×4=123\times4=12. Then add eight to get 2020.

Question 2

What is the value of (2.5+1.5)×3(2.5+1.5)\times3?
  1. 7.57.5
  2. 1212
  3. 1515
  4. 99
Show answer and explanation
1212
Add inside the brackets to get 44. Then multiply 44 by 33 to get 1212.

Question 3

What is the value of 16÷4×216\div4\times2?
  1. 22
  2. 88
  3. 44
  4. 1616
Show answer and explanation
1616
Division and multiplication have the same priority, so work from left to right: 16÷4=416\div4=4, then 4×2=84\times2=8.

Key terms

Expression
Numbers and operation signs written together, without an equals sign showing a value.
Evaluate
Find the value of an expression by carrying out its operations.
Brackets
Curved marks that show which part of an expression to calculate first.
Decimal tenths
A decimal amount with one digit after the decimal point, such as 4.74.7.
Estimate
A value close to the exact answer, used to check whether an answer makes sense.

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