Evaluate (1 1/2 + (-7/5)) × 2 2/3. Follow the order of operations and give an exact simplified answer.
Exact result: ____________________
CCSS 7.NS.A.1–A.2 · four-operation mixed review
Mixed Rational Number Operations Worksheet Generator
Combine addition, subtraction, multiplication, and division in numerical expressions that still stay inside the Grade 7 number-system domain. Parentheses and operation order add depth without introducing variables from the next 7.EE cluster.
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Mixed Rational Number Operations
Mixed rational-number operations · Grade 7 standard · Seed 271701
1.
2.
Evaluate (-2.14 - 33/10) ÷ 1/3. Follow the order of operations and give an exact simplified answer.
Exact result: ____________________
3.
Evaluate (-2 1/2 + (-3 2/3)) × 0.3. Follow the order of operations and give an exact simplified answer.
Exact result: ____________________
4.
Evaluate (1 1/3 + (-4 1/2)) × (-1/5). Follow the order of operations and give an exact simplified answer.
Exact result: ____________________
5.
Evaluate (3.9 + (-1.65)) × (-5/4). Follow the order of operations and give an exact simplified answer.
Exact result: ____________________
6.
Evaluate -2 3/4 - (-1) × 3. Follow the order of operations and give an exact simplified answer.
Exact result: ____________________
7.
Evaluate 4 5/6 - (-3) × (-3). Follow the order of operations and give an exact simplified answer.
Exact result: ____________________
8.
Evaluate 0.15 + (-4 1/2) ÷ (-1.5). Follow the order of operations and give an exact simplified answer.
Exact result: ____________________
9.
Evaluate 2.69 - 3 1/2 × 3/2. Follow the order of operations and give an exact simplified answer.
Exact result: ____________________
10.
Evaluate (-2 3/5 + (-3)) × 2 1/3. Follow the order of operations and give an exact simplified answer.
Exact result: ____________________
Exact-construction rule: operations use normalized integer numerator/denominator pairs, number-line positions use exact ticks, repeating decimals come from remainder cycles, and money contexts use exact cents. No answer depends on binary floating-point rounding.
Order of operations with signed rational numbers
Mixed operations combine all four operations in a single expression, with parentheses adding depth but no variables. The focus is on order and on carrying exact values from one step to the next.
Order errors and how they show up
- Working strictly left to right and adding before dividing.
- Treating a leading negative as a subtraction to be saved for the end.
- Converting to decimals partway through and losing an exact fraction.
Two expressions evaluated in order
- (−3/4 + 1/2) ÷ (−1/8): the parentheses give −1/4, and −1/4 ÷ −1/8 = 2.
- 2.5 × (−4) + 6 ÷ (−1.5): multiplication and division come first, giving −10 + (−4) = −14.
- −6 + 12 ÷ (−3) is −6 + (−4) = −10, because the division happens before the addition.
Diagnosing with mixed sets
A mixed set is a quick diagnostic. If a student misses only the problems with parentheses, the gap is in grouping; if they miss only division, the gap is in reciprocals. The answer key shows each intermediate value so the point of failure is easy to find.
Classroom note 1
Evaluate grouped expressions before operations outside the parentheses.
Classroom note 2
Multiplication and division come before addition and subtraction when no grouping symbol changes the order. Example: -6 + 12 divided by (-3) is -6 + (-4), which is -10.
Classroom note 3
A leading minus sign on a term is not a subtraction to save for last; -6 keeps its sign through the whole evaluation.
Classroom note 4
Carry exact fractions through intermediate steps instead of rounding a decimal halfway through.
Continue the 7.NS progression
Move to another Grade 7 rational-number skill
Questions people ask
Does this include variables?
No. This route stays numerical so it remains focused on the Grade 7 Number System rather than blending into expressions and equations.
Are there multiple operations in one problem?
Yes. Each problem uses at least two operations or an operation plus explicit grouping.
Which standard does this practice?
CCSS 7.NS.A.3: solve real-world and mathematical problems involving the four operations with rational numbers, here in a pure order-of-operations format.
Why does rounding partway through change the answer?
A rounded decimal is only an approximation. Multiplying or dividing it magnifies the error, so an exact fraction carried to the last step keeps the final result correct.