Testinar Grade 5 math

Introduction to Variables and Equations

Students will use variables and equations to represent unknown quantities in expressions.

CH07-05 Expressions and Patterns
Name
Date
Score
____ / 8
Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

  1. Which expression represents four groups of the quantity \((6+2)\)?

    1. \(4 \times (6 + 2)\)
    2. \((4 \times 6) + 2\)
    3. \(4 + (6 \times 2)\)
    4. \((4 + 6) \times 2\)

  2. Evaluate the expression: \((4 + 5) \times 2\)

    1. \(11\)
    2. \(14\)
    3. \(18\)
    4. \(20\)

  3. Evaluate: \(20 - (3 \times 4)\)

    1. \(6\)
    2. \(8\)
    3. \(17\)
    4. \(68\)

  4. Where should parentheses be placed to make the expression equal \(20\)? \(\)6 + 4 \times 2\(\)

    1. \((6 + 4) \times 2\)
    2. \(6 + (4 \times 2)\)
    3. \(6 \times (4 + 2)\)
    4. \((6 \times 4) + 2\)

  5. Evaluate the expression: \(\)[\,2 + (3 \times 4)\,] \div 7\(\)

    1. \(1\)
    2. \(2\)
    3. \(5\)
    4. \(14\)

  6. The expression tree shows how to evaluate the grouped expression \(((8+2)\times(7-3))\). What is the final value?

    Using Parentheses Brackets and Braces in Numerical Expressions visual for G5-C01-T01-Q006
    1. \(30\)
    2. \(60\)
    3. \(50\)
    4. \(40\)

  7. Evaluate: \(30 - \{\,4 + (2 \times 3)\,\}\)

    1. \(20\)
    2. \(24\)
    3. \(26\)
    4. \(34\)

  8. Evaluate: \((15 \div 3) + 7\)

    1. \(9\)
    2. \(10\)
    3. \(12\)
    4. \(22\)
Teacher and parent reference

Answer key and explanations

  1. A. \(4 \times (6 + 2)\)

    The words "four groups of the quantity \((6+2)\)" mean the grouped quantity is multiplied by 4. That is represented by \(4 \times (6+2)\).

  2. C. \(18\)

    Start with the part in parentheses: \(4 + 5 = 9\). Now multiply the result by 2: \(9 \times 2 = 18\). Nice careful grouping gives answer C.

  3. B. \(8\)

    The parentheses tell you what to do first. Since \(3 \times 4 = 12\), the expression becomes \(20 - 12\), which equals 8.

  4. A. \((6 + 4) \times 2\)

    To make 20, group the addition first: \((6+4) \times 2 = 10 \times 2 = 20\). The other choices give different values, so A is the only match.

  5. B. \(2\)

    Work from the inside out. First \(3 \times 4 = 12\), then the bracket becomes \([2+12]=14\), and finally \(14 \div 7 = 2\).

  6. D. \(40\)

    The tree says to find each branch first: \(8+2=10\) and \(7-3=4\). Then multiply the two results: \(10 \times 4 = 40\).

  7. A. \(20\)

    Begin with the innermost operation: \(2 \times 3 = 6\). That makes the braces \(\{4+6\}=10\), so the full expression is \(30-10=20\).

  8. C. \(12\)

    The parentheses come first, so \(15 \div 3 = 5\). After that, add 7: \(5+7=12\).

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