Testinar Grade 7 math

Rewriting Expressions to Solve Problems

Students will build Grade 7 mastery of rewriting expressions to solve problems using models, equations, and test-style reasoning.

CH04-06 Expressions
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 is equivalent to \(0.95p\)?

    1. \(p-0.95p\)
    2. \(p-0.05p\)
    3. \(p+0.05p\)
    4. \(0.95+p\)

  2. A shirt costs \($60\). With a \(15\%\) discount, which expression represents the final price?

    1. \(0.15 \times 60\)
    2. \(0.85 \times 60\)
    3. \(1.15 \times 60\)
    4. \(60 - 15\)

  3. Which expression is equivalent to \(1.08m\)?

    1. \(m+0.08m\)
    2. \(m-0.08m\)
    3. \(1.08+m\)
    4. \(0.92m\)

  4. A book costs \($25\). With sales tax of \(6\%\), what is the total cost?

    1. \(25 + 6\)
    2. \(25 \times 0.06\)
    3. \(25 \times 1.06\)
    4. \(25 - 0.06\)

  5. Use the distributive property to simplify \(3(x+5)-2x\).

    1. \(3x+15-2x=x+15\)
    2. \(x+5\)
    3. \(3x+5-2x\)
    4. \(3x+15\)

  6. Which expression is equivalent to \(2(4y-1)+3y\)?

    1. \(8y-2+3y=11y-2\)
    2. \(8y+1\)
    3. \(11y-1\)
    4. \(4y+2\)

  7. A pair of jeans costs \($80\). After a \(20\%\) discount, express the final price in factored form.

    1. \(80(1-0.2)\)
    2. \(80(0.2)\)
    3. \(0.8(80)\)
    4. \(80 \times 20\)

  8. Which of the following shows that \(0.9p=p-0.1p\)?

    1. Factoring: \(p-0.1p=p(1-0.1)=0.9p\)
    2. Distribution: \(0.1(p-p)=0\)
    3. Combining fractions: \(0.9+0.1=1\)
    4. All operations are equivalent
Teacher and parent reference

Answer key and explanations

  1. B. \(p-0.05p\)

    The decimal \(0.95\) means keeping \(95\%\) of the price (removing \(5\%\)). This is the same as \(p-0.05p=(1-0.05)p=0.95p\). Both forms show a \(5\%\) discount: one expanded (subtract the discount), one simplified (multiply by the remaining scale factor).

  2. B. \(0.85 \times 60\)

    A \(15\%\) discount removes \(15\%\) from the original price. You pay the remaining \(100\%-15\%=85\%\). The multiplier \(0.85\) scales the price by this remaining percent: \(0.85 \times 60=51\).

  3. A. \(m+0.08m\)

    \(m+0.08m=(1+0.08)m=1.08m\). An \(8\%\) tax adds \(8\%\) to the original price.

  4. C. \(25 \times 1.06\)

    With a \(6\%\) tax, you pay \(100\%+6\%=106\%\) of the original price: \(25 \times 1.06\).

  5. A. \(3x+15-2x=x+15\)

    Distribute: \(3(x+5)-2x=3x+15-2x\). Combine like terms: \(3x-2x+15=x+15\).

  6. A. \(8y-2+3y=11y-2\)

    Distribute \(2\): \(2(4y)-2(1)+3y=8y-2+3y\). Combine: \(8y+3y-2=11y-2\).

  7. A. \(80(1-0.2)\)

    A \(20\%\) discount means you keep \(100\%-20\%=80\%\) of the price. The factored form \(80(1-0.2)\) emphasizes the scale factor \((1-0.2)\), which equals \(0.8\). This form reveals the structure of the discount.

  8. A. Factoring: \(p-0.1p=p(1-0.1)=0.9p\)

    Factoring out \(p\) from \(p-0.1p\) gives \(p(1-0.1)=p(0.9)=0.9p\). This is the key rewriting.

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