Expressions and Equations: Working with Linear Expressions with Rational Coefficients (CCSS.7.EE.1)
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Common Core 7th Grade Math › Expressions and Equations: Working with Linear Expressions with Rational Coefficients (CCSS.7.EE.1)
A soccer ball costs $p$ dollars. With a 7% sales tax, Jordan wrote the total cost as $p + 0.07p$. Which expression shows the same total cost in a single multiplication?
$p + 7$
$1.07p$
$0.93p$
$1.7p$
Explanation
Adding 7% of $p$ to $p$ is the same as multiplying by \$1.07$: $p + 0.07p = (1 + 0.07)p = 1.07p$. The other choices either add a flat 7 dollars, apply a discount, or use the wrong decimal.
Which expression is equivalent to $3(x+2)-2x$?
$5x+6$
$x+6$
$x+2$
$3x+4$
Explanation
Distribute $3$ to get $3x+6$, then subtract $2x$: $(3x+6)-2x=x+6$. Common mistakes: adding $2x$ ($5x+6$), not distributing $3$ to $2$ ($x+2$), or subtracting $2$ from $6$ instead of $2x$ ($3x+4$).
A concert ticket costs 12 dollars, plus a 2 dollar service fee per ticket. For 6 friends, a structured expression is $6(12+2)$. Which expression shows the same total cost by first combining the price and fee?
$6\cdot 12 + 2$
$6\cdot 14$
$12(6+2)$
$6(12+2)+2$
Explanation
Combining inside the parentheses gives $12+2=14$, so $6(12+2)=6\cdot 14$. The other choices either add the fee only once or change the grouping/amounts.
Which expression is equivalent to $\tfrac{1}{2}(6y+4)-y$?
$3y+2$
$2y+4$
$3y+4-y$
$2y+2$
Explanation
Distribute $\tfrac{1}{2}$: $\tfrac{1}{2}\cdot 6y=3y$ and $\tfrac{1}{2}\cdot 4=2$, so $3y+2-y=2y+2$. Errors: forgetting to subtract $y$ ($3y+2$), adding constants incorrectly ($2y+4$), or not fully distributing/simplifying ($3y+4-y$).
An online store charges 1.50 per granola bar and one 4 dollar shipping fee per order. Sam buys 3 granola bars and wrote $3 \times 1.50 + 4$ for the total cost. Which expression shows the same total cost after multiplying?
$3(1.50 + 4)$
$1.50(3 + 4)$
$3(1.50) + 3(4)$
$4.50 + 4$
Explanation
$3 \times 1.50 = 4.50$, so the total is $4.50 + 4$. The other choices incorrectly make the shipping fee apply per bar or mix the quantities.
A jacket costs $p$ dollars and is 20% off. One expression for the sale price is $p - 0.20p$. Which expression shows the same price by factoring $p$?
$p(1+0.20)$
$p - 0.80$
$1.20p$
$p(0.80)$
Explanation
Factor out $p$: $p - 0.20p = p(1 - 0.20) = p(0.80)$. The other options represent an increase, subtract a flat amount, or add 20%.
A school fundraiser sells bundles that include a drink (2 dollars) and a snack (1.50 dollars). For $x$ bundles, a structured expression is $x(2+1.5)$. What does rewriting it as $3.5x$ show about the situation?
Each bundle costs 3.50 dollars.
Each bundle costs 5 dollars more than before.
You are buying 3.5 bundles.
A 35% tax is added to each bundle.
Explanation
Adding inside the parentheses gives $2+1.5=3.5$, so $x(2+1.5)=3.5x$, meaning each bundle costs 3.50 dollars.
A supply pack includes one notebook for 2.50 and one pen for 1.20. Buying $n$ identical packs costs $2.50n + 1.20n$. What does rewriting this as $(2.50 + 1.20)n$ show about the situation?
Each pack costs 3.70, and there are $n$ packs.
The price is 3.70 more than $n$.
Only notebooks are counted $n$ times.
A separate shipping fee of $n$ dollars is added.
Explanation
Factoring gives $(2.50 + 1.20)n = 3.70n$, which means each pack costs 3.70 and you buy $n$ packs. The other choices do not match the context.
Which expression is equivalent to $-4(2-x)+x$?
$5x-8$
$-8-3x$
$-8+3x$
$-8-5x$
Explanation
Distribute $-4$: $-4\cdot 2=-8$ and $-4\cdot(-x)=+4x$, then add $x$: $-8+4x+x=5x-8$. Errors come from sign mistakes when distributing or combining like terms.
A streaming plan costs $s$ dollars per month, and there is a 20% discount. The discounted price can be written as $s - 0.20s$. Which expression shows the same price more directly?
$s + 0.20s$
$1.2s$
$0.80s$
$s - 20$
Explanation
Subtracting 20% of $s$ from $s$ is multiplying by \$0.80$: $s - 0.20s = (1 - 0.20)s = 0.80s$. The other choices represent an increase or subtract a flat 20 dollars.