Task Sets: Solve multi-step real-life and mathematical problems with positive and negative rational numbers - Common Core Math - Grade 7

Recall

Which expression gives the product of $-\dfrac{3}{4}$ and $-8$ ?

$-6$

$6$

$-\dfrac{3}{32}$

$\dfrac{3}{32}$

Which decimal is equal to $\dfrac{3}{8}$ ?

$0.38$

$0.375$

$0.35$

$3.75$

Evaluate: $4 + 3 \times (10 - 4)$

Fluency

A store bought 24 items at $1.75 each. Six of the items were damaged and returned for a refund of $1.50 each. Which sequence of operations gives the net cost to the store?

Add $24 + 6 = 30$ total items, then multiply by $1.75.

Multiply $24 \times 1.75$ for the purchase cost, multiply $6 \times 1.50$ for the refund, then subtract the refund from the purchase cost.

Multiply $24 \times 1.50$ , then subtract $6 \times 1.75$ .

Subtract $24 - 6 = 18$ net items, then multiply $18 \times 1.75$ .

Compute $-\dfrac{2}{3} + 1.5 - \dfrac{3}{4}$ using fractions to keep the result exact. Enter your answer as a simplified fraction.

Use a mental-math shortcut to compute $36 \times (2.75 + 0.25)$ . What is the result?

Regroup to simplify: $\left(-\dfrac{5}{6}\right) + \dfrac{2}{3} + \left(-\dfrac{1}{6}\right)$ .

Enter your answer as a simplified fraction.

A student calculated that a plumber earned $146.25 by working 4.5 hours at $31.50 per hour and then paying a $15.75 supply fee. Which estimation best checks whether $146.25 is reasonable?

Round to $30 \times 5 - 16 = 150 - 16 = 134$ , which is close to $146.25.

Round to $30 \times 4 - 15 = 120 - 15 = 105$ , which is far from $146.25, so the answer is wrong.

Round to $35 \times 5 - 15 = 175 - 15 = 160$ , which shows $146.25 is too low.

"About $140" is close enough; no calculation is needed.

Solving Multi-Step Problems with Rational Numbers

Recall

Fluency