Arithmetic fluency — Topic practice

5 exercises · 3 automatically checked · 2 written self-checks · Untimed

Instructions and review guidance

3 questions · Shuffled order · Untimed practice

Work through the set before checking solutions. Guide question labels match the source lesson references. 2 written responses appear below the question bank, with model answers for self-review; these are not automatically graded.

Guide question labels stay the same when the order changes. Check answers when you are ready to review.

Written self-checks are below the question bank and are excluded from the automatic score.

Written responses are self-review exercises.

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Question 1

Guide question E2.1

Evaluate −5 − (−8) + 3(−2).

Your answer

Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.

Why this answer

−3. Subtracting −8 means adding 8, while $3(-2) = -6.$ Thus $-5 - (-8) + 3(-2) = -5 + 8 - 6 = 3 - 6 = -3.$ Keep the sign of each term attached as you simplify. Repair: Example 2.01.

Review lesson: Arithmetic fluency

Question 2

Guide question E2.2

Evaluate $\frac{5}{6}$ + $\frac{7}{15}$ .

Your answer

Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.

Why this answer

$13/10$ . The least common denominator of 6 and 15 is 30. Then $5/6 + 7/15 = 25/30 + 14/30 = 39/30 = 13/10.$ The result is greater than 1, which is reasonable because the two positive fractions together exceed a whole. Repair: Example 2.04.

Review lesson: Arithmetic fluency

Question 3

Guide question E2.3

Evaluate $\frac{3}{4}$ ÷ $\frac{9}{10}$ .

Your answer

Enter an integer, decimal or fraction without units. Use up to 5 characters, or 6 including a leading minus.

Why this answer

$5/6$ .

Multiply by the reciprocal of the divisor:

$\frac{3}{4}$

The quotient is a little larger than $3/4$ because you divided by 0.9, a number slightly less than 1. Repair: Example 2.07.

Review lesson: Arithmetic fluency

Question navigator and options

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Written self-checks

Write your complete response before opening the model answer. Compare both your answer and your reasoning.

Guide question E2.4

Write (6 × 10⁻³)(4 × 10⁵) in scientific notation.

Show model answerHide model answer

$2.4 \times 10 3$ . Multiply the coefficients and add exponents: $(6 \times 10 -3)(4 \times 10 5) = 24 \times 10 2 .$ Normalize the coefficient to a number from 1 up to, but not including, 10: $24 \times 10 2 = 2.4 \times 10 3 .$ Both equal 2,400, but the latter is standard scientific notation. Repair: Example 2.12.

Guide question E2.5

Seven equal pieces each have exact mass $\frac{2}{7}$ kilogram. What is the total mass, to the nearest tenth of a kilogram? Explain why rounding each piece first is unnecessary.

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2.0 kilograms. Retain the exact fraction: $7(2/7) = 2$ kilograms. Written to the nearest tenth, the result is 2.0. Rounding each $2/7$ to 0.3 first would give 2.1, an error introduced by early rounding. Repair: Example 2.14.

After the exit check

Five secure answers support moving on. Four suggest a targeted repair; three or fewer suggest reviewing the relevant lessons before a fresh check. These are teaching guidelines, not official mastery thresholds. Use the solution explanations to identify the operation that needs attention.

Section 2 readiness

Signs, grouping, and fraction structure should remain correct even when the numbers change. You should know why dividing by a positive number below 1 increases a positive quantity, and you should keep exact values until the requested rounding step.

The drill

Why this answer

Why this answer

Why this answer

Review practice

Written self-checks

Guide question E2.4

Guide question E2.5

After the exit check

Section 2 readiness