Workbook 2 · Operations, squares and roots · Answer guide
Accept equivalent correct explanations. Invite the learner to show how they checked.
1. Explain 7 + 5 using a complement.
7 + 10 − 5 = 12.
2. Regroup to explain 32 − 7.
32 = 2 tens + 12 units; subtract 7 units to leave 25.
3. Explain why 4 × 6 and 6 × 4 give the same answer.
Both equal 24. A four-by-six rectangular array can be turned to show six-by-four.
4. Divide 29 into groups of 4. Give the whole-group count and remainder.
29 = 4 × 7 + 1: seven groups, remainder one.
5. Find 12² using (10 + 2)². Include both cross terms.
100 + 20 + 20 + 4 = 144. The two cross terms must both be included.
6. Why is √49 equal to 7, although both 7² and (−7)² equal 49?
The square-root symbol denotes the nonnegative principal root. The equation x² = 49 has solutions ±7.
7. Bound √20 between two consecutive integers. Then try 4.4 and 4.5.
4² < 20 < 5²; 4.4² = 19.36 and 4.5² = 20.25, so 4.4 < √20 < 4.5.
8. Can the five-place website frame display 40² exactly? Can it display √2 exactly?
No: 1600 exceeds its 999.99 magnitude range. √2 is irrational and has no finite decimal representation.
9. Explain what can be displayed on the frame and what still requires a written method.
The frame represents intermediate or final values within its range and precision. A multiplication or root algorithm needs explicit steps; a displayed answer does not prove a physical procedure.