1. The problem asks to insert one pair of brackets in each expression so that the equation holds true. 2. For part a) $7 - 5 \times 4 + 8 = 16$, we want to find where to place brackets to make the left side equal 16. 3. The original expression without brackets is evaluated as $7 - (5 \times 4) + 8 = 7 - 20 + 8 = -5$, which is not 16. 4. Try placing brackets around $7 - 5$: $$ (7 - 5) \times 4 + 8 = 2 \times 4 + 8 = 8 + 8 = 16 $$ This satisfies the equation. 5. For part b) $7 - 5 \times 4 + 8 = -21$, again try placing brackets to make the left side equal -21. 6. Try placing brackets around $4 + 8$: $$ 7 - 5 \times (4 + 8) = 7 - 5 \times 12 = 7 - 60 = -53 $$ Not equal to -21. 7. Try placing brackets around $5 \times 4 + 8$ (which is the same as original, so no change). 8. Try placing brackets around $7 - 5 \times 4$: $$ (7 - 5 \times 4) + 8 = (7 - 20) + 8 = -13 + 8 = -5 $$ Not equal to -21. 9. Try placing brackets around $5 \times (4 + 8)$: $$ 7 - (5 \times (4 + 8)) = 7 - (5 \times 12) = 7 - 60 = -53 $$ No. 10. Try placing brackets around $(7 - 5) \times (4 + 8)$: $$ (7 - 5) \times (4 + 8) = 2 \times 12 = 24 $$ No. 11. Try placing brackets around $7 - (5 \times 4 + 8)$: $$ 7 - (5 \times 4 + 8) = 7 - (20 + 8) = 7 - 28 = -21 $$ This satisfies the equation. Final answers: - a) $(7 - 5) \times 4 + 8 = 16$ - b) $7 - (5 \times 4 + 8) = -21$