Question

place parentheses, if needed, to make each of the following equations true.
a. 5 + 4 × 6 = 54
b. 24 ÷ 6 + 1 = 5
c. 5 + 4 + 9 ÷ 2 = 9
d. 5 + 6 ÷ 2 + 6 = 14
a. choose the correct answer below.
a. parentheses are needed. the corrected equation is (5 + 4) × 6 = 54.
b. parentheses are needed. the corrected equation is 5 + (4 × 6) = 54.
c. parentheses are needed. the corrected equation is (5 + 4 × 6) = 54.
d. parentheses are not needed to make the equation true.
b. choose the correct answer below.
a. parentheses are needed. the corrected equation is 24 ÷ (6 + 1) = 5.
b. parentheses are needed. the corrected equation is (24 ÷ 6 + 1) = 5.
c. parentheses are needed. the corrected equation is (24 ÷ 6) + 1 = 5.
d. parentheses are not needed to make the equation true.
c. choose the correct answer below.
a. parentheses are needed. the corrected equation is (5 + 4 + 9) ÷ 2 = 9.
b. parentheses are needed. the corrected equation is (5 + 4) + (9 ÷ 2) = 9.
c. parentheses are needed. the corrected equation is 5 + (4 + 9) ÷ 2 = 9.
d. parentheses are not needed to make the equation true.
d. choose the correct answer below.
a. parentheses are needed. the corrected equation is (5 + 6) ÷ 2 + 6 = 14.
b. parentheses are needed. the corrected equation is 5 + 6 ÷ (2 + 6) = 14.
c. parentheses are needed. the corrected equation is (5 + 6) ÷ (2 + 6) = 14.
d. parentheses are not needed to make the equation true.

Explanation:

Part a

Step1: Evaluate without parentheses

Calculate \(5 + 4\times6\). By order of operations (multiplication first), \(4\times6 = 24\), then \(5+24 = 29
eq54\).

Step2: Check option A

Calculate \((5 + 4)\times6\). \(5 + 4 = 9\), then \(9\times6 = 54\). This works.

Step3: Check option B

Calculate \(5+(4\times6)\). \(4\times6 = 24\), \(5 + 24 = 29
eq54\).

Step4: Check option C

\((5 + 4\times6)\) is same as without parentheses (since order of operations already does multiplication first), which was 29.

Step1: Evaluate without parentheses

Calculate \(24\div6 + 1\). \(24\div6 = 4\), \(4 + 1 = 5\). Wait, but let's check options. Wait, original equation is \(24\div6 + 1 = 5\)? Wait, \(24\div6=4\), \(4 + 1 = 5\). But let's check options. Wait, maybe typo? Wait, no, the options: option D says parentheses not needed. Wait, let's recalculate. \(24\div6 + 1 = 4 + 1 = 5\), which matches the right - hand side. So parentheses are not needed.

Step1: Evaluate without parentheses

Calculate \(5 + 4 + 9\div2\). \(9\div2 = 4.5\), then \(5+4 + 4.5=13.5
eq9\).

Step2: Check option A

Calculate \((5 + 4 + 9)\div2\). \(5 + 4 + 9 = 18\), \(18\div2 = 9\). This works.

Step3: Check option B

Calculate \((5 + 4)+(9\div2)\). \(5 + 4 = 9\), \(9\div2 = 4.5\), \(9+4.5 = 13.5
eq9\).

Step4: Check option C

Calculate \(5+(4 + 9)\div2\). \(4 + 9 = 13\), \(13\div2 = 6.5\), \(5+6.5 = 11.5
eq9\).

Answer:

A. Parentheses are needed. The corrected equation is \((5 + 4)\times6 = 54\).

Part b