To determine which of the given expressions is equal to 4, let's evaluate each expression step-by-step.
Expression 1: [tex]\( 4 \times \left( \frac{1}{2} \times 6 \right) \div 3 \)[/tex]
1. First, evaluate the inner multiplication: [tex]\( \frac{1}{2} \times 6 = 3 \)[/tex].
2. Next, multiply by 4: [tex]\( 4 \times 3 = 12 \)[/tex].
3. Finally, divide by 3: [tex]\( 12 \div 3 = 4 \)[/tex].
So, [tex]\( 4 \times \left( \frac{1}{2} \times 6 \right) \div 3 = 4 \)[/tex].
Expression 2: [tex]\( 6 \div \left( \frac{1}{4} \times 3 \times \frac{5}{4} \right) \)[/tex]
1. Evaluate the multiplication inside the parenthesis: [tex]\( \frac{1}{4} \times 3 = \frac{3}{4} \)[/tex].
2. Then, multiply by [tex]\( \frac{5}{4} \)[/tex]: [tex]\( \frac{3}{4} \times \frac{5}{4} = \frac{15}{16} \)[/tex].
3. Finally, divide 6 by this value: [tex]\( 6 \div \frac{15}{16} = 6 \times \frac{16}{15} = \frac{96}{15} = 6.4 \)[/tex].
So, [tex]\( 6 \div \left( \frac{1}{4} \times 3 \times \frac{5}{4} \right) = 6.4 \)[/tex].
Expression 3: [tex]\( 8 + \left( \frac{1}{3} \times 6 \right) \div 5 \)[/tex]
1. First, evaluate the inner multiplication: [tex]\( \frac{1}{3} \times 6 = 2 \)[/tex].
2. Then, divide by 5: [tex]\( 2 \div 5 = 0.4 \)[/tex].
3. Finally, add to 8: [tex]\( 8 + 0.4 = 8.4 \)[/tex].
So, [tex]\( 8 + \left( \frac{1}{3} \times 6 \right) \div 5 = 8.4 \)[/tex].
Expression 4: [tex]\( 10 - \left( \frac{1}{5} \times 10 \right) + 1 \)[/tex]
1. Evaluate the multiplication inside the parenthesis: [tex]\( \frac{1}{5} \times 10 = 2 \)[/tex].
2. Subtract this value from 10: [tex]\( 10 - 2 = 8 \)[/tex].
3. Finally, add 1: [tex]\( 8 + 1 = 9 \)[/tex].
So, [tex]\( 10 - \left( \frac{1}{5} \times 10 \right) + 1 = 9 \)[/tex].
Thus, the expression that is equal to 4 is:
[tex]\[ 4 \times \left( \frac{1}{2} \times 6 \right) \div 3 \][/tex]
This is Expression 1.
