Solved on Sep 12, 2023

Place parentheses in equations to make them true. Choose the correct answer for each equation.
a. 6+74=526+7 \cdot 4=52 b. 28÷4+1=828 \div 4+1=8 c. 5+4+9÷2=95+4+9 \div 2=9 d. 5+6÷2+4=125+6 \div 2+4=12

STEP 1

Assumptions1. The equations given are 6+74=526+7 \cdot4=52, 5+4+9÷=95+4+9 \div=9, 28÷4+1=828 \div4+1=8, and 5+6÷+4=125+6 \div+4=12. . We need to place parentheses to make each equation true.
3. The order of operations is parentheses, exponents, multiplication and division (from left to right), addition and subtraction (from left to right). This is often remembered by the acronym PEMAS.

STEP 2

Let's start with the first equation 6+74=526+7 \cdot4=52. According to the order of operations, multiplication is performed before addition. So, 747 \cdot4 is performed first and then 66 is added to the result.

STEP 3

Calculate 77 \cdot and add 66 to the result.
6+7=6+28=346+7 \cdot =6+28 =34This does not equal 5252, so parentheses are needed. The correct equation is 6+(7)=526+(7 \cdot)=52.

STEP 4

Now, let's move to the second equation +4+9÷2=9+4+9 \div2=9. According to the order of operations, division is performed before addition. So, 9÷29 \div2 is performed first and then +4+4 is added to the result.

STEP 5

Calculate 9÷29 \div2 and add 5+45+4 to the result.
5+4+9÷2=5+4+4.5=13.55+4+9 \div2 =5+4+4.5 =13.5This does not equal 99, so parentheses are needed. The correct equation is (5+4)+(9÷2)=9(5+4)+(9 \div2)=9.

STEP 6

Next, let's consider the third equation 28÷4+1=828 \div4+1=8. According to the order of operations, division is performed before addition. So, 28÷428 \div4 is performed first and then 11 is added to the result.

STEP 7

Calculate 28÷428 \div4 and add 11 to the result.
28÷4+1=7+1=28 \div4+1 =7+1 =This equals $$, so parentheses are not needed to make the equation true.

STEP 8

Finally, let's consider the fourth equation 5+6÷2+4=125+6 \div2+4=12. According to the order of operations, division is performed before addition. So, 6÷26 \div2 is performed first and then 5+45+4 is added to the result.

STEP 9

Calculate 6÷26 \div2 and add 5+45+4 to the result.
5+6÷2+4=5+3+4=125+6 \div2+4 =5+3+4 =12This equals 1212, so parentheses are not needed to make the equation true.
The solutions area. Parentheses are needed. The corrected equation is 6+(74)=526+(7 \cdot4)=52. b. Parentheses are not needed to make the equation true. c. Parentheses are needed. The corrected equation is (5+4)+(9÷2)=9(5+4)+(9 \div2)=9. d. Parentheses are not needed to make the equation true.

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