Fill in the missing number to make each equation correct.

Fill in the missing number to make each equation correct. 1. 8 x 8 = 40 + 4 + _ 2. 50 – = 20 + 8 3. + 12 = 19 + 5 4. 8 + 8 + _ = 2 x 10 5. 40 – ( 6 + 5 ) = 11 + 10

The Correct Answer and Explanation is:

Let’s solve each equation step-by-step and then provide an explanation.

1. 8×8=40+4+___8 \times 8 = 40 + 4 + \_\_\_

Left side: 8×8=648 \times 8 = 64
Right side: 40+4=4440 + 4 = 44
64=44+___⇒64−44=2064 = 44 + \_\_\_ \Rightarrow 64 – 44 = 20
Answer: 20

2. 50−___=20+850 – \_\_\_ = 20 + 8

Right side: 20+8=2820 + 8 = 28
50−___=28⇒50−28=2250 – \_\_\_ = 28 \Rightarrow 50 – 28 = 22
Answer: 22

3. ___+12=19+5\_\_\_ + 12 = 19 + 5

Right side: 19+5=2419 + 5 = 24
___+12=24⇒24−12=12\_\_\_ + 12 = 24 \Rightarrow 24 – 12 = 12
Answer: 12

4. 8+8+___=2×108 + 8 + \_\_\_ = 2 \times 10

Left part: 8+8=168 + 8 = 16
Right side: 2×10=202 \times 10 = 20
16+___=20⇒20−16=416 + \_\_\_ = 20 \Rightarrow 20 – 16 = 4
Answer: 4

5. 40−(6+5)=11+1040 – (6 + 5) = 11 + 10

Inside parentheses: 6+5=116 + 5 = 11
Left side: 40−11=2940 – 11 = 29
Right side: 11+10=2111 + 10 = 21
29≠2129 \ne 21, so check if the equation is already correct or if there’s a missing number.

Let’s suppose the original expression is:
40−(6+5)=11+___40 – (6 + 5) = 11 + \_\_\_

Left side: 40−11=2940 – 11 = 29
29=11+___⇒29−11=1829 = 11 + \_\_\_ \Rightarrow 29 – 11 = 18
Answer: 18

Final Answers:

Explanation

These problems test your understanding of basic arithmetic operations—addition, subtraction, multiplication, and order of operations—and how to manipulate equations to find missing values.

In the first problem, we begin with multiplication: 8×8=648 \times 8 = 64. The other side of the equation is a sum that partially adds to 44. To make both sides equal, we determine what number must be added to 44 to get 64, which is 20.

The second problem uses subtraction. You are given a difference (50 minus a number) that equals a known sum (28). To find the missing number, subtract 28 from 50, giving 22.

In the third equation, a number plus 12 equals another known sum (24). To isolate the missing number, you subtract 12 from 24, which results in 12.

The fourth question tests your knowledge of both addition and multiplication. The total needs to equal 20. Since 8 + 8 = 16, we determine the missing number by subtracting 16 from 20, which gives 4.

Finally, the fifth problem involves both subtraction and parentheses. First, compute the value inside the parentheses (6 + 5 = 11), then subtract from 40 to get 29. The right side of the equation is 11 + a missing number. Solving 11+x=2911 + x = 29, we find x = 18.

Understanding how to isolate variables and balance both sides of an equation is essential for solving math problems like these efficiently and accurately.