Figure it Out 1. Fill in the blanks with numbers, and boxes with operation signs such that the expressions on both sides are equal. (a) (b) (c) (d) (e) (f)

Understand the Question To fill in the missing numbers and operation signs (, ), calculate the numerical value of the fully given side first. Key rules for expanding brackets with signs: When preceded by a plus sign: When preceded by a minus sign: and The value of the incomplete side must match the completed side. Part (a) Step 1 · Evaluate and Find Missing Values Calculate the LHS For the RHS to equal Since , the missing operation is and the number is . Answer > (a) Part (b) Step 1 · Evaluate and Find Missing Values Calculate the RHS For the LHS to equal From the RHS, . Thus, the numbers are and , and the operation is . Answer > (b) Part (c) Step 1 · Evaluate and Find Missing Sign Calculate the LHS For the RHS to equal Thus, the missing operation is . Answer > (c) Part (d) Step 1 · Evaluate and Find Missing Values Calculate the LHS For the RHS to equal Since , the missing operation is and the number is . Answer > (d) Part (e) Step 1 · Evaluate and Find Missing Signs Calculate the LHS Expanding brackets preceded by a minus sign changes all signs inside Checking RHS Thus, both missing operations are . Answer > (e) Part (f) Step 1 · Evaluate and Find Missing Values Calculate the RHS For the LHS to equal Since , the numbers are and , and the operation is . Answer > (f) Common Mistakes Sign Change Rule: Forgetting that a minus sign outside a bracket changes the signs inside the bracket, e.g., and . Order of Operations: Calculating left-to-right without respecting bracket groupings first.

Arithmetic Expressions

Question 1

Figure it Out

Fill in the blanks with numbers, and boxes with operation signs such that the expressions on both sides are equal.

(a) $24 + (6 - 4) = 24 + 6 \ \square \ \underline{\quad}$

(b) $38 + (\underline{\quad} \ \square \ \underline{\quad}) = 38 + 9 - 4$

(c) $24 - (6 + 4) = 24 \ \square \ 6 - 4$

(d) $24 - 6 - 4 = 24 - 6 \ \square \ \underline{\quad}$

(e) $27 - (8 + 3) = 27 \ \square \ 8 \ \square \ 3$

(f) $27 - (\underline{\quad} \ \square \ \underline{\quad}) = 27 - 8 + 3$

Solution

Understand the Question

To fill in the missing numbers and operation signs ( $+$ , $-$ ), calculate the numerical value of the fully given side first.
Key rules for expanding brackets with signs:
- When preceded by a plus sign: $a + (b - c) = a + b - c$
- When preceded by a minus sign: $a - (b + c) = a - b - c$ and $a - (b - c) = a - b + c$
The value of the incomplete side must match the completed side.

(a) $24 + (6 - 4) = 24 + 6 \ \square \ \underline{\quad}$

Step 1 · Evaluate and Find Missing Values

Diagram 1

Calculate the LHS

\begin{aligned} 24 + (6 - 4) &= 24 + 2 \\ &= 26 \end{aligned}

For the RHS to equal $26$ $24 + 6 \ \square \ \underline{\quad} = 30 \ \square \ \underline{\quad} = 26$

Since $30 - 4 = 26$ , the missing operation is $-$ and the number is $4$ .

Answer

(a) $24 + (6 - 4) = 24 + 6 - \underline{4}$

(b) $38 + (\underline{\quad} \ \square \ \underline{\quad}) = 38 + 9 - 4$

Step 1 · Evaluate and Find Missing Values

Calculate the RHS

\begin{aligned} 38 + 9 - 4 &= 47 - 4 \\ &= 43 \end{aligned}

For the LHS to equal $43$ $38 + (\underline{\quad} \ \square \ \underline{\quad}) = 43 \implies (\underline{\quad} \ \square \ \underline{\quad}) = 43 - 38 = 5$

From the RHS, $9 - 4 = 5$ . Thus, the numbers are $9$ and $4$ , and the operation is $-$ .

Answer

(b) $38 + (\underline{9} - \underline{4}) = 38 + 9 - 4$

(c) $24 - (6 + 4) = 24 \ \square \ 6 - 4$

Step 1 · Evaluate and Find Missing Sign

Calculate the LHS

\begin{aligned} 24 - (6 + 4) &= 24 - 10 \\ &= 14 \end{aligned}

For the RHS to equal $14$

\begin{aligned} 24 - 6 - 4 &= 18 - 4 \\ &= 14 \end{aligned}

Thus, the missing operation is $-$ .

Answer

(c) $24 - (6 + 4) = 24 - 6 - 4$

(d) $24 - 6 - 4 = 24 - 6 \ \square \ \underline{\quad}$

Step 1 · Evaluate and Find Missing Values

Calculate the LHS

\begin{aligned} 24 - 6 - 4 &= 18 - 4 \\ &= 14 \end{aligned}

For the RHS to equal $14$ $24 - 6 \ \square \ \underline{\quad} = 18 \ \square \ \underline{\quad} = 14$

Since $18 - 4 = 14$ , the missing operation is $-$ and the number is $4$ .

Answer

(d) $24 - 6 - 4 = 24 - 6 - \underline{4}$

(e) $27 - (8 + 3) = 27 \ \square \ 8 \ \square \ 3$

Step 1 · Evaluate and Find Missing Signs

Calculate the LHS

\begin{aligned} 27 - (8 + 3) &= 27 - 11 \\ &= 16 \end{aligned}

Expanding brackets preceded by a minus sign changes all signs inside $27 - (8 + 3) = 27 - 8 - 3$

Checking RHS

\begin{aligned} 27 - 8 - 3 &= 19 - 3 \\ &= 16 \end{aligned}

Thus, both missing operations are $-$ .

Answer

(e) $27 - (8 + 3) = 27 - 8 - 3$

(f) $27 - (\underline{\quad} \ \square \ \underline{\quad}) = 27 - 8 + 3$

Step 1 · Evaluate and Find Missing Values

Calculate the RHS

\begin{aligned} 27 - 8 + 3 &= 19 + 3 \\ &= 22 \end{aligned}

For the LHS to equal $22$ $27 - (\underline{\quad} \ \square \ \underline{\quad}) = 22 \implies (\underline{\quad} \ \square \ \underline{\quad}) = 27 - 22 = 5$

Since $8 - 3 = 5$ , the numbers are $8$ and $3$ , and the operation is $-$ .

Answer

(f) $27 - (\underline{8} - \underline{3}) = 27 - 8 + 3$

Common Mistakes

Sign Change Rule: Forgetting that a minus sign outside a bracket changes the signs inside the bracket, e.g., $-(a + b) = -a - b$ and $-(a - b) = -a + b$ .
Order of Operations: Calculating left-to-right without respecting bracket groupings first.

Question 1

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