Arithmetic Expressions

Question 3

  1. Find the values of the following expressions. For each pair, first try to guess whether they have the same value. When are the two expressions equal?

(a) (6+10)−2(6 + 10) - 2 and 6+(10−2)6 + (10 - 2)

(b) 16−(8−3)16 - (8 - 3) and (16−8)−3(16 - 8) - 3

(c) 27−(18+4)27 - (18 + 4) and 27+(−18−4)27 + (-18 - 4)

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Solution

We will calculate the value of each expression. Then we will compare their final results.

Step 1 — Evaluate expressions for part (a)

Let us find the value of the first expression. We calculate the sum inside the parentheses first. (6+10)−2(6 + 10) - 2 =16−2= 16 - 2

14\boxed{14}

Now, let us find the value of the second expression. We calculate the difference inside the parentheses first. 6+(10−2)6 + (10 - 2) =6+8= 6 + 8

14\boxed{14}

Both expressions give the same value. So, they are equal.

Step 2 — Evaluate expressions for part (b)

Let us find the value of the first expression. We calculate the difference inside the parentheses first. 16−(8−3)16 - (8 - 3) =16−5= 16 - 5

11\boxed{11}

Now, let us find the value of the second expression. We calculate the difference inside the parentheses first. (16−8)−3(16 - 8) - 3 =8−3= 8 - 3

5\boxed{5}

The expressions have different values. So, they are not equal.

Step 3 — Evaluate expressions for part (c)

Let us find the value of the first expression. We calculate the sum inside the parentheses first. 27−(18+4)27 - (18 + 4) =27−22= 27 - 22

5\boxed{5}

Now, let us find the value of the second expression. We calculate the sum inside the parentheses first. 27+(−18−4)27 + (-18 - 4) =27+(−22)= 27 + (-22)

5\boxed{5}

Both expressions give the same value. So, they are equal.

Answer

(a) The expressions have the same value. (b) The expressions do not have the same value. (c) The expressions have the same value.

More questions in this chapter

Q1

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) 24+(6−4)=24+6 □ ‾24 + (6 - 4) = 24 + 6 \ \square \ \underline{\quad}

    (b) 38+(‾ □ ‾)=38+9−438 + (\underline{\quad} \ \square \ \underline{\quad}) = 38 + 9 - 4

    (c) 24−(6+4)=24 □ 6−424 - (6 + 4) = 24 \ \square \ 6 - 4

    (d) 24−6−4=24−6 □ ‾24 - 6 - 4 = 24 - 6 \ \square \ \underline{\quad}

    (e) 27−(8+3)=27 □ 8 □ 327 - (8 + 3) = 27 \ \square \ 8 \ \square \ 3

    (f) 27−(‾ □ ‾)=27−8+327 - (\underline{\quad} \ \square \ \underline{\quad}) = 27 - 8 + 3

Q2
  1. Remove the brackets and write the expression having the same value.

(a) 14+(12+10)14 + (12 + 10)

(b) 14−(12+10)14 - (12 + 10)

(c) 14+(12−10)14 + (12 - 10)

(d) 14−(12−10)14 - (12 - 10)

(e) −14+(12−10)-14 + (12 - 10)

(f) 14−(−12−10)14 - (-12 - 10)

Q3
  1. Find the values of the following expressions. For each pair, first try to guess whether they have the same value. When are the two expressions equal?

(a) (6+10)−2(6 + 10) - 2 and 6+(10−2)6 + (10 - 2)

(b) 16−(8−3)16 - (8 - 3) and (16−8)−3(16 - 8) - 3

(c) 27−(18+4)27 - (18 + 4) and 27+(−18−4)27 + (-18 - 4)

Q4
  1. In each of the sets of expressions below, identify those that have the same value. Do not evaluate them, but rather use your understanding of terms.

(a) 319+537319 + 537, 319−537319 - 537, −537+319-537 + 319, 537−319537 - 319

(b) 87+46−10987 + 46 - 109, 87+46−10987 + 46 - 109, 87+46−10987 + 46 - 109, 87−46+10987 - 46 + 109, 87−(46+109)87 - (46 + 109), (87−46)+109(87 - 46) + 109

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