# Free Integers Subjective Test 02 Practice Test - 6th grade

### Question 1

Evaluate: [1 MARK]

−13+(−69)+57−(−89)−(53+(−49))

#### SOLUTION

Solution :Solution: 1 Mark

−13+(−69)+57−(−89)−(53+(−49))=−13−69+57+89−(53−49)

=−13−69+57+89−53+49

First, take all ‘−’ terms and then take all ‘+’ terms and add them,

=(−13−69−53)+(57+89+49)

=−135+195

=60

### Question 2

Add 3 and (-15) to the sum of 17 and (-5).** **[2 MARKS]

#### SOLUTION

Solution :Steps: 1 Mark

Answer: 1 Mark

Sum of 17 and -5

⇒17+(−5)=17−5=12

Now, adding 3 and (-15) to 12

⇒12+3+(−15)=15+(−15)

⇒15−15=0

### Question 3

Divide: [2 MARKS]

(i) 24 by the predecessor of -2

(ii) -82 by the successor of -2

#### SOLUTION

Solution :Each option: 1 Mark

(i) The predecessor of −2 is −3

because −3 is 1 less than −2

∴24−3=−8

(ii) The successor of −2 is −1

because −1 is 1 more than −2

∴−82−1=82

### Question 4

Numbers are said to be in descending order when they are arranged from the largest to the smallest number. E.g. 25, 21, 17, 13 and 9 are arranged in descending order.

Write the following integers in descending order? [3 MARKS]

(a). 15, -14, 13, 12, 0

(b). 3, -3, 5, -5, 7

(c). 6, -7, -8, 9, -10

#### SOLUTION

Solution :Each option: 1 Mark

(a). 15, 13, 12, 0, -14

⇒(15 is the largest and -14 is the smallest among the given integers)

(b). 7, 5, 3, -3, -5

⇒(7 is the largest and -5 is the smallest among the given integers)

(c). 9, 6, -7, -8, -10

⇒(9 is the largest and -10 is the smallest among the given integers)

### Question 5

Priya has a note of Rupees 10. She purchased a pencil of 75 paise and a rubber of 50 paise.

How much money she has now? [3 MARKS]

#### SOLUTION

Solution :Steps: 2 Marks

Answer: 1 Mark

75p+50p=125p

⇒Re1+25p=Rs 1.25Now, on subtracting Rs 1.25 from Rs 10, we get

⇒Rs(10−1.25)=Rs 8.75.

Thus, after her purchase, the money left with Priya is Rs 8.75.

### Question 6

Answer the following questions: [3 MARKS]

(a). Which integer divides the number line into two halves?

(b). The third integer greater than −6 is?

(c). Which integer is opposite of −5?

#### SOLUTION

Solution :Each option: 1 Mark

(a). 0

(b). −6+3=−3

(c). The opposite of −5 is +5

### Question 7

Using number line . [4 MARKS]

(a) Find the value of – 8 – (–10)

(b) Find the value of 6 – 2

#### SOLUTION

Solution :Number line: 2 Marks

Answers: 2 Marks

(a). – 8 – (– 10) is equal to – 8 + 10 as additive inverse of –10 is 10. On the number line, from – 8 we will move 10 steps towards the right.

We reach at 2. Thus, –8 – (–10) = 2 Hence, to subtract an integer from another integer it is enough to add the additive inverse of the integer that is being subtracted, to the other integer.

(b) In the number line, it has to move two steps left from 6. We reach at 4. Therefore, 6−2=4

### Question 8

(a). Choose the largest and smallest integer among the following: [4 MARKS]

32,−50,−75,120,−365,175

(b). Simplify:

(−3)+(−2)+(−5)+7

(c). −6÷3=?

(d). 3×6×2×(−40)=?

#### SOLUTION

Solution :Each option: 1 Mark

(a). Largest = 175, Smallest = −365

(b). [(−3)+(−2)]+[(−5)+7]

⇒[−3−2]+[−5+7]

⇒[−5+2]=−3

(c). −6÷−3=−6−3=2

(⇒−÷−=+)

(d). 3×6×2×(−40)

⇒18×2×(−40)

⇒36×(−40)=−1440

(⇒as+×−=−)

### Question 9

If walking 80 km towards south is denoted by −80,then what does the following denotes? [4 MARKS]

(i) +20 km

(ii) −30 km

(iii) −70 km

(iv) +45 km

#### SOLUTION

Solution :Each option: 1 Mark

(i) +20

⇒Walking 20 km towards north

(ii) −30

⇒Walking 30 km towards south

(iii) −70

⇒Walking 70 km towards south

(iv) +45

⇒Walking 45 km towards north

### Question 10

If +42 represents 42m above the water surface, what does each of the following represent: [4 MARKS]

(i) −87+55

(ii) +98−115

(ii) +36+57−73

(iv) −42−23+39

#### SOLUTION

Solution :Each point: 1 Mark

(i) −87+55=−32

⇒32m below the water surface

(ii) +98−115=−17

⇒17m below the water surface

(ii) +36+57−73=20

⇒20m above the water surface

(iv) −42−23+39=−26

⇒26m below the water surface