**Grade 7 math worksheet 8 answers :**

Here we are going to see 10 practice questions of mixed topics. We have been preparing this set of questions in order to test how you understood the topics.

**Question 1 :**

The unit digit of 13^{17} + 17^{13} is

(A) 0 (B) 9 (C) 1

**Solution :**

Unit digit of 13 Unit digit of 13 Unit digit of 13 Unit digit of 13 |
Unit digit of 17 Unit digit of 17 Unit digit of 17 Unit digit of 17 |

(The order is repeated after every multiple of 4)

Hence the unit digit of 13^{17 }is 3

Units digit of 17^{13} = 7

Units digit of sum of both the numbers = 3+7 = 0

Answer = 10

(The order is repeated after every multiple of 4)

**Question 2 :**

If the diameter of a circle is 376216 inches, using the approximation π = 3:14, compute the ratio of the its area, in square inches, to its circumference in inch.

(A) 94054:5 (B) 94554:1 (C) 94054:1

**Solution :**

Radius of circle = 376216/2 = 188108

Area of circle : Circumference of circle

πr^{2} : 2 πr

r : 2

188108 : 2

Divide both terms by 2

188108/2 : 2/2

94054 : 1

**Question 3 :**

If 1/7 is written in decimal form, then the 100th digit after the decimal point is

(A) 8 (B) 3 (C) 7

**Solution :**

1/7 = 0.142857142857............

From the above decimal value, we come to know that this 6 digits is repeating.

Now let us calculate how many 6 are in 100.

16 (6) = 96

1 is the 97^{th} digit

4 is the 98^{th} digit

2 is the 99^{th} digit

8 is the 100^{th} digit

**Question 4 :**

The length of the two parallel sides of a trapezium are 15 cm and 10 cm. If its area is 100 sq. cm. Find the distance between the parallel sides.

(A) 12 cm (B) 16 cm (C) 8 cm

**Solution**

Given: a = 15 cm, b = 10 cm, Area = 100 sq. cm.

Area of the trapezium = 100

(1/2) h (a + b) = 100

(1/2) h (15 + 10) = 100

h = 200/25

h = 8

Hence the distance between the parallel sides = 8 cm.

**Question 5 :**

.If a, b, and c are nonzero numbers satisfying 3a = 4b and 5b = 6c, what is c/(a + b) ?

(A) 5/14 (B) 3/10 (C) 2/19

**Solution :**

3a = 4b a = 4b/3 |
5b = 6c (5b/6) = c |

c/(a + b) = (5b/6)/((4b/3) + b)

= (5b/6)/(7b/3)

= (5b/6)**⋅**(3/7b)

= (5/2)**⋅**(1/7)

= 5/14

Hence the answer is 5/14.

**Question 6 :**

The radii of two spheres are of 2 and 6, then the ratio of the volume of the larger sphere to the volume of the smaller sphere is

(A) 1 : 27 (B) 2 : 15 (C) 5 : 14

**Solution :**

Volume of sphere = (4/3) πr^{3}

(4/3) πR^{3 }: (4/3) πr^{3}

R^{3 }: r^{3}

2^{3 }: 6^{3 }==> (2 ⋅ 2 ⋅ 2)/(6 ⋅ 6 ⋅ 6)

1 / 27

1 : 27

Hence the required ratio is 1 : 27

Let us look into solution of next problem on "Grade 7 math worksheet 8 answers".

**Question 7 :**

If P be the product of the first nine multiples of 19 (i.e. P = 19x38x57……….152x171). What is the unit digit of P?

(A) 5 (B) 9 (C) 0

**Solution :**

= 19 x 38 x 57……….152 x 171

= (1 x 19) x (2 x 19) x (3 x 19)……….(9 x 19)

= 19 (1 + 2 + 3 + .......... + 9)

= 19 ( 9(9+1) / 2)

= 19 (9 ⋅ 10 / 2)

= 19 ⋅ 45

= 855

Hence the unit digit is 5.

Let us look into solution of next problem on "Grade 7 math worksheet 8 answers".

**Question 8 :**

Find the perimeter of the rectangle whose length is 5cm and breadth is 3 cm.

(A) 10 cm (B) 16 cm (C) 15 cm

**Solution :**

Perimeter of rectangle = length x breadth

= 5 (3)

= 15 cm

Hence the perimeter of rectangle is 15 cm.

Let us look into solution of next problem on "Grade 7 math worksheet 8 answers".

**Question 9 :**

What is the value of 1 + 3 + 5 +…………………… + 195 + 197 + 199?

(A) 10500 (B) 10001 (C) 10000

**Solution :**

Sum of odd numbers = [(l + 1)/2]^{2}

= [(199 + 1)/2]^{2}

= (200/2)^{2}

= 100^{2}

= 10000

Hence the answer is 10000.

**Question 10 :**

The number of positive divisors of 120 are divisible by 4 are

(A) 7 (B) 3 (C) 8

**Solution :**

Divisors of 120 are 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, 120

From the above numbers 4, 8, 12, 20, 24, 40, 60, 120 are divisible by 4.

Hence the answer is 8.

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