Distributive Property of Integers | Integers | Assessment | English | Grade 7

Which property of the integers is represented by the following expression a × (b + c) = (a × b) + (a × c)?

• Closure property

• Commutative property

• Distributive property

• Associative property

Answer explanation

In the expression a × (b + c) = a × b + a × c, integer a is distributed over integer b and integer c. Therefore this expression represents the distributivity of multiplication over addition. Hence Option3 is the right answer.

Tags

CCSS.7.NS.A.2C

Multiplication is distributive over _______

• Addition

• Subtraction

• Both addition and subtraction

Answer explanation

Multiplication is distributive over addition and subtraction. For example 3 × (2 + 5) = (3 × 2) + (3 × 5)= 3 × 7 similarly 2 × (6 -3) = (2 × 6) - (2 × 3) = 2 × 3.

Tags

CCSS.3.OA.B.5

A cricket kit consists of a bat, a ball and a pair of gloves. If the cost of the bat is Rs. 120, the cost of the ball is Rs. 50 and the cost of the pair of gloves is Rs. 70, what is the total cost of 12 such cricket kits?

• 2880

• 8220

• 8280

• 8820

Answer explanation

Cost of one bat = Rs. 120, cost of one ball = Rs. 50 and the cost of a pair of gloves = Rs. 70. Therefore the cost of 12 cricket bats = Rs. (12 x 120) The cost of 12 cricket balls = Rs. (12 x 50) And, the cost of 12 pairs of gloves = Rs. (12 x 70) So, total cost of 12 cricket kits = Rs. (12 x 120) + (12 x 50) + (12 x 70) Using distributive property Total cost of 12 cricket kits = Rs. 12 x (120 + 50 + 70) = Rs. 12 x (240) = Rs. 2880

Tags

CCSS.7.EE.B.3

The shapes in the following picture represents integers. Then its RHS will be equal to:

• 
• 
• 
• 

Answer explanation

In the given picture we observe that it is like the expression (a + b) × c. In which triangle represents the integer a, square represents the integer b and circle represents the integer c. By distributivity of multiplication over addition its RHS will be = a × c + b × c. Means triangle × circle + square × circle. We find this pattern in option 3.

Mohan has sold 15 kg of apples and 15 kg of oranges on Monday. On selling apples he had a profit of ₹ 4/kg and on selling oranges he had a loss of ₹ 2/kg. What will be Mohan's net profit or loss on Monday?

• Profit of ₹ 30

• Loss of ₹ 30

• Profit of ₹ 90

• Loss of ₹ 30

Answer explanation

Mohan has sold 10 kg each for apples and oranges. In profit, money is gained therefore it will be represented by + sign but in loss money is lost therefore it will be represented by - sign. So on selling 1 kg of apples profit is +4 and on selling 1 kg of oranges loss is (-2). Equal amount of apples and oranges are sold. So by distributive property problem can be solved easily. Net profit or loss = 15 × (4 + (-2)) = 15 × (4 - 2) = 15 × 2 = 30, the integer is positive. Hence Mohan had a net profit of ₹ 30.

Tags

CCSS.7.NS.A.3

With the help of the image break (8 × 6) into an expression.

• 6 × 8 = 8 × 6

• 6 × 8 = 6 × 5 × 3

• 6 × 8 = (6 × 3) + (5 × 3)

• 6 × 8 = (6 × 5) + (6 × 3)

Answer explanation

The given picture consists of circles arranged in 6 rows and 8 columns. In which 5 columns of circles are red in colour and 3 columns of circles are blue in colour. But in 5 columns of red circles and 3 columns of blue circles there are 6 rows. So it can be written as 6 × 8 = 6 × (5 + 3) where 6 is the number of rows, 5 is the number of columns of red circles and 3 is the number of columns of blue circles. So 6 × 8 = (5 × 6) + 3 × 6, hence option 4 is the right answer.

Tags

CCSS.3.OA.B.5

Fill in the blank: 7 × 7 = (____× 7) + (2 × 7)

• 3

• 5

• 4

• 2

Answer explanation

7 × 7 = 49 therefore 49 = (5 × ____) + (2 × 7) on simplifying we get 49 = (5 × ____) + 14. Now 49 - 14 = (5 × ____) that is 35 = (5 × ____). Since 5 × 7 = 35. Therefore 7 × 7 = (5 × 7) + (2 × 7). So option 2 is the right answer.

Tags

CCSS.3.OA.B.5