CBSE Class 7 Mathematics Practice Assignment Set 05

Solve the following:

Question 1. Multiply:
a) \(1.25 \times 20\)
b) \(8.88 \times 10000\)
c) \(3.01 \times 1100\)
Answer:
a) \(1.25 \times 20 = \frac{125}{100} \times 20 = \frac{2500}{100} = 25\)
b) \(8.88 \times 10000 = 888 \times 100 = 88800\)
c) \(3.01 \times 1100 = \frac{301}{100} \times 1100 = 301 \times 11 = 3311\)
In simple words: To multiply decimals by powers of 10 or whole numbers, shift the decimal point to the right according to the number of zeros, or convert them into fractions for easier calculation.
Exam Tip: When multiplying a decimal by a multiple of 10, multiply the whole numbers first and then place the decimal point equal to the number of decimal places in the given decimal number.

Question 2. Evaluate:
a) \(5.134 \div 1.7\)
b) \(0.9257 \div 100\)
c) \(2.73 \div 1.3\)
Answer:
a) \(5.134 \div 1.7 = \frac{5.134}{1.7} = \frac{5134}{1700} = 3.02\)
b) \(0.9257 \div 100 = 0.009257\)
c) \(2.73 \div 1.3 = \frac{2.73}{1.3} = \frac{273}{130} = 2.1\)
In simple words: Division by decimals is simplified by making the divisor a whole number by multiplying both dividend and divisor by the same power of 10. Division by powers of 10 involves shifting the decimal point to the left.
Exam Tip: Count the number of decimal places in the divisor, remove the decimal point by multiplying both numbers by the corresponding power of 10, and then perform standard long division.

Question 3. What should be added to 4.187 to get 9?
Answer:
Let the required number be \(x\).
\(4.187 + x = 9\)
\(x = 9 - 4.187\)
\(x = 4.813\)
In simple words: To find the missing addend, subtract the given number from the target sum.
Exam Tip: While subtracting decimals, make sure to pad the whole number with trailing zeros (i.e., write 9 as 9.000) so that both numbers have the same number of decimal places.

Question 4. Convert 75m into cm.
Answer:
We know that \(1\text{ m} = 100\text{ cm}\).
\(75\text{ m} = 75 \times 100\text{ cm} = 7500\text{ cm}\)
In simple words: Multiply the value in meters by 100 to convert it into centimeters.
Exam Tip: Remember the metric conversion scale: kilo, hecto, deca, base, deci, centi, milli. Moving from a larger unit to a smaller unit requires multiplication.

Question 5. What is the perimeter of a rectangle with length 0.42m & breadth 31.5cm?
Answer:
Length \((l) = 0.42\text{ m} = 0.42 \times 100\text{ cm} = 42\text{ cm}\)
Breadth \((b) = 31.5\text{ cm}\)
Perimeter of rectangle = \(2 \times (l + b)\)
Perimeter = \(2 \times (42 + 31.5)\)
Perimeter = \(2 \times 73.5\)
Perimeter = \(147\text{ cm} \text{ (or } 1.47\text{ m)}\)
In simple words: First convert both dimensions to the same unit, then apply the standard perimeter formula for a rectangle.
Exam Tip: Always check that all dimensions are in the same unit before substituting them into a formula.

Question 6. Mrs. Sunita uses 3.204 litres of oil to make 9 dishes of equal proportion. How much oil was used for each dish?
Answer:
Total quantity of oil = \(3.204\text{ litres}\)
Total number of dishes = 9
Oil used for each dish = \(\frac{3.204}{9}\)
Oil used for each dish = \(0.356\text{ litres}\)
In simple words: Divide the total quantity of oil by the number of dishes to find the amount used per dish.
Exam Tip: Write proper statement lines in word problems to secure full marks.

Question 7. By what number 0.014 be multiplied to get 1.4?
Answer:
Let the required number be \(x\).
\(0.014 \times x = 1.4\)
\(x = \frac{1.4}{0.014}\)
\(x = \frac{1.4 \times 1000}{0.014 \times 1000}\)
\(x = \frac{1400}{14} = 100\)
In simple words: Divide the target product by the given number to find the multiplier.
Exam Tip: Shift the decimal points equally in both numerator and denominator to eliminate decimals before dividing.

Question 8. Write in the exponential form:
a) \(m \times m\)
b) \(4 \times 4 \times y \times y \times y\)
c) \(5 \times 5 \times 3 \times 3 \times 3 \times 2 \times 2\)
Answer:
a) \(m^2\)
b) \(4^2 y^3\)
c) \(5^2 \times 3^3 \times 2^2\)
In simple words: Count how many times each factor repeats and write it as the exponent over that base.

Answer:
a) \(2^2 \times 3^2 = (2 \times 2) \times (3 \times 3) = 4 \times 9 = 36\)
b) \(6^2 \times 10^3 = (6 \times 6) \times (10 \times 10 \times 10) = 36 \times 1000 = 36000\)
c) \((-3) \times (-2)^4 = (-3) \times [(-2) \times (-2) \times (-2) \times (-2)] = (-3) \times 16 = -48\)
In simple words: Expand each exponent into regular multiplication, follow the rules of signs, and then compute the final product.
Exam Tip: A negative base raised to an even power yields a positive result, while an odd power yields a negative result.

Question 10. Find the value of:
a) \((5x)^3\), where \(x = -\frac{2}{5}\)
b) \((-ab)^2\), where \(a = 2\) and \(b = -1\)
Answer:
a) Substitute \(x = -\frac{2}{5}\) into \((5x)^3\):
\(= \left( 5 \times \left(-\frac{2}{5}\right) \right)^3\)
\(= (-2)^3\)
\(= -2 \times -2 \times -2 = -8\)
b) Substitute \(a = 2\) and \(b = -1\) into \((-ab)^2\):
\(= [-(2) \times (-1)]^2\)
\(= (2)^2 = 4\)
In simple words: Substitute the given variable values into the algebraic expression first, simplify inside the parentheses, and then evaluate the exponent.
Exam Tip: Always use parentheses when substituting negative numbers to avoid sign errors during multiplication.