CBSE Class 7 Mathematics Decimals Assignment Set 05

VII - Mathematics Assignment No - 3 - Fractions and Decimals

Q1. Multiply \(37.14\) by \(25\)
Answer: Multiply \(37.14\) by \(25\):
\(37.14 \times 25 = 928.5\)
In simple words: Multiply the numbers normally as integers, then place the decimal point two places from the right because there are two decimal places in \(37.14\).

Exam Tip: Count the total number of decimal places in the given numbers to place the decimal correctly in the final product.

Q2. Multiply \(671.07\) by \(1.3\)
Answer: Multiply \(671.07\) by \(1.3\):
\(671.07 \times 1.3 = 872.391\)
In simple words: Multiply \(67107\) by \(13\) to get \(872391\), then place the decimal point after three digits from the right because there are three total decimal places (\(2 + 1 = 3\)).

Exam Tip: The number of decimal places in the product is equal to the sum of the decimal places in the multiplier and multiplicand.

Q3. Multiply \(27.57\) by \(10, 100, 1000\) respectively
Answer: Multiply \(27.57\) by powers of 10:
\(27.57 \times 10 = 275.7\)
\(27.57 \times 100 = 2757\)
\(27.57 \times 1000 = 27570\)
In simple words: When multiplying by powers of 10, shift the decimal point to the right by as many places as there are zeros.

Exam Tip: Shifting the decimal point to the right makes the number larger.

Q4. Multiply \(27.325\) by \(0.75\)
Answer: Multiply \(27.325\) by \(0.75\):
\(27.325 \times 0.75 = 20.49375\)
In simple words: Multiply \(27325\) by \(75\) and place the decimal point after five digits from the right since \(27.325\) has 3 decimal places and \(0.75\) has 2 decimal places (\(3 + 2 = 5\)).

Exam Tip: Always double-check the placement of the decimal point by counting total digits after the decimal in both factors.

Q5. Find the continued product of \(2.5\), \(7.3\) and \(8.04\)
Answer: First, multiply \(2.5\) and \(7.3\):
\(2.5 \times 7.3 = 18.25\)
Next, multiply the result by \(8.04\):
\(18.25 \times 8.04 = 146.73\)
In simple words: Multiply the first two numbers, then multiply that result by the third number.

Exam Tip: Multiplication is associative, so you can multiply any two numbers first, but doing them in order helps avoid calculation errors.

Q6. Verify the following product
(i) \(37.25 \times 1.25 = 1.25 \times 37.25\)
Answer: LHS = \(37.25 \times 1.25 = 46.5625\)
RHS = \(1.25 \times 37.25 = 46.5625\)
Since LHS = RHS, the commutative property of multiplication is verified.
In simple words: Changing the order of numbers in multiplication does not change the answer.

Exam Tip: This illustrates the commutative property of multiplication (\(a \times b = b \times a\)).

(ii) \(2.05 \times (3.75 \times 5.67) = (2.05 \times 3.75) \times 5.67\)
Answer: LHS = \(2.05 \times (3.75 \times 5.67) = 2.05 \times 21.2625 = 43.588125\)
RHS = \((2.05 \times 3.75) \times 5.67 = 7.6875 \times 5.67 = 43.588125\)
Since LHS = RHS, the associative property of multiplication is verified.
In simple words: The grouping of numbers in multiplication does not change the final product.

Exam Tip: This illustrates the associative property of multiplication (\(a \times (b \times c) = (a \times b) \times c\)).

Q7. Multiply \(7.777\) by \(7.7\)
Answer: Multiply \(7.777\) by \(7.7\):
\(7.777 \times 7.7 = 59.8829\)
In simple words: Multiply \(7777\) by \(77\) and put the decimal point after four places from the right because there are 3 decimal places in \(7.777\) and 1 in \(7.7\).

Exam Tip: Ensure proper alignment and column addition when performing long multiplication by hand.

Q8. If \(4.123 \times 15 = 61.845\) then without actual multiplication, find
(i) \(41.23 \times 15\)
Answer: Given \(4.123 \times 15 = 61.845\).
In \(41.23 \times 15\), the decimal point in the first factor is shifted one place to the right compared to \(4.123\) (since \(41.23 = 4.123 \times 10\)).
Therefore, \(41.23 \times 15 = 618.45\).
In simple words: Shift the decimal point one place to the right in the answer because the number being multiplied became 10 times larger.

Exam Tip: Use given results to solve related decimal problems without recalculating from scratch.

(ii) \(412.3 \times 1.5\)
Answer: Given \(4.123 \times 15 = 61.845\).
We can write \(412.3 \times 1.5\) as \((4.123 \times 100) \times (\frac{15}{10}) = (4.123 \times 15) \times \frac{100}{10} = 61.845 \times 10 = 618.45\).
In simple words: Adjust the decimal shifts: multiplying one factor by 100 and dividing the other by 10 results in a net multiplication by 10.

Exam Tip: Balance shifts in decimal places: multiplying one number by 10 and dividing another by 10 keeps the product unchanged.