CBSE Class 6 Mathematics Revision Assignment 4

Qno1. Write each of the following in the decimal form:
a) \(40 + 6 + \frac{7}{10} + \frac{9}{100}\)
b) \(500 + 70 + 8 + \frac{3}{10} + \frac{1}{100} + \frac{6}{1000}\)
Answer:
a) \(40 + 6 + 0.7 + 0.09 = 46.79\)
b) \(500 + 70 + 8 + 0.3 + 0.01 + 0.006 = 578.316\)
In simple words: Add the whole numbers and place value parts together to form the decimal number.
Exam Tip: Align the decimal points properly when converting expanded forms into standard decimals.

Qno2. Arrange the following decimals in a descending order:
a) 7.3, 8.73, 73.03, 7.33, 8.073
b) 8.88, 8.088, 888.8, 88.08, 8.008
Answer:
a) To arrange in descending order (from greatest to least):
Make all numbers have the same number of decimal places: 7.300, 8.730, 73.030, 7.330, 8.073
Comparing whole number parts first: 73.03 is largest.
Comparing numbers starting with 8: 8.730 > 8.073.
Comparing numbers starting with 7: 7.330 > 7.300.
Descending order: 73.03, 8.73, 8.073, 7.33, 7.3
b) Equalizing decimal places: 8.880, 8.088, 888.800, 88.080, 8.008
Descending order: 888.8, 88.08, 8.88, 8.088, 8.008
In simple words: Descending order means arranging numbers from the largest value to the smallest value.

Exam Tip: Pad decimals with trailing zeros so all numbers have an equal number of decimal digits before comparing.

Qno3. Convert each of the following decimals as a mixed fraction:
a) 7.5
b) 24.8
c) 13.25
Answer:
a) \(7.5 = 7\frac{5}{10} = 7\frac{1}{2}\)
b) \(24.8 = 24\frac{8}{10} = 24\frac{4}{5}\)
c) \(13.25 = 13\frac{25}{100} = 13\frac{1}{4}\)
In simple words: Write the whole number part as it is, and convert the decimal part into a fraction by placing it over 10, 100, or 1000, then simplify.

Exam Tip: Always reduce the fractional part to its lowest terms in the final answer.

Qno4. Convert \(\frac{29}{4}\) into a decimal fraction.
Answer:
Divide 29 by 4 using long division:
\(29 \div 4 = 7\) with a remainder of 1.
\(\frac{29}{4} = 7\frac{1}{4} = 7 + \frac{25}{100} = 7.25\)
In simple words: Divide the numerator by the denominator to get the decimal value.

Exam Tip: Alternatively, multiply the numerator and denominator by 25 to make the denominator 100, making decimal conversion immediate.

Qno5. Convert each of the following into a fraction in its simplest form:
a) 0.48
b) 0.053
c) 0.224
Answer:
a) \(0.48 = \frac{48}{100} = \frac{48 \div 4}{100 \div 4} = \frac{12}{25}\)
b) \(0.053 = \frac{53}{1000}\) (Since 53 is a prime number, it is already in simplest form)
c) \(0.224 = \frac{224}{1000} = \frac{224 \div 8}{1000 \div 8} = \frac{28}{125}\)
In simple words: Remove the decimal point, write the number over a power of 10, and cancel out common factors from numerator and denominator.

Exam Tip: Find the HCF of the numerator and denominator to reduce fractions directly in one step.

Qno6. Convert each of the following into a decimal:
a) \(\frac{23}{10}\)
b) \(\frac{21415}{1000}\)
c) \(\frac{3}{40}\)
Answer:
a) \(\frac{23}{10} = 2.3\)
b) \(\frac{21415}{1000} = 21.415\)
c) \(\frac{3}{40} = \frac{3 \times 25}{40 \times 25} = \frac{75}{1000} = 0.075\)
In simple words: Shift the decimal point to the left by as many zeros as there are in the denominator.

Exam Tip: For denominators like 40, convert them to a power of 10 (like 1000) by multiplying both numerator and denominator by a suitable number.

Qno7. Write a fraction for each of the following:
a) Three-fourths
b) Two-fifths
c) Seven-twelfths
Answer:
a) \(\frac{3}{4}\)
b) \(\frac{2}{5}\)
c) \(\frac{7}{12}\)
In simple words: The first word gives the numerator and the second word gives the denominator.

Exam Tip: Read carefully: numerator comes first, denominator comes second.

Qno8. Write four fractions equivalent to each of the following:
a) \(\frac{8}{11}\)
b) \(\frac{5}{7}\)
Answer:
a) Multiply numerator and denominator by 2, 3, 4, and 5:
\(\frac{8 \times 2}{11 \times 2} = \frac{16}{22}\)
\(\frac{8 \times 3}{11 \times 3} = \frac{24}{33}\)
\(\frac{8 \times 4}{11 \times 4} = \frac{32}{44}\)
\(\frac{8 \times 5}{11 \times 5} = \frac{40}{55}\)
Four equivalent fractions are \(\frac{16}{22}, \frac{24}{33}, \frac{32}{44}, \frac{40}{55}\).
b) Multiply numerator and denominator by 2, 3, 4, and 5:
\(\frac{5 \times 2}{7 \times 2} = \frac{10}{14}\)
\(\frac{5 \times 3}{7 \times 3} = \frac{15}{21}\)
\(\frac{5 \times 4}{7 \times 4} = \frac{20}{28}\)
\(\frac{5 \times 5}{7 \times 5} = \frac{25}{35}\)
Four equivalent fractions are \(\frac{10}{14}, \frac{15}{21}, \frac{20}{28}, \frac{25}{35}\).
In simple words: Multiply both the top and bottom numbers by the same whole number to find equivalent fractions.

Exam Tip: You can multiply by any non-zero integers sequentially to generate multiple equivalent fractions.

Qno9. Write a fraction equivalent to \(\frac{5}{8}\) with denominator 32.
Answer:
To get a denominator of 32, divide 32 by 8, which gives 4.
Multiply both numerator and denominator by 4:
\(\frac{5 \times 4}{8 \times 4} = \frac{20}{32}\)
In simple words: Find what number multiplies the given denominator to reach the target denominator, then multiply the numerator by that same number.

Exam Tip: Setting up an equation \(\frac{5}{8} = \frac{x}{32}\) and cross-multiplying is a foolproof method.

Qno10. Which of the following are the pairs of equivalent fractions?
a) \(\frac{5}{6}\) and \(\frac{20}{24}\)
b) \(\frac{3}{8}\) and \(\frac{15}{40}\)
Answer:
a) Check by cross-multiplication or simplification:
Simplifying \(\frac{20}{24}\) by dividing numerator and denominator by 4 gives \(\frac{5}{6}\).
Since both reduce to \(\frac{5}{6}\), they are equivalent fractions.
b) Check by cross-multiplication:
\(3 \times 40 = 120\)
\(8 \times 15 = 120\)
Since the cross products are equal (\(120 = 120\)), they are equivalent fractions.
In simple words: Two fractions are equivalent if their cross-products are equal or if they simplify to the same fraction.

Exam Tip: Cross-multiplication (\(a \times d = b \times c\)) is the quickest way to test if two fractions are equivalent.