CBSE Class 5 Mathematics Mental Mathematics Worksheet Set 09

SECTION - A [MENTAL MATHS]

I. Fill in the blanks:-

Question 1.(a) A number having more than two different factors is called a _________ number.
Answer: composite
In simple words: A composite number has more than two factors, unlike a prime number which only has two factors (1 and itself).

Exam Tip: Remember that 1 is neither prime nor composite.

Question 1.(b) The largest 2 - digit prime number is _______________.
Answer: 97
In simple words: 97 is only divisible by 1 and 97, making it the highest two-digit prime number.

Exam Tip: Memorize prime numbers up to 100 to quickly solve such questions.

Question 2. Prime numbers between 80 and 90 are _________ and ________.
Answer: 83 and 89
In simple words: Between 80 and 90, only 83 and 89 have no factors other than 1 and themselves.

Exam Tip: Check divisibility by 2, 3, 5, and 7 to test primality for numbers up to 100.

Question 3. 20,000 + 4000 + 20 + 7 = ___________
Answer: 24,027
Add the place values:
\(20000 + 4000 = 24000\)
\(24000 + 20 + 7 = 24027\)
In simple words: Combine the digits according to their place values to get 24,027.

Exam Tip: Ensure all place values (like hundreds here) are accounted for with zeros if missing.

Question 4. 6087 \times 1000 = ___________
Answer: 6,087,000
In simple words: When multiplying by 1000, simply add three zeros to the right of the number.

Exam Tip: For powers of 10, shift the decimal point to the right by the number of zeros.

Question 5.(a) 2658 \div ________ = 1
Answer: 2658
In simple words: Any non-zero number divided by itself equals 1.

Question 5.(b) ________ \times (1030 \times 975) = (2460 \times 1030) \times 975
Answer: 2460
In simple words: By the associative property of multiplication, the missing factor on the left side is 2460.

Exam Tip: Look at both sides of the equation to match corresponding grouping factors.

SECTION - B [TABLES]

II. Fill in the blanks:-

Question 1. 12 \times 8 = ________
Answer: 96
In simple words: Twelve times eight is 96.

Exam Tip: Regular table practice prevents silly arithmetic errors.

Question 2. 14 \times 2 = ________
Answer: 28
In simple words: Fourteen multiplied by two gives 28.

Question 3. 8 \times 5 = _________
Answer: 40
In simple words: Eight fives are 40.

Question 4. ________ \times 6 = 42
Answer: 7
In simple words: Divide 42 by 6 to find the missing factor, which is 7.

Exam Tip: Use division to find a missing multiplier.

Question 5. ________ \times 7 = 63
Answer: 9
In simple words: Nine times seven is 63.

Exam Tip: Recall standard multiplication facts.

Question 6. 17 \times ______ = 51
Answer: 3
In simple words: Seventeen multiplied by 3 gives 51.

Exam Tip: \(17 \times 3 = (10 \times 3) + (7 \times 3) = 30 + 21 = 51\).

Question 7. 6 \times 4 = ________
Answer: 24
In simple words: Six fours are 24.

Exam Tip: Basic table recall.

Question 8. 5 \times 9 = ________
Answer: 45
In simple words: Five nines are 45.

Exam Tip: Basic table recall.

Question 9. 9 \times 8 = ________
Answer: 72
In simple words: Nine eights are 72.

Exam Tip: Basic table recall.

Question 10. 12 \times 7 = _______
Answer: 84
In simple words: Twelve sevens are 84.

Exam Tip: Basic table recall.

SECTION - C [CONCEPT]

Question III. (a) Add the following: \(\frac{3}{4} + \frac{5}{6}\)
Answer:
Find the LCM of denominators 4 and 6, which is 12.
Convert fractions to equivalent fractions with denominator 12:
\(\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}\)
\(\frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12}\)
Add the numerators:
\(\frac{9}{12} + \frac{10}{12} = \frac{9 + 10}{12} = \frac{19}{12} = 1\frac{7}{12}\)
In simple words: Make denominators equal using LCM, then add numerators.

Exam Tip: Always express improper fraction answers as mixed fractions if required.

Question III. (b) Add the following: \(\frac{4}{5} + \frac{2}{3} + \frac{1}{10}\)
Answer:
Find the LCM of denominators 5, 3, and 10, which is 30.
Convert each fraction:
\(\frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30}\)
\(\frac{2}{3} = \frac{2 \times 10}{3 \times 10} = \frac{20}{30}\)
\(\frac{1}{10} = \frac{1 \times 3}{10 \times 3} = \frac{3}{30}\)
Add the numerators:
\(\frac{24 + 20 + 3}{30} = \frac{47}{30} = 1\frac{17}{30}\)
In simple words: Find the common denominator for all three fractions and add their numerators.

Exam Tip: Double-check your LCM calculation to avoid errors.

Question III. (c) Add the following: \(2\frac{3}{8} + 2\frac{5}{16} + 2\frac{7}{24}\)
Answer:
Add whole numbers and fractions separately:
Sum of whole numbers = \(2 + 2 + 2 = 6\)
Sum of fractions = \(\frac{3}{8} + \frac{5}{16} + \frac{7}{24}\)
LCM of 8, 16, and 24 is 48.
Convert fractions:
\(\frac{3}{8} = \frac{3 \times 6}{48} = \frac{18}{48}\)
\(\frac{5}{16} = \frac{5 \times 3}{48} = \frac{15}{48}\)
\(\frac{7}{24} = \frac{7 \times 2}{48} = \frac{14}{48}\)
Add fractions: \(\frac{18 + 15 + 14}{48} = \frac{47}{48}\)
Total sum = \(6 + \frac{47}{48} = 6\frac{47}{48}\)
In simple words: Add the whole numbers first, then add the fractional parts using a common denominator.

Exam Tip: Separating whole numbers and fractions makes addition much simpler.

Question IV. Simplify: \(1\frac{5}{8} - 2\frac{2}{3} + 9\frac{7}{12}\)
Answer:
Convert all mixed fractions to improper fractions:
\(1\frac{5}{8} = \frac{13}{8}\)
\(2\frac{2}{3} = \frac{8}{3}\)
\(9\frac{7}{12} = \frac{115}{12}\)
Expression becomes: \(\frac{13}{8} - \frac{8}{3} + \frac{115}{12}\)
LCM of 8, 3, and 12 is 24.
Convert each fraction to have denominator 24:
\(\frac{13 \times 3}{8 \times 3} = \frac{39}{24}\)
\(\frac{8 \times 8}{3 \times 8} = \frac{64}{24}\)
\(\frac{115 \times 2}{12 \times 2} = \frac{230}{24}\)
Combine numerators according to signs:
\(\frac{39 - 64 + 230}{24} = \frac{-25 + 230}{24} = \frac{205}{24} = 8\frac{13}{24}\)
In simple words: Convert mixed numbers to improper fractions, find a common denominator, and combine them.

Exam Tip: Be very careful with subtraction and addition signs during combination.

Question V. (a) Subtract the following: \(\frac{4}{21} - \frac{3}{14}\)
Answer:
LCM of 21 and 14 is 42.
Convert fractions:
\(\frac{4}{21} = \frac{4 \times 2}{21 \times 2} = \frac{8}{42}\)
\(\frac{3}{14} = \frac{3 \times 3}{14 \times 3} = \frac{9}{42}\)
Subtract numerators:
\(\frac{8}{42} - \frac{9}{42} = \frac{8 - 9}{42} = -\frac{1}{42}\)
In simple words: Find the common denominator and subtract the second numerator from the first.

Question V. (b) Subtract the following: \(11\frac{1}{6} - 9\frac{7}{8}\)
Answer:
Convert mixed fractions to improper fractions:
\(11\frac{1}{6} = \frac{67}{6}\)
\(9\frac{7}{8} = \frac{79}{8}\)
LCM of 6 and 8 is 24.
Convert fractions:
\(\frac{67 \times 4}{6 \times 4} = \frac{268}{24}\)
\(\frac{79 \times 3}{8 \times 3} = \frac{237}{24}\)
Subtract numerators:
\(\frac{268 - 237}{24} = \frac{31}{24} = 1\frac{7}{24}\)
In simple words: Convert to improper fractions, find the common denominator, and subtract.

Exam Tip: Converting to improper fractions is the safest method for mixed number subtraction.

Question VI. (a) Multiply: \(4\frac{3}{8} \times 1\frac{2}{5}\)
Answer:
Convert mixed fractions to improper fractions:
\(4\frac{3}{8} = \frac{35}{8}\)
\(1\frac{2}{5} = \frac{7}{5}\)
Multiply numerators and denominators:
\(\frac{35}{8} \times \frac{7}{5}\)
Cancel out common factors (5 divides 35 seven times):
\(\frac{7}{8} \times \frac{7}{1} = \frac{49}{8} = 6\frac{1}{8}\)
In simple words: Convert to improper fractions, cross-simplify if possible, and multiply straight across.

Exam Tip: Always simplify before multiplying to keep numbers small and manageable.

Question VI. (b) Multiply: \(2\frac{3}{4} \times 4\frac{4}{5} \times 6\frac{3}{8}\)
Answer:
Convert all mixed fractions to improper fractions:
\(2\frac{3}{4} = \frac{11}{4}\)
\(4\frac{4}{5} = \frac{24}{5}\)
\(6\frac{3}{8} = \frac{51}{8}\)
Expression: \(\frac{11}{4} \times \frac{24}{5} \times \frac{51}{8}\)
Simplify across terms: \(4 \times 8 = 32\), and 24 can be simplified with denominators. Notice \(4 \times 8 = 32\), but let us cancel \(24\) with \(4\) and \(8\):
\(4 \times 8 = 32\) in denominator, and numerator has 24. \(\frac{24}{32} = \frac{3}{4}\), or directly cancel \(24\) by \(8\) to get 3, then \(3\) divided by \(4\) gives fractional parts. Let us do step by step:
\(\frac{11 \times 24 \times 51}{4 \times 5 \times 8}\)
\(24 \div 8 = 3\)
Now we have: \(\frac{11 \times 3 \times 51}{4 \times 5} = \frac{1683}{20} = 84\frac{3}{20}\)
In simple words: Convert to improper fractions, cancel common factors between numerators and denominators, then multiply the rest.

Exam Tip: Look carefully for cancellation opportunities to save calculation time.

Question VII. If a length of \(3\frac{2}{3}\) metres is cut from a wire which is \(5\frac{1}{2}\) metres long, how much of the wire is left?
Answer:
Total length of wire = \(5\frac{1}{2}\) m
Length cut = \(3\frac{2}{3}\) m
Remaining wire = \(5\frac{1}{2} - 3\frac{2}{3}\)
Convert to improper fractions:
\(5\frac{1}{2} = \frac{11}{2}\)
\(3\frac{2}{3} = \frac{11}{3}\)
LCM of 2 and 3 is 6.
\(\frac{11 \times 3}{2 \times 3} = \frac{33}{6}\)
\(\frac{11 \times 2}{3 \times 2} = \frac{22}{6}\)
Subtract: \(\frac{33}{6} - \frac{22}{6} = \frac{11}{6} = 1\frac{5}{6} \text{ metres}\)
In simple words: Subtract the cut length from the total length using fraction subtraction.

Exam Tip: Include proper units (metres) in your final answer statement.

Question VIII. A car goes \(45\frac{1}{3}\) km in 1 hour. How much distance will it cover in \(1\frac{4}{5}\) hours.
Answer:
Speed of car = \(45\frac{1}{3} \text{ km/h}\)
Time = \(1\frac{4}{5} \text{ hours}\)
Distance = Speed \(\times\) Time = \(45\frac{1}{3} \times 1\frac{4}{5}\)
Convert mixed fractions to improper fractions:
\(45\frac{1}{3} = \frac{136}{3}\)
\(1\frac{4}{5} = \frac{9}{5}\)
Multiply: \(\frac{136}{3} \times \frac{9}{5}\)
Cancel 9 and 3 (9 divided by 3 is 3):
\(\frac{136 \times 3}{5} = \frac{408}{5} = 81\frac{3}{5} \text{ km}\)
In simple words: Multiply the speed per hour by the total time to find the total distance covered.

Exam Tip: Distance equals speed multiplied by time. Always write the formula first.