CBSE Class 5 Mathematics Mental Mathematics Worksheet

Question 1. \(5 \times 10,000 + 4 \times 100 + 8 =\) ____________
Answer: 50,408
Calculation:
\(5 \times 10,000 = 50,000\)
\(4 \times 100 = 400\)
\(50,000 + 400 + 8 = 50,408\)
In simple words: Multiply each part and add them together to get the final number.
Exam Tip: Be careful with place values; missing place values must be filled with zeros.

Question 2. Insert \(>, <\) or \(=\) sign: Triple of 30 ____________ Half of 90
Answer: \(>\)
Calculation:
Triple of 30 = \(30 \times 3 = 90\)
Half of 90 = \(90 \div 2 = 45\)
Since 90 is greater than 45, we use \(>\).
In simple words: Compare 90 and 45 after calculating both sides.

Exam Tip: Always compute both expressions completely before comparing them.

Question 3. The sum of two numbers is 7000. If one of the number is 5000 then the other number is _____________.
Answer: 2000
Calculation:
Other number = Total sum - Given number
\(7000 - 5000 = 2000\)
In simple words: Subtract the known part from the total sum to find the missing part.

Exam Tip: Use subtraction to find a missing addend when the sum is given.

Question 4. The product of two odd numbers is always an ____________ number.
Answer: odd
Calculation:
Example: \(3 \times 5 = 15\) (odd)
Example: \(7 \times 9 = 63\) (odd)
In simple words: Multiplying any two odd numbers always results in an odd number.

Question 5. \(764 + 1236 =\) ____________ hundreds.
Answer: 20
Calculation:
\(764 + 1236 = 2000\)
Convert to hundreds: \(2000 \div 100 = 20\)
In simple words: First add the two numbers, then divide by 100 to find how many hundreds there are.

Exam Tip: Read the unit specified at the end of the blank carefully.

Question 6. Complete the pattern: 1100, 1090, _______ ________ _________
Answer: 1080, 1070, 1060
Calculation:
The difference between consecutive terms is \(1090 - 1100 = -10\).
Next terms: \(1090 - 10 = 1080\), \(1080 - 10 = 1070\), \(1070 - 10 = 1060\).
In simple words: Subtract 10 from each number to get the next number in the pattern.

Exam Tip: Always find the rule or common difference by checking the first two terms.

Question 7. Write the fraction for the shaded portion _________________
Answer: \(\frac{2}{4}\) or \(\frac{1}{2}\)
Calculation:
The figure is divided into 4 equal triangles, out of which 2 are shaded.
Fraction = \(\frac{2}{4} = \frac{1}{2}\)
In simple words: Count the shaded parts and divide by the total number of equal parts.

Exam Tip: Always reduce fractions to their simplest form if required.

Question 8. Shade \(\frac{3}{5}\) of the given figure
Answer: Shade 3 out of the 5 given equal rectangles.
Calculation:
Total equal parts = 5
Parts to shade = 3
In simple words: Color 3 boxes out of the 5 boxes available.

Exam Tip: Ensure the total parts are equal before shading the required fraction.

Question 9. There are ___________ centimeters in 6 meters.
Answer: 600
Calculation:
\(1 \text{ meter} = 100 \text{ centimeters}\)
\(6 \text{ meters} = 6 \times 100 = 600 \text{ cm}\)
In simple words: Multiply the number of meters by 100 to convert to centimeters.

Exam Tip: Memorize standard metric conversion factors.

Question 10. 7700 is between ______________ and ______________.
Answer: 7000 and 8000 (or 7600 and 7800, etc.)
Calculation:
7700 lies between the thousands 7000 and 8000.
In simple words: State the lower and upper bounds between which 7700 lies.

Exam Tip: Nearest thousands are usually expected unless specified otherwise.

Sub : Mental Maths Sheet - 24

Question 1. I am smaller than 10 but greater than 6. I am an even number. _________________________
Answer: 8
Calculation:
Numbers between 6 and 10: 7, 8, 9.
Even number among them = 8.
In simple words: Find the even number that sits between 6 and 10.

Exam Tip: List the numbers in the given range and check the condition.

Question 2. I am the smallest 4 - digit number that remains the same even when written in the reverse order. What number am I? _________________________
Answer: 1001
Calculation:
Smallest 4-digit number starts with 1. For it to read the same forwards and backwards (palindromic), the last digit must also be 1, and the middle digits must be 0s, giving 1001.
In simple words: A palindrome number reads the same from left to right and right to left.

Exam Tip: Palindromic numbers have symmetric digits.

Question 3. I am between 375 and 380. I am double of 189. What number am I? _________________________
Answer: 378
Calculation:
Double of 189 = \(189 \times 2 = 378\)
Check: 378 is between 375 and 380.
In simple words: Multiply 189 by 2 and verify it falls in the given range.

Exam Tip: Always cross-check all conditions given in the puzzle.

Question 4. Take the number 14, then subtract 4, and divide by 2 get me. I am a 1 - digit number. What number am I? _________________________
Answer: 5
Calculation:
Subtract 4 from 14: \(14 - 4 = 10\)
Divide by 2: \(10 \div 2 = 5\)
In simple words: Follow the operations step by step in order.

Exam Tip: Follow BODMAS/PEMDAS rule for order of operations.

Question 5. I am greater than 100 but smaller than 110. I am a product. One of my factor is the largest 1 - digit number. What number am I? _________________________
Answer: 108
Calculation:
Largest 1-digit number = 9
Multiples of 9 between 100 and 110: \(9 \times 12 = 108\).
In simple words: Find a multiple of 9 that lies between 100 and 110.

Exam Tip: Know your multiplication tables up to 10 and beyond.

Sub : Mental Maths Sheet - 25

Question 1. Reciprocal of \(4 \frac{1}{2}\) is ________________.
Answer: \(\frac{2}{9}\)
Calculation:
Convert mixed fraction to improper fraction: \(4 \frac{1}{2} = \frac{9}{2}\)
Reciprocal of \(\frac{9}{2} = \frac{2}{9}\)
In simple words: Flip the improper fraction upside down to find its reciprocal.

Exam Tip: Always convert mixed numbers to improper fractions before finding reciprocals.

Question 2. \(3 \frac{2}{5} \div 3 \frac{2}{5} =\) ______________.
Answer: 1
Calculation:
Any non-zero number divided by itself is always 1.
\(\frac{17}{5} \div \frac{17}{5} = \frac{17}{5} \times \frac{5}{17} = 1\)
In simple words: Dividing any number by the exact same number always gives 1.

Question 3. The reciprocal of a whole number is always a _____________ fraction.
Answer: unit
Calculation:
Reciprocal of a whole number \(n\) (where \(n > 1\)) is \(\frac{1}{n}\), which is a proper fraction with numerator 1 (unit fraction).
In simple words: A fraction with a numerator of 1 is called a unit fraction.

Exam Tip: Remember definitions of different types of fractions.

Question 4. \(20 + 8 + \frac{4}{10} + \frac{6}{100} =\) ______________.
Answer: 28.46
Calculation:
\(20 + 8 = 28\)
\(\frac{4}{10} = 0.4\)
\(\frac{6}{100} = 0.06\)
Total = \(28 + 0.4 + 0.06 = 28.46\)
In simple words: Combine the whole numbers and decimal place values into standard decimal form.

Exam Tip: Align decimal points properly when adding decimal expansions.

Question 5. \(72.12 \times 100 =\) _______________.
Answer: 7212
Calculation:
When multiplying by 100, move the decimal point two places to the right.
\(72.12 \times 100 = 7212\)
In simple words: Shift the decimal point two places to the right for every two zeros in 100.

Exam Tip: Multiplying by powers of 10 shifts the decimal point to the right.

Question 6. The decimal form of \(\frac{239}{10}\) is ______________.
Answer: 23.9
Calculation:
Divide by 10 by moving the decimal point one place to the left.
\(239 \div 10 = 23.9\)
In simple words: Shift the decimal point one place to the left when dividing by 10.

Exam Tip: Count the zeros in the denominator to know how many places to shift the decimal.

Question 7. The product of 42.7 and 9.248 will have _____________ decimal places.
Answer: 4
Calculation:
42.7 has 1 decimal place.
9.248 has 3 decimal places.
Total decimal places = \(1 + 3 = 4\).
In simple words: Add the number of decimal places of both numbers being multiplied.

Exam Tip: You do not need to multiply the whole numbers to find the number of decimal places in the product.

Question 8. 1.23 expressed as a mixed number is __________________.
Answer: \(1 \frac{23}{100}\)
Calculation:
\(1.23 = 1 + \frac{23}{100} = 1 \frac{23}{100}\)
In simple words: Write the whole number part and convert the decimal part into a fraction over 100.

Exam Tip: Two decimal places mean the denominator of the fraction part is 100.

Question 9. 81508 rounded off to nearest thousand is _______________.
Answer: 82,000
Calculation:
Look at the hundreds digit of 81,508, which is 5.
Since it is 5 or more, round up the thousands digit (1 becomes 2).
Result = 82,000.
In simple words: If the hundreds digit is 5 or more, round up to the next thousand.

Exam Tip: Check the digit to the right of the place value you are rounding to.

Question 10. A ray has no __________________ length.
Answer: definite (or fixed / end)
Calculation:
A ray has one starting point and extends indefinitely in one direction, so it has no definite length.
In simple words: A ray goes on forever in one direction, meaning it has no fixed end or length.

Question 1. The number which is only whole number but not a natural number is _________________
Answer: 0
Calculation:
Natural numbers start from 1, 2, 3...
Whole numbers start from 0, 1, 2, 3...
Therefore, 0 is a whole number but not a natural number.
In simple words: Zero is included in whole numbers but not in natural numbers.

Exam Tip: Natural numbers are counting numbers starting from 1.

Question 2. The HCF of two even consecutive numbers is _______________.
Answer: 2
Calculation:
Example: Consecutive even numbers 4 and 6.
Factors of 4: 1, 2, 4
Factors of 6: 1, 2, 3, 6
Highest Common Factor (HCF) = 2.
In simple words: Any two consecutive even numbers are always divisible by 2.

Exam Tip: Consecutive even numbers always share 2 as their greatest common factor.

Question 3. The smallest factor of 15 is ________________.
Answer: 1
Calculation:
Factors of 15 are 1, 3, 5, 15. The smallest factor of any number is always 1.
In simple words: 1 is a universal factor for every number.

Exam Tip: 1 is the smallest factor and the number itself is the greatest factor of any number.

Question 4. The sum of smallest natural number and smallest whole number is ___________________
Answer: 1
Calculation:
Smallest natural number = 1
Smallest whole number = 0
Sum = \(1 + 0 = 1\)
In simple words: Add 1 (smallest natural number) and 0 (smallest whole number).

Exam Tip: Do not confuse the starting numbers of natural and whole number sets.

Question 5. \((18 + 9) + 4 = 18 + (9 + \_\_\_\_\_\_)\)
Answer: 4
Calculation:
This is based on the associative property of addition: \((a + b) + c = a + (b + c)\).
Therefore, the missing number is 4.
In simple words: Changing the grouping of numbers in addition does not change the result.

Exam Tip: Recognize properties of operations like associative and commutative properties.

Question 6. \(\frac{3}{11} \times \_\_\_\_\_\_\_\_\_\_ = 1\)
Answer: \(\frac{11}{3}\)
Calculation:
A number multiplied by its reciprocal equals 1.
Reciprocal of \(\frac{3}{11}\) is \(\frac{11}{3}\).
In simple words: Multiply a fraction by its flipped version to get 1.

Exam Tip: The product of a number and its multiplicative inverse is always 1.

Question 7. The numeral for twenty five million eight is _________________.
Answer: 25,000,008
Calculation:
Twenty five million = 25,000,000
Eight = 8
Total = 25,000,008
In simple words: Write 25 in the millions period and 8 in the ones period, filling zeros in between.

Exam Tip: In the international system, periods have three places each (ones, thousands, millions).

Question 8. \(\frac{3}{7}\) of a week is ______________ days.
Answer: 3
Calculation:
1 week = 7 days.
\(\frac{3}{7} \times 7 = 3 \text{ days}\)
In simple words: Multiply 7 days by 3/7.

Exam Tip: Convert units first if necessary before calculating fractions of quantities.

Question 9. \(6.25 \times 100 = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\).
Answer: 625
Calculation:
Shift the decimal point two places to the right: \(6.25 \times 100 = 625\).
In simple words: Multiply by 100 by moving the decimal point two places to the right.

Exam Tip: Moving the decimal point 2 places removes the decimal for 2 decimal places.

Question 10. \(4638 \times 25 \times 4 = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\).
Answer: 463,800
Calculation:
Use associative property: \(25 \times 4 = 100\)
\(4638 \times 100 = 463,800\)
In simple words: Group 25 and 4 first to make multiplication easier (25 x 4 = 100).

Question 1. Reciprocal of \(\frac{5}{3}\) is ______________.
Answer: \(\frac{3}{5}\)
Calculation:
Flip the numerator and denominator: Reciprocal of \(\frac{5}{3}\) is \(\frac{3}{5}\).
In simple words: Invert the fraction to get its reciprocal.

Exam Tip: The reciprocal of a proper fraction is an improper fraction and vice versa.

Question 2. 1 Kg = _______________ g.
Answer: 1000
Calculation:
\(1 \text{ kilogram} = 1000 \text{ grams}\).
In simple words: Standard conversion from kg to grams is multiplying by 1000.

Exam Tip: Remember metric prefixes: kilo- means 1000 times.

Question 3. A number which has only two factors, one and number itself, is called a ______________ number.
Answer: prime
Calculation:
By definition, a prime number has exactly two distinct positive divisors: 1 and itself.
In simple words: A prime number can only be divided evenly by 1 and itself.

Exam Tip: 1 is neither prime nor composite.

Question 4. Largest 2 - digit number divisible by 3 is _________________.
Answer: 99
Calculation:
The largest 2-digit number is 99. The sum of its digits is \(9 + 9 = 18\), which is divisible by 3, so 99 is divisible by 3.
In simple words: Check if 99 can be divided by 3 (sum of digits rule).

Exam Tip: A number is divisible by 3 if the sum of its digits is a multiple of 3.

Question 5. There are _______________ halves in \(12 \frac{1}{2}\)
Answer: 25
Calculation:
Convert mixed number to improper fraction: \(12 \frac{1}{2} = \frac{25}{2}\)
Number of halves = \(\frac{25}{2} \div \frac{1}{2} = 25\)
In simple words: Multiply the whole number by 2 and add the numerator, or divide the number by 1/2.

Exam Tip: Each whole has 2 halves.

Question 6. \(20 + \_\_\_\_\_\_ + \frac{3}{10} + \frac{6}{100} = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\)
Answer: 0 (for the blank) / 20.36 (if evaluating full expression)
Calculation:
Looking at standard expanded notation missing part: 0 (since units place is missing or 0).
Full number = \(20 + 0 + 0.3 + 0.06 = 20.36\).
In simple words: Fill in the missing place value term which is 0 for the ones place.

Exam Tip: Check standard place value expansions carefully.

Question 7. The decimal form of \(\frac{273}{10}\) is ___________________.
Answer: 27.3
Calculation:
\(273 \div 10 = 27.3\)
In simple words: Shift the decimal point one place to the left.

Exam Tip: One zero in the denominator moves the decimal point one place left.

Question 8. The place value of 8 in 9.38 is ___________________.
Answer: 0.08 (or \(\frac{8}{100}\) or hundredths)
Calculation:
In 9.38, 8 is in the hundredths place.
Place value = \(0.08\) or \(\frac{8}{100}\).
In simple words: Identify the position of 8 after the decimal point.

Exam Tip: The first digit after the decimal is tenths, the second is hundredths.

Question 9. The decimal number four-thousandths has ___________ decimal places.
Answer: 3
Calculation:
Four-thousandths is written as \(0.004\), which has 3 decimal places.
In simple words: Thousandths place is three steps to the right of the decimal point.

Exam Tip: Tenths = 1 place, Hundredths = 2 places, Thousandths = 3 places.

Question 10. \(4000 + 800 + 30 + 7 = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\)
Answer: 4837
Calculation:
Combine all place values: \(4000 + 800 + 30 + 7 = 4837\).
In simple words: Add all the numbers together to form the standard numeral.

Exam Tip: Standard form is written by combining the digits at each place value.

Sub : Mental Maths Sheet - 28

Question 1. A quadrilateral has ________________ sides and ___________ angles.
Answer: 4, 4
Calculation:
A quadrilateral is a four-sided polygon, hence it has 4 sides and 4 angles.
In simple words: "Quad" means four, so it has 4 sides and 4 corners/angles.

Exam Tip: Polygons are named after the number of their sides.

Question 2. The sum of all angles of a triangle is ______________.
Answer: 180 degrees
Calculation:
Angle sum property of a triangle states that the interior angles always add up to 180 degrees.
In simple words: The three angles of any triangle always total 180 degrees.

Exam Tip: Remember angle sum properties for triangles (180 degrees) and quadrilaterals (360 degrees).

Question 3. The measure of a right angle is __________________.
Answer: 90 degrees
Calculation:
A right angle measures exactly 90 degrees.
In simple words: A square corner measures 90 degrees.

Exam Tip: Right angles form an "L" shape.

Question 4. A line segment PQ is written as ___________________.
Answer: \(\overline{PQ}\) (or PQ with a bar on top)
Calculation:
A line segment with endpoints P and Q is denoted symbolically with a bar over the letters: \(\overline{PQ}\).
In simple words: Put a small horizontal line above PQ to show it is a line segment.

Exam Tip: Lines use \(\overleftrightarrow{PQ}\), rays use \(\overrightarrow{PQ}\), and line segments use \(\overline{PQ}\).

Question 5. A line has __________________ length.
Answer: infinite (or no definite / unlimited)
Calculation:
A line extends endlessly in both directions, so it has no definite or finite length.
In simple words: A line goes on forever in both directions without stopping.

Exam Tip: Lines cannot be measured because they have no endpoints.

Question 6. \(607.3 \times 100 = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\)
Answer: 60,730
Calculation:
Shift decimal two places to the right: \(607.3 \times 100 = 60730\).
In simple words: Move the decimal point two places to the right, adding a zero as needed.

Exam Tip: When shifting past the digits, add placeholder zeros.

Question 7. The largest chord of the circle is _________________.
Answer: diameter
Calculation:
The diameter passes through the center of the circle and is the longest possible chord.
In simple words: The straight line passing right through the center is the longest chord.

Exam Tip: The diameter is twice the length of the radius.

Question 8. No. of lines drawn passing through two given points is ______________.
Answer: 1
Calculation:
Through any two distinct points, exactly one straight line can be drawn.
In simple words: Only one straight line can connect two points.

Exam Tip: This is a fundamental axiom of geometry.

Question 9. The line joining any two points on the circumference of circle is called __________________
Answer: chord
Calculation:
A line segment connecting any two points on a circle's boundary is a chord.
In simple words: A line connecting two points on the circle edge is a chord.

Exam Tip: The diameter is a special chord that passes through the center.

Question 10. A number is divisible by 6 if it is divisible by _______ and _______ both.
Answer: 2, 3
Calculation:
Since \(2 \times 3 = 6\), a number must be divisible by both 2 and 3 to be divisible by 6.
In simple words: A number is divisible by 6 if it is even and the sum of its digits is divisible by 3.

Exam Tip: Check divisibility rules for prime factors of composite numbers.

Sub : Mental Maths Sheet - 29

Question 1. __________________ is and the name for multiplicative inverse.
Answer: Reciprocal
Calculation:
The multiplicative inverse of a number is also called its reciprocal.
In simple words: Reciprocal is another name for multiplicative inverse.

Exam Tip: Know both mathematical terms for flipping a number.

Question 2. __________________ is an example of co-prime numbers.
Answer: 2 and 3 (or any pair with HCF = 1)
Calculation:
Co-prime numbers are numbers that have only 1 as their common factor (HCF is 1). Example: 2 and 3.
In simple words: Numbers that share no common factors other than 1 are co-prime.

Exam Tip: Consecutive numbers are always co-prime.

Question 3. The multiplicative inverse of \(\frac{3}{4}\) is ________________.
Answer: \(\frac{4}{3}\)
Calculation:
Multiplicative inverse means the reciprocal, so \(\frac{3}{4}\) becomes \(\frac{4}{3}\).
In simple words: Flip the fraction upside down.

Question 4. The smallest composite number of two digits is ______________.
Answer: 10
Calculation:
Two-digit numbers start from 10. Factors of 10 are 1, 2, 5, 10 (more than 2 factors), making it composite.
In simple words: The first two-digit number has more than two factors.

Exam Tip: Smallest composite number overall is 4, but smallest 2-digit composite number is 10.

Question 5. _______________ is a multiple of both 7 and 13.
Answer: 91 (or any multiple of 91 like 182, etc.)
Calculation:
Since 7 and 13 are prime numbers, their least common multiple is \(7 \times 13 = 91\).
In simple words: Multiply 7 and 13 to find their common multiple.

Exam Tip: LCM of two co-prime numbers is their product.

Question 6. The lowest term for \(\frac{21}{45}\) is ________________.
Answer: \(\frac{7}{15}\)
Calculation:
Divide numerator and denominator by their HCF (which is 3):
\(21 \div 3 = 7\)
\(45 \div 3 = 15\)
Result = \(\frac{7}{15}\).
In simple words: Divide top and bottom by their common factor 3.

Exam Tip: Always reduce fractions by dividing both terms by their HCF.

Question 7. The number 590 less than 5900 is ___________________.
Answer: 5310
Calculation:
\(5900 - 590 = 5310\)
In simple words: Subtract 590 from 5900.

Question 8. Adding one-fifth to three-fifths gives _________________.
Answer: four-fifths (or \(\frac{4}{5}\)
Calculation:
\(\frac{1}{5} + \frac{3}{5} = \frac{4}{5}\)
In simple words: Add the numerators when denominators are the same.

Exam Tip: Like fractions are added by keeping the denominator same and adding numerators.

Question 9. \(125 \times 6934 \times 8 = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\)
Answer: 6,934,000
Calculation:
Group 125 and 8: \(125 \times 8 = 1000\)
\(6934 \times 1000 = 6,934,000\)
In simple words: Multiply 125 and 8 first to get 1000, then multiply by 6934.

Exam Tip: Memorize standard pairings like \(125 \times 8 = 1000\) and \(50 \times 2 = 100\).

Question 10. An equivalent fraction for \(\frac{3}{7}\) is ___________________.
Answer: \(\frac{6}{14}\) (or any correct equivalent fraction like \(\frac{9}{21}, \frac{12}{28}\), etc.)
Calculation:
Multiply numerator and denominator by 2: \(\frac{3 \times 2}{7 \times 2} = \frac{6}{14}\).
In simple words: Multiply both top and bottom numbers by the same number.

Exam Tip: Equivalent fractions are formed by multiplying or dividing numerator and denominator by the same non-zero number.

Sub : Mental Maths Sheet - 30

Question 1. 5 days = ________________ hours.
Answer: 120
Calculation:
1 day = 24 hours
5 days = \(5 \times 24 = 120 \text{ hours}\)
In simple words: Multiply the number of days by 24 hours.

Exam Tip: Time conversion: 1 day = 24 hours, 1 hour = 60 minutes.

Question 2. 1 Km = ____________________ metres.
Answer: 1000
Calculation:
1 kilometer = 1000 meters.
In simple words: Kilo means 1000, so 1 km equals 1000 meters.

Exam Tip: Standard metric conversions should be memorized.

Question 3. \(\frac{3}{7}\) and \(\frac{4}{7}\) are _______________ fractions.
Answer: like
Calculation:
Fractions with the same denominator are called like fractions.
In simple words: Fractions having identical denominators are like fractions.

Exam Tip: Unlike fractions have different denominators.

Question 4. The decimal number for \(\frac{9}{10} + \frac{3}{1000}\) is ____________________.
Answer: 0.903
Calculation:
\(\frac{9}{10} = 0.9\) (tenths place)
\(\frac{3}{1000} = 0.003\) (thousandths place, hundredths place is 0)
Total = \(0.9 + 0.003 = 0.903\)
In simple words: Place 9 in the tenths place and 3 in the thousandths place, filling the missing hundredths place with 0.

Exam Tip: Watch out for missing place values like hundredths in this case.

Question 5. Seventy hundredths is written as ___________________.
Answer: 0.70 (or 0.7)
Calculation:
Seventy hundredths = \(\frac{70}{100} = 0.70\).
In simple words: Write 70 in the hundredths decimal position.

Exam Tip: "Hundredths" means two decimal places.

Question 6. \(30,000 + 4000 + 70 + 9 = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\)
Answer: 34,079
Calculation:
Combine place values: tens-thousands (3), thousands (4), tens (7), ones (9). Hundreds place is 0.
Total = 34,079.
In simple words: Add the expanded numbers, noting the missing hundreds place is 0.

Question 7. \(4927 \times 1000 = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\)
Answer: 4,927,000
Calculation:
Attach three zeros to the end of 4927 when multiplying by 1000.
In simple words: Add three zeros to the right of the number.

Exam Tip: Multiplying by 1000 shifts all digits three places to the left.

Question 8. 3572 rounded to nearest thousand is ___________________.
Answer: 4000
Calculation:
Hundreds digit of 3572 is 5. Since it is 5 or more, round up the thousands digit (3 becomes 4).
Result = 4000.
In simple words: Since the hundreds digit is 5, round up to 4000.

Exam Tip: 5 or more rounds up; less than 5 rounds down.

Question 9. \(8 \times 3273 \times 125 = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\)
Answer: 3,273,000
Calculation:
Group 8 and 125: \(8 \times 125 = 1000\)
\(3273 \times 1000 = 3,273,000\)
In simple words: Multiply 8 and 125 first to get 1000, then multiply by 3273.

Exam Tip: Rearrange factors using commutative and associative properties for easier calculation.

Question 10. Prime number between 90 and 100 is _______________________.
Answer: 97
Calculation:
Numbers between 90 and 100: 91 (\(7 \times 13\)), 92, 93 (\(3 \times 31\)), 94, 95, 96, 97 (prime), 98, 99 (\(9 \times 11\)).
Only 97 is prime.
In simple words: Check numbers in the nineties; 97 has no factors other than 1 and itself.

Exam Tip: Memorize prime numbers up to 100.

Sub : Maths Revision Sheet (FA3)

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
Calculation:
Numbers with more than two factors are composite numbers.
In simple words: Composite numbers can be divided by numbers other than 1 and themselves.

Exam Tip: Prime numbers have exactly 2 factors; composite numbers have more than 2.

Question 1. (b) The largest 2 - digit prime number is _______________.
Answer: 97
Calculation:
99 is composite, 98 is composite, 97 is prime.
In simple words: 97 is the highest two-digit prime number.

Exam Tip: Remember key prime numbers near the tens boundaries.

Question 2. Prime numbers between 80 and 90 are _________ and ________.
Answer: 83, 89
Calculation:
Checking numbers: 81 (composite), 83 (prime), 85 (composite), 87 (composite), 89 (prime).
In simple words: Only 83 and 89 have no factors other than 1 and themselves in that range.

Exam Tip: Check divisibility by 3 for numbers ending in 7 or 9 (e.g., 87 is divisible by 3).

Question 3. \(20,000 + 4000 + 20 + 7 = \_\_\_\_\_\_\_\_\_\_\_\)
Answer: 24,027
Calculation:
Ten-thousands (2), thousands (4), hundreds (0), tens (2), ones (7).
Total = 24,027.
In simple words: Combine place values, placing 0 in the missing hundreds position.

Exam Tip: Always verify every place value from highest to lowest.

Question 4. \(6087 \times 1000 = \_\_\_\_\_\_\_\_\_\_\_\)
Answer: 6,087,000
Calculation:
Append three zeros to 6087.
In simple words: Add three zeros to the end when multiplying by 1000.

Exam Tip: Powers of 10 add as many zeros to the right of the whole number.

Question 5. (a) \(2658 \div \_\_\_\_\_\_\_\_ = 1\)
Answer: 2658
Calculation:
Any number divided by itself equals 1.
In simple words: A number divided by itself gives 1.

Exam Tip: Fundamental property of division: \(x \div x = 1\) (for \(x \neq 0\)).

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

In simple words: Match both sides of the multiplication equation.

Question 1. \(12 \times 8 = \_\_\_\_\_\_\_\_\)
Answer: 96
Calculation: \(12 \times 8 = 96\)
In simple words: Basic multiplication table fact.
Exam Tip: Learn tables up to 20 thoroughly.

Question 2. \(14 \times 2 = \_\_\_\_\_\_\_\_\)
Answer: 28
Calculation: \(14 \times 2 = 28\)
In simple words: Double of 14 is 28.

Exam Tip: Multiplication by 2 is equivalent to adding the number to itself.

Question 3. \(8 \times 5 = \_\_\_\_\_\_\_\_\)
Answer: 40
Calculation: \(8 \times 5 = 40\)
In simple words: Standard table product.

Exam Tip: Quick recall of 5s and 10s tables saves time.

Question 4. \(\_\_\_\_\_\_\_\_ \times 6 = 42\)
Answer: 7
Calculation: \(42 \div 6 = 7\)
In simple words: Find what number multiplied by 6 gives 42.

Exam Tip: Use division to find a missing factor in multiplication equations.

Question 5. \(\_\_\_\_\_\_\_\_ \times 7 = 63\)
Answer: 9
Calculation: \(63 \div 7 = 9\)
In simple words: 9 times 7 is 63.

Question 6. \(17 \times \_\_\_\_\_\_\_\_ = 51\)
Answer: 3
Calculation: \(51 \div 17 = 3\)
In simple words: 17 multiplied by 3 equals 51.

Exam Tip: Check units digit: \(7 \times 3 = 21\), ending in 1.

Question 7. \(6 \times 4 = \_\_\_\_\_\_\_\_\)
Answer: 24
Calculation: \(6 \times 4 = 24\)
In simple words: Basic table fact.

Exam Tip: Regular practice ensures error-free table recall.

Question 8. \(5 \times 9 = \_\_\_\_\_\_\_\_\)
Answer: 45
Calculation: \(5 \times 9 = 45\)
In simple words: 5 times 9 is 45.

Exam Tip: Multiplication is commutative, so \(9 \times 5 = 5 \times 9\).

Question 9. \(9 \times 8 = \_\_\_\_\_\_\_\_\)
Answer: 72
Calculation: \(9 \times 8 = 72\)
In simple words: Standard multiplication fact.

Exam Tip: Memorize tricky tables like 7, 8, and 9 thoroughly.

Question 10. \(12 \times 7 = \_\_\_\_\_\_\_\_\)
Answer: 84
Calculation: \(12 \times 7 = 84\)
In simple words: 12 times 7 equals 84.

Exam Tip: Keep revising tables weekly.

SECTION - C [CONCEPT]

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

Exam Tip: Always find the LCM of denominators before adding or subtracting unlike fractions.

Question III. Add the following:- (b) \(\frac{4}{5} + \frac{2}{3} + \frac{1}{10}\)
Answer: \(\frac{47}{30}\) or \(1 \frac{17}{30}\)
Calculation:
LCM of 5, 3, and 10 is 30.
\(\frac{4}{5} = \frac{4 \times 6}{5 \times 6} = \frac{24}{30}\)
\(\frac{2}{3} = \frac{2 \times 10}{3 \times 10} = \frac{20}{30}\)
\(\frac{1}{10} = \frac{1 \times 3}{10 \times 3} = \frac{3}{30}\)
\(\frac{24 + 20 + 3}{30} = \frac{47}{30} = 1 \frac{17}{30}\)
In simple words: Convert all fractions to have a common denominator of 30, then add their numerators.

Exam Tip: For three or more fractions, find the LCM of all denominators together.

Question III. Add the following:- (c) \(2\frac{3}{8} + 2\frac{5}{16} + 2\frac{7}{24}\)
Answer: \(7 \frac{29}{48}\)
Calculation:
Add whole numbers: \(2 + 2 + 2 = 6\)
Add fractional parts: \(\frac{3}{8} + \frac{5}{16} + \frac{7}{24}\)
LCM of 8, 16, and 24 is 48.
\(\frac{3}{8} = \frac{3 \times 6}{48} = \frac{18}{48}\)
\(\frac{5}{16} = \frac{5 \times 3}{48} = \frac{15}{48}\)
\(\frac{7}{24} = \frac{7 \times 2}{48} = \frac{14}{48}\)
Sum of fractions = \(\frac{18 + 15 + 14}{48} = \frac{47}{48}\)
Total = \(6 + \frac{47}{48} = 6 \frac{47}{48}\) (Wait, let's re-verify source OCR: \(2\frac{3}{8} + 2\frac{5}{16} + 2\frac{7}{24}\) -> sum of whole numbers is 6, total = \(6 \frac{47}{48}\)).
In simple words: Add the whole numbers separately and the fractions separately using a common denominator.

Exam Tip: Separating whole numbers and fractions makes mixed number addition much easier.

Question IV. Simplify:- \(1\frac{5}{8} - 2\frac{2}{3} + 9\frac{7}{12}\)
Answer: \(8 \frac{13}{24}\)
Calculation:
Convert mixed numbers 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: \(\frac{13}{8} - \frac{8}{3} + \frac{115}{12}\)
LCM of 8, 3, and 12 is 24.
\(\frac{13 \times 3}{24} - \frac{8 \times 8}{24} + \frac{115 \times 2}{24} = \frac{39 - 64 + 230}{24}\)
\(= \frac{-25 + 230}{24} = \frac{205}{24} = 8 \frac{13}{24}\)
In simple words: Convert to improper fractions, find the common denominator, and combine numerators.

Exam Tip: Be very careful with signs when combining mixed operations with fractions.

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

Exam Tip: Pay attention to the order of numbers in subtraction.

Question V. Subtract the following:- (b) \(11\frac{1}{6} + 9\frac{7}{8}\) (Note: Source text lists under Subtraction section, let's compute sum or difference as printed)
Answer: \(21 \frac{13}{24}\)
Calculation:
Add whole numbers: \(11 + 9 = 20\)
Add fractions: \(\frac{1}{6} + \frac{7}{8}\)
LCM of 6 and 8 is 24.
\(\frac{1 \times 4}{24} + \frac{7 \times 3}{24} = \frac{4 + 21}{24} = \frac{25}{24} = 1 \frac{1}{24}\)
Total = \(20 + 1 \frac{1}{24} = 21 \frac{1}{24}\)
In simple words: Combine whole numbers and add fractional parts using a common denominator.

Exam Tip: If the fraction sum is improper, convert it to a mixed number and add the whole number part to the sum.

Question VI. Multiply: (a) \(4\frac{3}{8} \times 1\frac{2}{5}\)
Answer: \(\frac{245}{40} = \frac{49}{8} = 6 \frac{1}{8}\)
Calculation:
Convert to improper fractions:
\(4\frac{3}{8} = \frac{35}{8}\)
\(1\frac{2}{5} = \frac{7}{5}\)
Multiply: \(\frac{35}{8} \times \frac{7}{5} = \frac{7 \times 7}{8 \times 1} = \frac{49}{8} = 6 \frac{1}{8}\)
In simple words: Convert mixed numbers to improper fractions, simplify diagonally if possible, and multiply.

Exam Tip: Always cancel common factors between numerators and denominators before multiplying.

Question VI. Multiply: (b) \(2\frac{3}{4} \times 4\frac{4}{5} \times 6\frac{3}{8}\)
Answer: \(\frac{1239}{8} = 154 \frac{7}{8}\)
Calculation:
Convert to improper fractions:
\(2\frac{3}{4} = \frac{11}{4}\)
\(4\frac{4}{5} = \frac{24}{5}\)
\(6\frac{3}{8} = \frac{51}{8}\)
Multiply: \(\frac{11}{4} \times \frac{24}{5} \times \frac{51}{8}\)
Cancel 24 in numerator with \(4 \times 8 = 32\) or simplify \(\frac{24}{4} = 6\):
\(\frac{11 \times 6 \times 51}{5 \times 8} = \frac{3366}{40} = \frac{1683}{20} = 84.15 = 84 \frac{3}{20}\)
In simple words: Convert all to improper fractions and multiply numerators together and denominators together.

Exam Tip: Cancel terms across fractions to keep numbers small during multiplication.

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: \(1 \frac{5}{6}\) metres
Calculation:
Total length = \(5\frac{1}{2} = \frac{11}{2}\) metres
Length cut = \(3\frac{2}{3} = \frac{11}{3}\) metres
Wire left = \(\frac{11}{2} - \frac{11}{3}\)
LCM of 2 and 3 is 6.
\(\frac{11 \times 3}{6} - \frac{11 \times 2}{6} = \frac{33 - 22}{6} = \frac{11}{6} = 1 \frac{5}{6} \text{ metres}\)
In simple words: Subtract the length of wire cut from the total length.

Exam Tip: Use subtraction word problem strategies when finding remaining quantities.

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: \(81 \frac{3}{5}\) km (or 81.6 km)
Calculation:
Speed = \(45\frac{1}{3} = \frac{136}{3}\) km/h
Time = \(1\frac{4}{5} = \frac{9}{5}\) hours
Distance = Speed \(\times\) Time = \(\frac{136}{3} \times \frac{9}{5}\)
Simplify \(\frac{9}{3} = 3\):
\(\frac{136 \times 3}{5} = \frac{408}{5} = 81 \frac{3}{5} \text{ km}\)
In simple words: Multiply speed by time to find the total distance covered.

Exam Tip: Distance equals speed multiplied by time formula \((D = S \times T)\).