CBSE Class 7 Mathematics Working with Fractions MCQs Set J

Question. Maria bought 8 m of lace and used 1/4 m for each bag. The expression to find the number of bags is
(a) 8 × 1/4
(b) 1/8 × 1/4
(c) 8 ÷ 1/4
(d) 1/4 ÷ 8

Answer: C

Question. Maria decorated 32 bags using 8 m of lace, with 1/4 m per bag. This result is obtained by which calculation?
(a) 8 multiplied by 1/4
(b) 1/4 multiplied by 8
(c) 8 divided by 1/4
(d) 1/4 divided by 8

Answer: C

Question. Which statement is true?
(a) Product of any two fractions is always more than one
(b) Order of multiplication affects the result
(c) 1/2 × 1/3 = 1/6
(d) Fraction × 1 = 0

Answer: C

Question. If 1/2 meter of ribbon is used for 8 badges, the length of ribbon used for each badge is given by the expression
(a) 8 × 1/2
(b) 1/2 ÷ 1/8
(c) 8 ÷ 1/2
(d) 1/2 ÷ 8

Answer: D

Question. A baker has 5 kg of flour and needs 1/6 kg per loaf. The correct expression to find the number of loaves is
(a) 5 × 1/6
(b) 1/6 ÷ 5
(c) 5 ÷ 1/6
(d) 5 × 6

Answer: C

Question. The number of loaves the baker can make with 5 kg of flour, needing 1/6 kg per loaf, is
(a) 30 loaves
(b) 5 loaves
(c) 6 loaves
(d) 1/30 loaves

Answer: A

Question. To find how much flour is used for 1 roti, when 1/4 kg is used for 12 rotis, we calculate
(a) 1/4 multiplied by 12
(b) 1/4 divided by 12
(c) 12 divided by 1/4
(d) 12 minus 1/4

Answer: B

Question. Division by a fraction is same as:
(a) Multiplication by its reciprocal
(b) Multiplication by same fraction
(c) Addition
(d) Subtraction

Answer: A

Question. If 1/4 kg of flour makes 12 rotis, the amount of flour needed for 6 rotis is
(a) 1/2 kg
(b) 1/4 kg
(c) 1/8 kg
(d) 1/12 kg

Answer: C

Question. To evaluate 1 divided by 1/6, we multiply 1 by the reciprocal of 1/6, which is
(a) 1/6
(b) 6
(c) 1
(d) 0

Answer: B

Question. The sum of (1 ÷ 1/6) + (1 ÷ 1/10) + (1 ÷ 1/13) + (1 ÷ 1/9) + (1 ÷ 1/2) is
(a) 40
(b) 10
(c) 1/40
(d) 39

Answer: A

Question. Mira read 1/5 and 3/10 of her 400-page novel. The total fraction of the novel read is
(a) 4/15
(b) 1/2
(c) 3/10
(d) 4/10

Answer: B

Question. What is the reciprocal of 3?
(a) 1/3
(b) 3
(c) 0
(d) 3/1

Answer: A

Question. Mira read 1/2 of her 400-page novel. How many pages did she read today?
(a) 80 pages (1/5 of 400)
(b) 120 pages (3/10 of 400)
(c) 200 pages
(d) 400 pages

Answer: B

Question. Mira's novel has 400 pages. If she read 1/2 of the novel, the number of pages she still needs to read is
(a) 80
(b) 120
(c) 200
(d) 400

Answer: C

Question. Bhāskara I's geometric interpretation of fraction multiplication was a commentary on the work of which earlier mathematician?
(a) Brahmagupta
(b) Aryabhata
(c) Śhrīdharāchārya
(d) Mahāvīrāchārya

Answer: B

Question. The Indian theory of fractions was later transmitted to and developed by Arab and African mathematicians like al-Hassâr of
(a) India
(b) Europe
(c) Morocco
(d) China

Answer: C

Question. The modern usage of the Indian theory of fractions in Europe became common around the
(a) 12th century
(b) 17th century
(c) 19th century
(d) 20th century

Answer: B

Question. In the ant colony splitting problem, at the first split, the fraction of the original group moving along each path is
(a) 1/4
(b) 1/8
(c) 1/2
(d) 1/16

Answer: C

Question. A car runs 16 km per litre. Using 2 3/4 litres of petrol, the distance it will go is
(a) 16 km
(b) 32 km
(c) 44 km
(d) 11 km

Answer: C

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FRACTIONS & DECIMALS

DIFFINITION : FRACTION

A fraction is a number which can be written in the form \( \frac{a}{b} \), where both a and b are natural numbers and the number ‘a’ is called numerator and ‘b’ is called the denominator of the fraction \( \frac{a}{b} \), \( b \neq 0 \).

For example, \( \frac{2}{5}, \frac{1}{3}, \frac{0}{5}, \frac{7}{15} \), are fractions.

TYPES OF FRACTION

• Proper Fraction : A proper fraction is a fraction in which the numerator is smaller than the denominator. For example, \( \frac{2}{9}, \frac{3}{7}, \frac{12}{29} \),..., etc. are proper fractions.
• Improper Fraction : An improper fractions is a fraction in which the numerator is greater than the denominator. For example, \( \frac{7}{5}, \frac{29}{17}, \frac{17}{13} \), ...... , etc. are improper fractions.
• Like Fractions : The fractions with the same denominator are called like fractions. For example, \( \frac{7}{12}, \frac{5}{12}, \frac{11}{12} \), ..... , etc. are like fractions.
• Unlike Fractions : The fractions with different denominators are called unlike fractions. For example, \( \frac{2}{3}, \frac{4}{5}, \frac{11}{13}, \frac{7}{8} \), .... , etc. are unlike fractions.
• Unit Fractions : The fraction with numerator 1 are called unit fractions. For example, \( \frac{1}{2}, \frac{1}{4}, \frac{1}{3}, \frac{1}{7} \), ...., etc. are unit fractions.
• Mixed Numerals : Mixed numerals are combination of a whole number and a proper fraction. For example, fractions \( 3\frac{1}{2}, 5\frac{1}{3}, 8\frac{1}{4} \), etc. are mixed numerals or mixed fractions.
• Equivalent Fractions : If \( \frac{c}{d} = \frac{a \times m}{b \times m} \), then the fractions \( \frac{a}{b} \) and \( \frac{c}{d} \) are called equivalent fractions because they represent the same portion of the whole. For example, \( \frac{4}{6} = \frac{2 \times 2}{3 \times 2} \); \( \frac{15}{48} = \frac{5 \times 3}{16 \times 3} \)
• Decimal fractions : A fraction whose denominator is any of the number 10, 100, 1000 etc. is called a decimal fraction. For example : \( \frac{8}{10}, \frac{11}{100}, \frac{17}{1000} \) etc. are decimal fractions.
• Vulgar fractions : A fraction whose denominator is a whole number, other than 10, 100, 1000 etc. is called a vulgar fractions. For example, \( \frac{2}{7}, \frac{3}{8}, \frac{11}{17} \) etc. are vulgar fractions.

ADDITION AND SUBTRACTION OF FRACTIONS

There are two case of adding and subtracting fractions :
1. Fractions with Similar Denominators. (Like fractions)
2. Fractions with Different Denominators (Unlike fractions)

Question. Ex. Solve the following : (i) \( \frac{2}{5} + \frac{3}{5} \) (ii) \( \frac{4}{7} - \frac{3}{7} \)
Answer: (i) \( \frac{2}{5} + \frac{3}{5} = \frac{2 + 3}{5} = \frac{5}{5} = 1 \) (ii) \( \frac{4}{7} - \frac{3}{7} = \frac{4 - 3}{7} = \frac{1}{7} \)

Question. Ex. Solve the following : (i) \( \frac{2}{5} + \frac{4}{3} \) (ii) \( \frac{3}{9} - \frac{1}{8} \)
Answer: (i) \( \frac{2}{5} + \frac{4}{3} \) [L.C.M. of 5 and 3 = 15] \( = \frac{2 \times 3 + 4 \times 5}{15} = \frac{6 + 20}{15} = \frac{26}{15} = 1\frac{11}{15} \)
(ii) \( \frac{3}{9} - \frac{1}{8} \) [L.C.M. of 8 and 9 = 72] \( = \frac{3 \times 8 - 9 \times 1}{72} = \frac{24 - 9}{72} = \frac{15}{72} = \frac{5}{24} \)

MULTIPLICATION OF FRACTIONS

Rule : Product of fractions = \( \frac{\text{Product of their Numerators}}{\text{Product of their Denominators}} \)

Question. Ex. Find the product (i) \( 3 \times \frac{2}{7} \) (ii) \( 3 \times \frac{1}{8} \) (iii) \( \frac{7}{9} \times 6 \)
Answer: (i) \( 3 \times \frac{2}{7} = \frac{3}{1} \times \frac{2}{7} = \frac{3 \times 2}{1 \times 7} = \frac{6}{7} \)
(ii) \( 3 \times \frac{1}{8} = \frac{3}{1} \times \frac{1}{8} = \frac{3 \times 1}{1 \times 8} = \frac{3}{8} \)
(iii) \( \frac{7}{9} \times 6 = \frac{7}{9} \times \frac{6}{1} = \frac{14}{3} = 4\frac{2}{3} \)

Question. Ex. Find the product : (i) \( \frac{5}{8} \times \frac{3}{7} \) (ii) \( \frac{6}{14} \times \frac{7}{9} \) (iii) \( 2\frac{4}{7} \times \frac{3}{4} \times 1\frac{2}{5} \)
Answer: (i) \( \frac{5}{8} \times \frac{3}{7} = \frac{5 \times 3}{8 \times 7} = \frac{15}{56} \)
(ii) \( \frac{6}{14} \times \frac{7}{9} = \frac{2 \times 3}{2 \times 7} \times \frac{7}{3 \times 3} = \frac{1 \times 1}{1 \times 3} = \frac{1}{3} \)
(iii) \( 2\frac{4}{7} \times \frac{3}{4} \times 1\frac{2}{5} = \frac{18}{7} \times \frac{3}{4} \times \frac{7}{5} = \frac{18 \times 3 \times 7}{7 \times 4 \times 5} = \frac{9 \times 11 \times 1}{1 \times 2 \times 5} = \frac{99}{10} = 9\frac{9}{10} \)

Question. Ex. Find \( 8 \times 5\frac{1}{6} \)
Answer: \( 8 \times 5\frac{1}{6} = 8 \times \frac{31}{6} \) (Converting the mixed fraction into an improper fraction).
\( = \frac{248}{6} \) (Multiplying the numerator by the whole number)
\( = \frac{124}{3} \) (Simplifying into lowest term).
\( = 41\frac{1}{3} \) (Converting the improper fraction into a mixed numeral).

Question. Ex. Find the product of : (i) \( 3\frac{4}{5} \times \frac{10}{21} \) (ii) \( \frac{15}{22} \times 4\frac{5}{7} \) (iii) \( 5\frac{2}{15} \times 3\frac{4}{7} \)
Answer: (i) \( 3\frac{4}{5} \times \frac{10}{21} = \frac{19}{5} \times \frac{10}{21} = \frac{38}{21} = 1\frac{17}{21} \)
(ii) \( \frac{15}{22} \times 4\frac{5}{7} = \frac{15}{22} \times \frac{33}{7} = \frac{15 \times 3}{2 \times 7} = \frac{45}{14} = 3\frac{3}{14} \)
(iii) \( 5\frac{2}{15} \times 3\frac{4}{7} = \frac{77}{15} \times \frac{25}{7} = \frac{11 \times 5}{3 \times 1} = \frac{55}{3} = 18\frac{1}{3} \)

DIVISION OF FRACTIONAL NUMBERS

\( \because \) We know Division = Dividend \( \div \) Divisor
When a fraction number (or whole no.) divide by fractional number (or whole no.) then we multiply dividend to reciprocal of divisor.

Question. Ex. Find the value of (i) \( \frac{5}{7} \div \frac{25}{21} \) (ii) \( \frac{7}{8} \div \frac{15}{8} \) (iii) \( 1\frac{2}{7} \div 2\frac{1}{14} \)
Answer: (i) \( \frac{5}{7} \div \frac{25}{21} = \frac{5}{7} \times \frac{21}{25} = \frac{3}{5} \)
(ii) \( \frac{7}{8} \div \frac{15}{8} = \frac{7}{8} \times \frac{8}{15} = \frac{7}{15} \)
(iii) \( 1\frac{2}{7} \div 2\frac{1}{14} = \frac{9}{7} \div \frac{29}{14} = \frac{9}{7} \times \frac{14}{29} = \frac{18}{29} \)

DECIMALS

Let us consider 6598302

moving from right to left

When we move from right to left place value is increase (by 10 times) but from left to right, place value is decreasing (by one tenth of place value)

Again consider 9321. Let us proceed from 9 to the right.
The place value of 9 is 9 thousand.
The place value of 3 is 3 hundred.
The place value of 2 is 2 tens.
The place value of 1 is 1 ones.

So, a number right to 1 must have for its value on-tenth of one. This fractional part is usually separated from the whole number by means of a dot (.) called the decimal point.

Consider 9321.6, The place value of 6 is 6 tenths or \( \frac{6}{10} \).
Consider 9321.65, The place value of 5 is 5 hundredths or \( \frac{5}{100} \).

DEFINITION : DECIMALS

The numbers expressed in decimal forms are called decimals. For example, 5.2, 21.32, 8.469, ... etc. are decimals.
Decimal has two parts : (i) whole number part (ii) decimal part.
For example, in 21.32
21 \( \rightarrow \) whole part
32 \( \rightarrow \) decimal part
and read as twenty one point three two.

Decimal places : The number of decimal places is equal to the number of digits contained in decimal part of a decimal. For example, in 8.3, 6.23, 10.145 all the numbers have one, two three digits in decimal parts respectively.

Types of Decimals :

• (i) Like decimals : Definition : Decimals having the same number of decimal places. For example, 2.37, 9.01, 14.23 are like decimals, having 2 decimal places.
• (ii) Unlike decimals : Definition : Decimals having the different number of decimal places. For example, 1.12, 2.329, 42.8 are unlike decimals having 2, 3 and 1 decimal places respectively.

Note : 2.7 = 2.70 = 2.700 = 2.7000 = ...... i.e. we can put any number of zero after extreme right decimal part.

COMPARING DECIMALS

Methods :
(i) Convert the given decimals into like decimals if it is unlike.
(ii) First compare the whole numbers.
(iii) If whole-number parts are equal, compare the tenths digits.
(iv) If tenth’s digit are equal, compare the hundredths’ digits and so on.

Question. Ex. Compare : (i) 173.856 and 173.456 (ii) 235.67 and 254.98
Answer: (i) \( \because \) 1, 7, 3 are same in both numbers but 8 > 4 \( \therefore \) 173.856 > 173.456 (ii) \( \because \) In whole part ten's place 3 < 5 but hundreds place is same. \( \therefore \) 235.67 < 254.98

ADDITION & SUBTRACTION OF DECIMALS

Addition of Decimals : Let us add 24.06 and 8.2. Hence we write each of them as two place decimal by putting zeroes wherever necessary at the right of the numbers: 24.06 and 8.20.
24.06
+ 8.20
-------
32.26

Question. Ex. Subtract 0.7342 from 1.
Answer:
  1.0000
- 0.7342
---------
  0.2658

MULTIPLICATION OF DECIMAL NUMBERS

Multiplication of a decimal by 10, 100, 1000 etc. : The decimal point is shifted to the right by one, two, three, … places respectively.
673.234 × 10 = 6732.34
673.234 × 100 = 67323.4
673.234 × 1000 = 673234.0

DIVISION OF DECIMAL NUMBERS

Dividing a decimal by 10, 100, 1000 etc. : The decimal point in the quotient shifts to left by one, two, three, … places.
3.27 \( \div \) 10 = 0.327
3.27 \( \div \) 100 = 0.0327
3.27 \( \div \) 1000 = 0.00327

EXERCISE - I (COMPETITIVE CORNER)

Question. 1. 0.088 \( \div \) 2.2 is equal to
(a) 4
(b) 0.4
(c) 0.04
(d) none of these
Answer: C

Question. 2. 0.8007 × 1000 is equal to
(a) 800.7
(b) 8.007
(c) 8007.0
(d) none of these
Answer: A

Question. 3. The value of 25.75 \( \div \) 100 is equal to
(a) 2.575
(b) 257.5
(c) 0.2575
(d) none of these
Answer: C

Question. 4. The value of 2.2 × 0.2 × 0.001 is equal to
(a) 4.2
(b) 0.00044
(c) 4.4
(d) none of these
Answer: B

Question. 5. If 14 × 4 = 56 then value of 0.14 × 4 is
(a) 5.6
(b) 0.056
(c) 0.56
(d) none of these
Answer: C

Question. 6. 0.35 × 0.2 is equal to
(a) 7.0
(b) 0.7
(c) 70.0
(d) 0.070
Answer: D

Question. 7. If 256 \( \div \) 16 = 16 then value of 2.56 \( \div \) 16 is equal to
(a) 1.6
(b) 16.0
(c) 0.16
(d) none of these
Answer: C

Question. 8. The fraction in which the numerator is less than the denominator is called ________ fraction
(a) like
(b) unlike
(c) improper
(d) proper
Answer: D

Question. 9. The value of product of two proper fractions is always________ than each of the fractions.
(a) greater
(b) equal
(c) less
(d) none of these
Answer: C

Question. 10. The reciprocal of \( \frac{3}{7} \) is
(a) \( \frac{7}{3} \)
(b) \( 2\frac{1}{3} \)
(c) (A) and (B) both
(d) none of these
Answer: C

Question. 11. \( \frac{5}{7} \) of a week is ___ days
(a) 5 days
(b) 7 days
(c) 2 days
(d) none of these
Answer: A

Question. 12. 7.235 kg is equal to ______
(a) 72.35 gm
(b) 7235 gm
(c) 0.7235 gm
(d) none of these
Answer: B

Question. 13. 7204 m is equal to ______
(a) 7.204 km
(b) 72.04 km
(c) 0.7204 km
(d) none of these
Answer: A

Question. 14. 1245 \( \div \) 100 is equal to ______
(a) 12.45
(b) 1.245
(c) 124.5
(d) none of these
Answer: A

EXERCISE - II (CBSE CORNER)

Question. 1. Ramesh can iron a shirt in \( 4\frac{3}{4} \) minutes, how long will he take to iron 16 shirts ?
Answer: 76 minutes or 1 Hour 16 minutes

Question. 2. A bags of flour weighs \( 35\frac{1}{4} \) kg. What is the weight of 105 bags ?
Answer: \( \frac{14805}{4} \) kg

Question. 3. A cook adds \( 4\frac{3}{7} \) cups of water to a stew. If the cup holds \( \frac{3}{14} \) of a litre, how many litres of water were added ?
Answer: \( \frac{93}{98} \) litre

Question. 10. Simplify each of the following : (i) 4.032 – 3.947 – 3.472 + 0.943 (ii) 9.069 – 10.2 + 12.321 – 27.957
Answer: (i) – 2.444 (ii) –16.767

Question. 11. In the given figure the perimeter (the distance all round) of the triangle is 6.5 cm. Two sides are 1.6 cm and 2.3 cm. What is the length of third side ?
Answer: 2.6 cm

Question. 12. Find the perimeter of the rectangle shown in fig. sides are 7.1 cm and 4.2 cm.
Answer: 22.6 cm

Question. 13. A piece of webbing is 17.6 m long. If 2.37 m is cut off, how much is left ?
Answer: 15.23 cm

Question. 39. The perimeter of a square is 244.56 cm. What is the length of one side ?
Answer: 61.14 cm

Question. 48. While helping father put in a new driveway, Shyam carried 14 bags of sand from the garage to the cement mixer. If each bag weighed \( 25\frac{1}{4} \) kg, what was the total weight of all the sand that Shyam carried ?
Answer: \( 353\frac{1}{2} \) kg

Question. 51. Shahina has a \( 7\frac{1}{2} \) metres long ribbon. How many \( 1\frac{1}{2} \) metres long pieces can she cut from the ribbon ?
Answer: 5 ribbons

Question. 52. On a trip last summer, Shashi drove 100 km in \( 2\frac{1}{2} \) hours. How many km did she run in one hour ?
Answer: 40 km