Chapter 7 exercise answers: Fractions

Open NCERT p. 152Matches NCERT’s answer

1. Three guavas together weigh 1 kg, and they are all roughly the same size.
2. So the 1 kg is shared equally into 3 parts, one part per guava.
3. Each guava weighs 1 kg ÷ 3 = 1/3 kg.

Answer1/3 kg

Watch this explained “Sharing when weights are involved”, 5:22 into A fraction as an equal share, and why one-ninth is less than one-fifth · हिंदी में देखें

Open NCERT p. 152Matches NCERT’s answer

1. 1 kg of rice is packed into 4 packets of equal weight.
2. So the 1 kg is split into 4 equal parts.
3. Each packet weighs 1 kg ÷ 4 = 1/4 kg.

Answer1/4 kg

Watch this explained “Sharing when weights are involved”, 5:22 into A fraction as an equal share, and why one-ninth is less than one-fifth · हिंदी में देखें

Open NCERT p. 152Matches NCERT’s answer

1. There are 3 glasses of juice shared equally among 4 friends.
2. Each glass is split 4 ways, so each friend gets a quarter from every glass.
3. 3 glasses ÷ 4 friends = 3/4 glass per friend.

Answer3/4 glass

Watch this explained “Three glasses, four friends — a share of three pieces”, 6:08 into A fraction as an equal share, and why one-ninth is less than one-fifth · हिंदी में देखें

Open NCERT p. 153Matches NCERT’s answer

1. The big fish is 1/2 kg, which is the same as 2/4 kg.
2. The small fish is 1/4 kg.
3. Together: 2/4 kg + 1/4 kg = 3/4 kg.

Answer3/4 kg

Watch this explained “Putting two unequal parts together”, 6:57 into A fraction as an equal share, and why one-ninth is less than one-fifth · हिंदी में देखें

Open NCERT p. 153Matches NCERT’s answer

1. Write each word as a number: quarter=1/4, half=1/2, three quarters=3/4, one and a quarter=5/4, one and a half=3/2, two and a half=5/2.
2. Compare these six numbers: 1/4 < 1/2 < 3/4 < 5/4 < 3/2 < 5/2.
3. So, smallest to biggest: quarter, half, three quarters, one and a quarter, one and a half, two and a half.

Answerquarter, half, three quarters, one and a quarter, one and a half, two and a half

Watch this explained “Six spoken fraction words, put in order”, 8:51 into A fraction as an equal share, and why one-ninth is less than one-fifth · हिंदी में देखें

Open NCERT p. 155Matches NCERT’s answer

a.

1. The whole chikki is scored into a grid 6 blocks across and 4 blocks down, so it has 6 × 4 = 24 equal blocks.
2. Piece a is 1 block across and 2 blocks down, so it covers 2 blocks.
3. 2 blocks out of 24 is 2/24 = 1/12: twelve such pieces rebuild the whole chikki.

Answer1/12

b.

1. Piece b is a right triangle with straight sides 3 blocks and 4 blocks long.
2. It is half of a 3-by-4 rectangle of 12 blocks, so it covers 6 blocks.
3. 6 blocks out of 24 is 6/24 = 1/4.

Answer1/4

c.

1. Piece c is a right triangle with straight sides 3 blocks and 2 blocks long.
2. It is half of a 3-by-2 rectangle of 6 blocks, so it covers 3 blocks.
3. 3 blocks out of 24 is 3/24 = 1/8.

Answer1/8

d.

1. Piece d is a strip 1 block across and 4 blocks down, so it covers 4 blocks.
2. 4 blocks out of 24 is 4/24 = 1/6.

Answer1/6

e.

1. Piece e is an L-shape: a 2-by-2 square of 4 blocks with one block missing, so it covers 3 blocks.
2. 3 blocks out of 24 is 3/24 = 1/8.

Answer1/8

f.

1. Piece f is a triangle whose straight edge is 4 blocks long and whose tip sticks out 2 blocks.
2. Its area is (1/2) × 4 × 2 = 4 blocks.
3. 4 blocks out of 24 is 4/24 = 1/6.

Answer1/6

g.

1. Piece g is a single block.
2. 1 block out of 24 is 1/24.

Answer1/24

h.

1. Piece h is a thin right triangle with straight sides 1 block and 2 blocks long.
2. It is half of a 2-block strip, so it covers 1 block.
3. 1 block out of 24 is 1/24.

Answer1/24

Watch this explained “Eight pieces to name, on a grid of twenty-four”, 7:03 into A fraction as a part of one whole · हिंदी में देखें

Open NCERT p. 158Matches NCERT’s answer

1. The table's running total after n halves is n × 1/2.
2. 6 times 1/2 = 6/2 = 3.
3. 7 times 1/2 = 7/2.

Answer6 times 1/2 = 3; 7 times 1/2 = 7/2

Watch this explained “Same idea, a different unit — collecting halves”, 4:12 into Measuring a length by choosing a smaller unit · हिंदी में देखें

Open NCERT p. 158Checked by computerReads two ways: both answers shown

1. In the book's table for 1/2, each column adds one more half. Do the same with quarters of a roti.
2. Column 1: 1/4 = 1 times quarter.
3. Column 2: 1/4 + 1/4 = 2 times quarter = 2/4 (the same as 1/2).
4. Column 3: 1/4 + 1/4 + 1/4 = 3 times quarter = 3/4.
5. Column 4: 1/4 + 1/4 + 1/4 + 1/4 = 4 times quarter = 4/4 = 1 whole roti.
6. NCERT's answer key stops here, at one whole roti, so we lead with this 4-column table.
7. The book's table for 1/2 has 5 columns. Made just as long, the table for 1/4 gets a fifth column: 1/4 + 1/4 + 1/4 + 1/4 + 1/4 = 5 times quarter = 5/4. You can keep going the same way.

AnswerRead as a table up to one whole roti (NCERT's key): 1/4, 2/4 (= 1/2), 3/4, 4/4 (= 1). Read as 5 columns like the table for 1/2: 1/4, 2/4, 3/4, 4/4, 5/4.

Watch this explained “The same run with a smaller step”, 5:37 into Measuring a length by choosing a smaller unit · हिंदी में देखें

Open NCERT p. 158One way to think about it

1. Fold the strip into three equal layers (like the letter Z), sliding the layers until the ends line up exactly, then press the creases. Open it: the two creases cut the strip into 3 equal parts, so each part is 1/3 of the strip.
2. Fold the strip back into its three layers, then fold that folded bundle in half once and press. Open it out.
3. Each third has now been cut into 2 equal parts, so the strip has 3 × 2 = 6 equal parts, and each part is 1/6 of the strip.
4. So yes: half of 1/3 is 1/6, and two of the 1/6 parts together make 1/3.

In shortYes. Fold the strip into 3 equal parts to get 1/3, then fold each third in half: the strip is now in 6 equal parts, so each part is 1/6.

Watch this explained “A fold that is not a halving — thirds, and sixths for free”, 6:26 into Measuring a length by choosing a smaller unit · हिंदी में देखें

Open NCERT p. 158Matches NCERT’s answer

a 5 times 1/4 of a roti

1. Draw 5 quarter-pieces of roti: four of them fit together into 1 whole roti, and 1 quarter is left over.
2. Addition statement: 1/4 + 1/4 + 1/4 + 1/4 + 1/4 = 5 times quarter = 5/4.

Answer5/4

b 9 times 1/4 of a roti

1. Draw 9 quarter-pieces of roti: they make 2 whole rotis (8 quarters) and 1 quarter left over.
2. Addition statement: 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 + 1/4 = 9 times quarter = 9/4.

Answer9/4

Watch this explained “The same run with a smaller step”, 5:37 into Measuring a length by choosing a smaller unit · हिंदी में देखें

Open NCERT p. 158Checked by computer

1. Count the equal sectors in each circle, since a fractional unit is 1 divided by that count.
2. The first circle is cut into 8 equal sectors, so its shaded piece is 1/8.
3. The second circle is cut into 6 equal sectors, so its shaded piece is 1/6.
4. The third circle is cut into 3 equal sectors, so its shaded piece is 1/3.
5. The fourth circle is cut into 5 equal sectors, so its shaded piece is 1/5.

Answerfirst picture = 1/8, second picture = 1/6, third picture = 1/3, fourth picture = 1/5

Watch this explained “Naming it: fractional unit, and its second name”, 4:34 into A fraction as an equal share, and why one-ninth is less than one-fifth · हिंदी में देखें

Open NCERT p. 160One way to think about it

1. Draw a number line and cut the 0-to-1 gap into 10 equal parts (tenths).
2. A bar from 0 to the 1st tenth mark has length 1/10; a bar from 0 to the 3rd tenth mark has length 3/10.
3. 4/5 is the same length as 8/10 (multiply top and bottom by 2), so draw a bar from 0 to the 8th tenth mark.

In shortMark the 0-to-1 gap in tenths, then draw bars ending at the 1st, 3rd and 8th tenth mark (since 4/5 = 8/10).

Watch this explained “Draw your own — tenths and fifths on one line”, 3:38 into Every fraction has one place on the number line · हिंदी में देखें

Open NCERT p. 160Checked by computerAnswers can differ: one example

1. Any five fractions you choose are correct, as long as each is marked in the right place. Here is one choice: 1/2, 1/4, 3/4, 1/8 and 5/8.
2. Halves, quarters and eighths can all be read off one line cut into eighths, because 1/2 = 4/8 and 1/4 = 2/8. So cut the gap from 0 to 1 into 8 equal parts.
3. Draw each line from 0: 1/8 ends at the 1st mark, 1/4 = 2/8 at the 2nd, 1/2 = 4/8 at the 4th, 5/8 at the 5th, and 3/4 = 6/8 at the 6th.

AnswerOne possible answer: 1/2, 1/4, 3/4, 1/8, 5/8, marked on a line from 0 to 1 cut into 8 equal parts.

Watch this explained “Draw your own — tenths and fifths on one line”, 3:38 into Every fraction has one place on the number line · हिंदी में देखें

Open NCERT p. 160One way to think about it

1. Take any fraction between 0 and 1, such as 1/2.
2. The average of 0 and 1/2, which is 1/4, also lies between 0 and 1, and is different from 1/2.
3. This averaging trick can be repeated forever between any two fractions you already have, so no list of fractions between 0 and 1 can ever be complete.

In shortThere are infinitely many fractions between 0 and 1.

Watch this explained “How many fractions fit between 0 and 1?”, 4:29 into Every fraction has one place on the number line · हिंदी में देखें

Open NCERT p. 160Matches NCERT’s answer

1. The 0-to-1 gap is cut into halves, so each half-step is 1/2 long, and the blue line (1 half-step) is 1/2.
2. The black line runs from 0 past 1 to the next half-mark after 1, which is 3 half-steps from 0.
3. 3 half-steps = 3 × 1/2 = 3/2.

Answer3/2

Watch this explained “Bars that run past the 1”, 6:10 into Every fraction has one place on the number line · हिंदी में देखें

Open NCERT p. 160Matches NCERT’s answer

1. The gap from 0 to 1 is cut into 5 equal parts, so each step is 1/5, and 5 steps reach 1.
2. Count the steps from 0 to the end of each black line. The top (longest) line ends 4 steps past 1, which is 9 steps: 9/5.
3. The second line is 8 steps: 8/5. The third is 7 steps: 7/5. The bottom (shortest) line is 6 steps: 6/5.
4. The boxes sit under the ends of the lines, so from left to right they read 6/5, 7/5, 8/5, 9/5.

AnswerTop to bottom: 9/5, 8/5, 7/5, 6/5 (boxes left to right: 6/5, 7/5, 8/5, 9/5)

Watch this explained “A whole row of them — the fifths beyond 1”, 6:55 into Every fraction has one place on the number line · हिंदी में देखें

Open NCERT p. 162Matches NCERT’s answer

1. Two halves make one whole unit, so ask how many pairs of halves fit inside 7 halves.
2. 7 halves = 3 pairs (6 halves, making 3 wholes) with 1 half left over.
3. So there are 3 whole units in 7/2.

Answer3

Watch this explained “Counting the whole units inside three halves and five halves”, 2:32 into Mixed fractions: naming what lies past 1 · हिंदी में देखें

Open NCERT p. 162Matches NCERT’s answer

1. Three thirds make one whole unit.
2. 4/3 is 3 thirds (1 whole) with 1 third left over, so it has 1 whole unit.
3. 7/3 is 6 thirds (2 wholes) with 1 third left over, so it has 2 whole units.

Answer4/3 has 1 whole unit; 7/3 has 2 whole units

Watch this explained “Your turn: seven halves, four thirds, seven thirds”, 3:58 into Mixed fractions: naming what lies past 1 · हिंदी में देखें

Open NCERT p. 162Matches NCERT’s answer

a 8/3

1. 3 thirds make one whole unit.
2. 8/3 is 6 thirds (2 wholes) with 2 thirds left over.
3. So 8/3 has 2 whole units.

Answer2

b 11/5

1. 5 fifths make one whole unit.
2. 11/5 is 10 fifths (2 wholes) with 1 fifth left over.
3. So 11/5 has 2 whole units.

Answer2

c 9/4

1. 4 quarters make one whole unit.
2. 9/4 is 8 quarters (2 wholes) with 1 quarter left over.
3. So 9/4 has 2 whole units.

Answer2

Watch this explained “Writing the leftover beside the whole”, 4:37 into Mixed fractions: naming what lies past 1 · हिंदी में देखें

Open NCERT p. 162Checked by computerReads two ways: both answers shown

1. A fraction greater than 1 can always be split into whole units and a leftover. Divide the numerator by the denominator: the quotient is the number of whole units and the remainder is the number of pieces left over.
2. Example: 19/6. 19 ÷ 6 = 3 remainder 1, so 19/6 = 3 + 1/6 = 3 1/6. The leftover is always less than 1, because the remainder is always less than the denominator.
3. But when the remainder is 0, nothing is left over: 6/3 = 2 and 8/4 = 2. These fractions are whole numbers and have no fractional part.
4. So the answer depends on what counts as a mixed number. We lead with the kind the book shows, 8/3 = 2 + 2/3, which has a fractional part: then not all fractions greater than 1 can be written this way. Those equal to a whole number (6/3, 10/5, …) cannot; every other one can.
5. If a fractional part of 0 is allowed (writing 6/3 as 2 + 0/3), then yes, every fraction greater than 1 can be written as whole part + a part less than 1.

AnswerRead as a mixed number with a fractional part, like 2 2/3: no, not all. Fractions equal to a whole number, such as 6/3 = 2, cannot; all others can. Read as allowing a fractional part of 0: yes, all can.

Watch this explained “Does it always work?”, 6:14 into Mixed fractions: naming what lies past 1 · हिंदी में देखें

Open NCERT p. 162Matches NCERT’s answer

a 9/2

1. 9/2 = 8/2 + 1/2 = 4 + 1/2.

Answer4 1/2

b 9/5

1. 9/5 = 5/5 + 4/5 = 1 + 4/5.

Answer1 4/5

c 21/19

1. 21/19 = 19/19 + 2/19 = 1 + 2/19.

Answer1 2/19

d 47/9

1. 47/9 = 45/9 + 2/9 = 5 + 2/9.

Answer5 2/9

e 12/11

1. 12/11 = 11/11 + 1/11 = 1 + 1/11.

Answer1 1/11

f 19/6

1. 19/6 = 18/6 + 1/6 = 3 + 1/6.

Answer3 1/6

Watch this explained “Both directions, on one number line”, 7:54 into Mixed fractions: naming what lies past 1 · हिंदी में देखें

Open NCERT p. 163Matches NCERT’s answer

(a) 3 1/4

1. 3 1/4 means 3 whole units plus 1/4.
2. Each whole unit is 4/4, so 3 wholes = 12/4.
3. 12/4 + 1/4 = 13/4.

Answer13/4

(b) 7 2/3

1. 7 2/3 means 7 wholes plus 2/3.
2. Each whole is 3/3, so 7 wholes = 21/3.
3. 21/3 + 2/3 = 23/3.

Answer23/3

(c) 9 4/9

1. 9 4/9 means 9 wholes plus 4/9.
2. Each whole is 9/9, so 9 wholes = 81/9.
3. 81/9 + 4/9 = 85/9.

Answer85/9

(d) 3 1/6

1. 3 1/6 means 3 wholes plus 1/6.
2. Each whole is 6/6, so 3 wholes = 18/6.
3. 18/6 + 1/6 = 19/6.

Answer19/6

(e) 2 3/11

1. 2 3/11 means 2 wholes plus 3/11.
2. Each whole is 11/11, so 2 wholes = 22/11.
3. 22/11 + 3/11 = 25/11.

Answer25/11

(f) 3 9/10

1. 3 9/10 means 3 wholes plus 9/10.
2. Each whole is 10/10, so 3 wholes = 30/10.
3. 30/10 + 9/10 = 39/10.

Answer39/10

Watch this explained “The route back — from the mixed form to a single fraction”, 7:04 into Mixed fractions: naming what lies past 1 · हिंदी में देखें

Open NCERT p. 165Matches NCERT’s answer

1. Reduce each fraction to its lowest terms.
2. 3/6 = 1/2 (divide top and bottom by 3).
3. 4/8 = 1/2 (divide top and bottom by 4).
4. 5/10 = 1/2 (divide top and bottom by 5).
5. All three simplify to the same fraction, 1/2.

AnswerYes, they are all equal to 1/2.

Watch this explained “The wall carried down to tenths”, 2:19 into Equivalent fractions: many names, one number, and lowest terms · हिंदी में देखें

Open NCERT p. 165Checked by computerAnswers can differ: one example

1. 2/6 stays the same value if we multiply the top and bottom by the same number.
2. Multiply top and bottom by 2: 2/6 = 4/12.
3. Multiply top and bottom by 3: 2/6 = 6/18.

Answer4/12 and 6/18 (many other correct answers exist).

Watch this explained “The wall carried down to tenths”, 2:19 into Equivalent fractions: many names, one number, and lowest terms · हिंदी में देखें

Open NCERT p. 165Checked by computerAnswers can differ: one example

1. 4 and 6 share a common factor of 2, so divide both by 2: 4/6 = 2/3. This is the lowest terms.
2. From 2/3, multiply top and bottom by 4: 2/3 = 8/12.
3. From 2/3, multiply top and bottom by 6: 2/3 = 12/18.

Answer4/6 = 2/3 = 8/12 = 12/18 (many other correct answers exist).

Watch this explained “Draw and share — the same plate three times”, 5:35 into Equivalent fractions: many names, one number, and lowest terms · हिंदी में देखें

Open NCERT p. 166Matches NCERT’s answer

1. Cut each of the 3 rotis into 4 equal pieces, so there are 12 quarter-pieces in all.
2. Share the 12 pieces equally among 4 children: each child gets 3 pieces, i.e. 3/4 of a roti.
3. Division fact: 3 rotis ÷ 4 children = 3/4 roti each.
4. Addition fact: the 4 children's shares add back to the 3 rotis: 3/4 + 3/4 + 3/4 + 3/4 = 3.
5. Multiplication fact: 4 children × 3/4 roti each = 3 rotis.

AnswerEach child gets 3/4 of a roti.

Watch this explained “Three facts for one picture”, 3:56 into Equivalent fractions: many names, one number, and lowest terms · हिंदी में देखें

Open NCERT p. 166Matches NCERT’s answer

1. Cut each of the 2 rotis into 4 equal pieces, giving 8 quarter-pieces in all.
2. Share the 8 pieces equally among 4 children: each child gets 2 pieces, i.e. 2/4 roti, which is 1/2 roti.
3. Division fact: 2 rotis ÷ 4 children = 1/2 roti each.
4. Addition fact: the 4 shares add back to the 2 rotis: 1/2 + 1/2 + 1/2 + 1/2 = 2.
5. Multiplication fact: 4 children × 1/2 roti each = 2 rotis.

AnswerEach child gets 1/2 a roti.

Watch this explained “Three facts for one picture”, 3:56 into Equivalent fractions: many names, one number, and lowest terms · हिंदी में देखें

Open NCERT p. 166Matches NCERT’s answer

1. 2 cakes are shared equally among 5 children.
2. Each child's share = 2 cakes ÷ 5 children = 2/5 of a cake.

AnswerAnil gets 2/5 of a cake.

Watch this explained “Scale the whole situation”, 4:47 into Equivalent fractions: many names, one number, and lowest terms · हिंदी में देखें

Open NCERT p. 168Checked by computerAnswers can differ: one example

(a) shared equally among 4 friends is the same as ___ glasses

1. 8 friends is 4 friends doubled.
2. Double the juice too, so it stays a fair share: 5 glasses doubled is 10 glasses.
3. Check: 5/4 = 10/8.

Answer10 glasses

(b) 4 kg of potatoes divided equally in 3 bags

1. 12 kg is 4 kg tripled (4 × 3 = 12).
2. Multiply the number of bags by the same 3: 3 bags becomes 9 bags.
3. Check: 4/3 = 12/9.

Answer9 bags

(c) 7 rotis divided among 5 children is the same as

1. Multiply both the rotis and the children by the same number, say 2.
2. 7 rotis becomes 14 rotis; 5 children becomes 10 children.
3. Check: 7/5 = 14/10, so the share per child is unchanged.

Answer14 rotis divided among 10 children (any equal multiple of 7 and 5 works).

Watch this explained “Scale the whole situation”, 4:47 into Equivalent fractions: many names, one number, and lowest terms · हिंदी में देखें

Open NCERT p. 173Matches NCERT’s answer

(a) 17/51

1. 51 = 17 × 3, so 17 and 51 share the factor 17.
2. Divide top and bottom by 17: 17/51 = 1/3.

Answer1/3

(b) 64/144

1. 64 and 144 are both divisible by 16.
2. Divide top and bottom by 16: 64/144 = 4/9.
3. 4 and 9 share no common factor, so this is lowest terms.

Answer4/9

(c) 126/147

1. 126 and 147 are both divisible by 21 (21 × 6 = 126, 21 × 7 = 147).
2. Divide top and bottom by 21: 126/147 = 6/7.
3. 6 and 7 share no common factor, so this is lowest terms.

Answer6/7

(d) 525/112

1. 525 and 112 are both divisible by 7 (7 × 75 = 525, 7 × 16 = 112).
2. Divide top and bottom by 7: 525/112 = 75/16.
3. 75 and 16 share no common factor, so this is lowest terms.

Answer75/16

Watch this explained “Lowest terms, and the test that settles it”, 8:02 into Equivalent fractions: many names, one number, and lowest terms · हिंदी में देखें

Open NCERT p. 174Matches NCERT’s answer

(a) 8/3, 5/2

1. 6 is a common multiple of 3 and 2.
2. 8/3 = 16/6 and 5/2 = 15/6.
3. 16/6 > 15/6, so 8/3 > 5/2.

Answer8/3 > 5/2

(b) 4/9, 3/7

1. 63 is a common multiple of 9 and 7.
2. 4/9 = 28/63 and 3/7 = 27/63.
3. 28/63 > 27/63, so 4/9 > 3/7.

Answer4/9 > 3/7

(c) 7/10, 9/14

1. 70 is a common multiple of 10 and 14.
2. 7/10 = 49/70 and 9/14 = 45/70.
3. 49/70 > 45/70, so 7/10 > 9/14.

Answer7/10 > 9/14

(d) 12/5, 8/5

1. Both fractions already have the same fractional unit, fifths.
2. Compare the numerators: 12 > 8.
3. So 12/5 > 8/5.

Answer12/5 > 8/5

(e) 9/4, 5/2

1. 4 is a common multiple of 4 and 2.
2. 9/4 stays 9/4 and 5/2 = 10/4.
3. 9/4 < 10/4, so 9/4 < 5/2.

Answer9/4 < 5/2

Watch this explained “The method, in two steps”, 8:05 into Comparing two fractions by giving them a common fractional unit · हिंदी में देखें

Open NCERT p. 174Matches NCERT’s answer

(a) 7/10, 11/15, 2/5

1. 30 is a common multiple of 10, 15 and 5.
2. 7/10 = 21/30, 11/15 = 22/30, 2/5 = 12/30.
3. Ordering the counts: 12 < 21 < 22.
4. So ascending order is 2/5, 7/10, 11/15.

Answer2/5, 7/10, 11/15

(b) 19/24, 5/6, 7/12

1. 24 is a common multiple of 24, 6 and 12.
2. 19/24 stays 19/24, 5/6 = 20/24, 7/12 = 14/24.
3. Ordering the counts: 14 < 19 < 20.
4. So ascending order is 7/12, 19/24, 5/6.

Answer7/12, 19/24, 5/6

Watch this explained “Ranking more than two”, 8:54 into Comparing two fractions by giving them a common fractional unit · हिंदी में देखें

Open NCERT p. 174Matches NCERT’s answer

(a) 25/16, 7/8, 13/4, 17/32

1. 32 is a common multiple of 16, 8, 4 and 32.
2. 25/16 = 50/32, 7/8 = 28/32, 13/4 = 104/32, 17/32 stays 17/32.
3. Ordering the counts from biggest: 104 > 50 > 28 > 17.
4. So descending order is 13/4, 25/16, 7/8, 17/32.

Answer13/4, 25/16, 7/8, 17/32

(b) 3/4, 12/5, 7/12, 5/4

1. 60 is a common multiple of 4, 5 and 12.
2. 3/4 = 45/60, 12/5 = 144/60, 7/12 = 35/60, 5/4 = 75/60.
3. Ordering the counts from biggest: 144 > 75 > 45 > 35.
4. So descending order is 12/5, 5/4, 3/4, 7/12.

Answer12/5, 5/4, 3/4, 7/12

Watch this explained “Ranking more than two”, 8:54 into Comparing two fractions by giving them a common fractional unit · हिंदी में देखें

Open NCERT p. 179Matches NCERT’s answer

(a)

1. Same fractional unit already (sevenths).
2. Add the numerators: 2 + 5 + 6 = 13.
3. 2/7 + 5/7 + 6/7 = 13/7.

Answer13/7

(b)

1. 12 is a common multiple of 4 and 3.
2. 3/4 = 9/12, 1/3 = 4/12.
3. 9/12 + 4/12 = 13/12.

Answer13/12

(c)

1. 6 is a common multiple of 3 and 6.
2. 2/3 = 4/6, 5/6 stays 5/6.
3. 4/6 + 5/6 = 9/6, which simplifies to 3/2.

Answer3/2

(d)

1. 21 is a common multiple of 3 and 7.
2. 2/3 = 14/21, 2/7 = 6/21.
3. 14/21 + 6/21 = 20/21.

Answer20/21

(e)

1. 60 is a common multiple of 4, 3 and 5.
2. 3/4 = 45/60, 1/3 = 20/60, 1/5 = 12/60.
3. 45/60 + 20/60 + 12/60 = 77/60.

Answer77/60

(f)

1. 15 is a common multiple of 3 and 5.
2. 2/3 = 10/15, 4/5 = 12/15.
3. 10/15 + 12/15 = 22/15.

Answer22/15

(g)

1. 15 is a common multiple of 5 and 3.
2. 4/5 = 12/15, 2/3 = 10/15.
3. 12/15 + 10/15 = 22/15 (same sum as (f), only the order changed).

Answer22/15

(h)

1. 40 is a common multiple of 5 and 8.
2. 3/5 = 24/40, 5/8 = 25/40.
3. 24/40 + 25/40 = 49/40.

Answer49/40

(i)

1. 4 is a common multiple of 2 and 4.
2. 9/2 = 18/4, 5/4 stays 5/4.
3. 18/4 + 5/4 = 23/4.

Answer23/4

(j)

1. 21 is a common multiple of 3 and 7.
2. 8/3 = 56/21, 2/7 = 6/21.
3. 56/21 + 6/21 = 62/21.

Answer62/21

(k)

1. Same three fractions as (e): 60 is a common multiple of 4, 3 and 5.
2. 3/4 = 45/60, 1/3 = 20/60, 1/5 = 12/60.
3. 45/60 + 20/60 + 12/60 = 77/60.

Answer77/60

(l)

1. 105 is a common multiple of 3, 5 and 7.
2. 2/3 = 70/105, 4/5 = 84/105, 3/7 = 45/105.
3. 70/105 + 84/105 + 45/105 = 199/105.

Answer199/105

(m)

1. 12 is a common multiple of 2, 4 and 6.
2. 9/2 = 54/12, 5/4 = 15/12, 7/6 = 14/12.
3. 54/12 + 15/12 + 14/12 = 83/12.

Answer83/12

Watch this explained “The method, in three steps”, 4:04 into Brahmagupta's method: you can only add units of the same size · हिंदी में देखें

Open NCERT p. 179Matches NCERT’s answer

1. The green paint is the yellow paint plus the blue paint: 2/3 + 3/4.
2. 12 is a common multiple of 3 and 4.
3. 2/3 = 8/12 and 3/4 = 9/12.
4. 8/12 + 9/12 = 17/12 litres.

Answer17/12 litres (1 and 5/12 litres) of green paint.

Watch this explained “Problems that arrive as sentences”, 7:47 into Brahmagupta's method: you can only add units of the same size · हिंदी में देखें

Open NCERT p. 179Matches NCERT’s answer

1. Total lace bought = Geeta's lace + Shamim's lace = 2/5 + 3/4.
2. 20 is a common multiple of 5 and 4.
3. 2/5 = 8/20 and 3/4 = 15/20.
4. 8/20 + 15/20 = 23/20 metres, which is 1 and 3/20 metres.
5. The border needs only 1 metre, and 23/20 metres is more than 1 metre.

AnswerThey bought 23/20 metres of lace in all, which is enough — 3/20 metre will be left over.

Watch this explained “Problems that arrive as sentences”, 7:47 into Brahmagupta's method: you can only add units of the same size · हिंदी में देखें

Open NCERT p. 181Matches NCERT’s answer

1. Both fractions already have the same fractional unit, eighths.
2. Subtract the numerators: 5 − 3 = 2.
3. 5/8 − 3/8 = 2/8, which simplifies to 1/4.

Answer1/4

Watch this explained “Subtraction, same step size”, 6:19 into Brahmagupta's method: you can only add units of the same size · हिंदी में देखें

Open NCERT p. 181Matches NCERT’s answer

1. Both fractions already have the same fractional unit, ninths.
2. Subtract the numerators: 7 − 5 = 2.
3. 7/9 − 5/9 = 2/9.

Answer2/9

Watch this explained “Subtraction, same step size”, 6:19 into Brahmagupta's method: you can only add units of the same size · हिंदी में देखें

Open NCERT p. 181Matches NCERT’s answer

1. Both fractions already have the same fractional unit, 27ths.
2. Subtract the numerators: 10 − 1 = 9.
3. 10/27 − 1/27 = 9/27, which simplifies to 1/3.

Answer1/3

Watch this explained “Subtraction, same step size”, 6:19 into Brahmagupta's method: you can only add units of the same size · हिंदी में देखें

Open NCERT p. 182Matches NCERT’s answer

(a) 8/15−3/15

1. Same fractional unit already (15ths).
2. Subtract the numerators: 8 − 3 = 5.
3. 8/15 − 3/15 = 5/15, which simplifies to 1/3.

Answer1/3

(b) 2/5−4/15

1. 15 is a common multiple of 5 and 15.
2. 2/5 = 6/15, 4/15 stays 4/15.
3. 6/15 − 4/15 = 2/15.

Answer2/15

(c) 5/6−4/9

1. 18 is a common multiple of 6 and 9.
2. 5/6 = 15/18, 4/9 = 8/18.
3. 15/18 − 8/18 = 7/18.

Answer7/18

(d) 2/3−1/2

1. 6 is a common multiple of 3 and 2.
2. 2/3 = 4/6, 1/2 = 3/6.
3. 4/6 − 3/6 = 1/6.

Answer1/6

Watch this explained “Subtraction, different step sizes”, 7:07 into Brahmagupta's method: you can only add units of the same size · हिंदी में देखें

Open NCERT p. 182Matches NCERT’s answer

(a) 13/4 from 10/3

1. "13/4 from 10/3" means 10/3 − 13/4.
2. 12 is a common multiple of 3 and 4.
3. 10/3 = 40/12, 13/4 = 39/12.
4. 40/12 − 39/12 = 1/12.

Answer1/12

(b) 18/5 from 23/3

1. "18/5 from 23/3" means 23/3 − 18/5.
2. 15 is a common multiple of 3 and 5.
3. 23/3 = 115/15, 18/5 = 54/15.
4. 115/15 − 54/15 = 61/15.

Answer61/15

(c) 29/7 from 45/7

1. "29/7 from 45/7" means 45/7 − 29/7.
2. Same fractional unit already (sevenths).
3. 45/7 − 29/7 = 16/7.

Answer16/7

Watch this explained “Subtraction, different step sizes”, 7:07 into Brahmagupta's method: you can only add units of the same size · हिंदी में देखें

Open NCERT p. 182Matches NCERT’s answer

(a) walks the remaining distance to reach her school

1. Total distance to school = 7/10 km. Auto covers 1/2 km.
2. Walking distance = 7/10 − 1/2.
3. 10 is a common multiple of 10 and 2: 7/10 stays 7/10, 1/2 = 5/10.
4. 7/10 − 5/10 = 2/10, which simplifies to 1/5 km.

AnswerJaya walks 1/5 km daily.

(b) Who takes less time and by how much?

1. Compare 10/3 minutes and 13/4 minutes using a common fractional unit, 12ths.
2. 10/3 = 40/12 and 13/4 = 39/12.
3. 39/12 is smaller than 40/12, so Namit takes less time.
4. Difference = 40/12 − 39/12 = 1/12 minute.

AnswerNamit takes less time, by 1/12 of a minute.

Watch this explained “Problems that arrive as sentences”, 7:47 into Brahmagupta's method: you can only add units of the same size · हिंदी में देखें