Chapter 2 exercise answers: Arithmetic Expressions

Open NCERT p. 25Matches NCERT’s answer

(a) 13 + 4 = ____ + 6

1. 13 + 4 = 17.
2. So ____ + 6 must also be 17.
3. 17 − 6 = 11.

Answer11

(b) 22 + ____ = 6 × 5

1. 6 × 5 = 30.
2. So 22 + ____ must be 30.
3. 30 − 22 = 8.

Answer8

(c) 8 × ____ = 64 ÷ 2

1. 64 ÷ 2 = 32.
2. So 8 × ____ must be 32.
3. 32 ÷ 8 = 4.

Answer4

(d) 34 − ____ = 25

1. 34 − ____ = 25.
2. 34 − 25 = 9.

Answer9

Watch this explained “The equality sign is a claim, not a button”, 1:34 into Writing a situation as an expression before computing it · हिंदी में देखें

Open NCERT p. 25Matches NCERT’s answer

1. These five expressions share no common parts to reason with, so find each value.
2. (a) 67 − 19 = 48
3. (b) 67 − 20 = 47
4. (c) 35 + 25 = 60
5. (d) 5 × 11 = 55
6. (e) 120 ÷ 3 = 40
7. Smallest to largest: 40, 47, 48, 55, 60.

Answer(e), (b), (a), (d), (c)

Watch this explained “When to stop reasoning and just compute”, 7:46 into Comparing two expressions by reasoning, not by evaluating · हिंदी में देखें

Open NCERT p. 34Checked by computer

(a) 28 − 7 + 8

1. Only + and − cut an expression into terms.
2. 28 − 7 + 8 has terms 28, −7, 8.
3. 28 − 7 + 8 = 29.

Answer29

(b) 39 − 2 × 6 + 11

1. A × does not cut a term, so 2 × 6 stays together.
2. Terms: 39, −(2×6) = −12, 11.
3. 39 − 12 + 11 = 38.

Answer38

(c) 40 − 10 + 10 + 10

1. Terms: 40, −10, 10, 10.
2. 40 − 10 + 10 + 10 = 50.

Answer50

(d) 48 − 10 × 2 + 16 ÷ 2

1. Terms: 48, −(10×2) = −20, (16÷2) = 8.
2. 48 − 20 + 8 = 36.

Answer36

(e) 6 × 3 − 4 × 8 × 5

1. Terms: (6×3) = 18, −(4×8×5) = −160.
2. The minus sign belongs to the whole product 4×8×5.
3. 18 − 160 = −142.
4. The answer key at the back of the book lists the terms of (e) as 6 × 3 and 4 × 8 × 5, but the minus sign belongs to the second term, so the terms are 18 and –160, which add up to –142.

Answer−142

Watch this explained “Counting the terms”, 3:55 into Every expression can be rewritten as a sum of terms · हिंदी में देखें

Open NCERT p. 34Matches NCERT’s answer

(a) 89 + 21 – 10

1. Story: Rani had ₹89, earned ₹21 more, then spent ₹10.
2. 89 + 21 − 10 = 100.

Answer100

(b) 5 × 12 – 6

1. Story: 5 crates hold 12 mangoes each; 6 mangoes are rotten and removed.
2. 5 × 12 − 6 = 60 − 6 = 54.

Answer54

(c) 4 × 9 + 2 × 6

1. Story: 4 packets of 9 pencils and 2 packets of 6 pencils are bought.
2. 4 × 9 + 2 × 6 = 36 + 12 = 48.

Answer48

Watch this explained “Turning a situation into a line”, 6:39 into Every expression can be rewritten as a sum of terms · हिंदी में देखें

Open NCERT p. 34Matches NCERT’s answer

(a) doubled her coins … has only half of the coins left

1. Elsa doubles her 100 coins: 100 × 2.
2. Anna keeps half of her 100 coins: 100 ÷ 2.
3. Expression: 100×2 + 100÷2, terms 200 and 50.
4. 200 + 50 = 250 coins.

Answer250 gold coins

(b)(i) for four adults and three children

1. 4 adults pay 4 × 40, 3 children pay 3 × 20.
2. Terms: 160 and 60.
3. 160 + 60 = ₹220.

Answer₹220

(b)(ii) for two groups having three adults each

1. 2 groups of 3 adults = 6 adults in all.
2. 6 × 40 = ₹240 (one single term, no addition needed).

Answer₹240

(c) Find the total height of the window

1. The picture shows a border of 3 cm, a grill of 2 cm and a gap of 5 cm, repeating down the window.
2. Counting the picture: 6 grill bars and 7 gaps between/around them, with a 3 cm border strip at both the top and the bottom.
3. Expression: 2×3 + 6×2 + 7×5 (two borders, six grills, seven gaps).
4. 2×3 + 6×2 + 7×5 = 6 + 12 + 35 = 53 cm.

Answer53 cm

Watch this explained “Turning a situation into a line”, 6:39 into Every expression can be rewritten as a sum of terms · हिंदी में देखें

Open NCERT p. 37Checked by computer

(a) 24 + (6 – 4) = 24 + 6

1. A bracket with + in front can simply be removed; nothing inside changes.
2. 24 + (6 − 4) = 24 + 6 − 4.
3. Check: both sides are 26.

Answerbox: −, blank: 4, so 24 + 6 − 4

(b) 38 + (_____ _____) = 38 + 9 – 4

1. The right side 38 + 9 − 4 has the terms 9 and −4.
2. Put them back inside the bracket: 38 + (9 − 4).
3. Check: both sides are 43.
4. (Any pair making 5 also works, such as 2 + 3, but 9 − 4 matches the right side.)

Answer9, box: −, 4, so 38 + (9 − 4)

(c) 24 – (6 +4) = 24 6 – 4

1. Taking away (6 + 4) means taking away 6 and taking away 4.
2. 24 − (6 + 4) = 24 − 6 − 4.
3. Check: both sides are 14.

Answerbox: −, so 24 − 6 − 4

(d) 24 – 6 – 4 = 24 – 6

1. The left side 24 − 6 − 4 has no bracket, so the right side is the same expression.
2. 24 − 6 − 4 = 24 − 6 − 4.
3. Check: both sides are 14.

Answerbox: −, blank: 4, so 24 − 6 − 4

(e) 27 – (8 + 3) = 27 8 3

1. Two signs are missing, between 27 and 8 and between 8 and 3.
2. Taking away (8 + 3) means taking away 8 and taking away 3.
3. 27 − (8 + 3) = 27 − 8 − 3.
4. Check: both sides are 16.

Answerboth signs are −, so 27 − 8 − 3

(f) 27– (_____ _____) = 27 – 8 + 3

1. The right side 27 − 8 + 3 takes away 8 and gives back 3.
2. That is the same as taking away 8 − 3 in one go: 27 − (8 − 3).
3. Check: both sides are 22.
4. (Any pair making 5 also works, but 8 − 3 matches the right side.)

Answer8, box: −, 3, so 27 − (8 − 3)

Watch this explained “Work it out, do not remember it”, 5:57 into Removing a bracket after a minus sign flips every term inside · हिंदी में देखें

Open NCERT p. 37Checked by computer

(a) 14 + (12 + 10)

1. The bracket has + in front, so the signs inside stay as they are.
2. 14 + (12 + 10) = 14 + 12 + 10.
3. 14 + 12 + 10 = 36.

Answer14 + 12 + 10, which is 36

(b) 14 – (12 + 10)

1. The bracket has − in front, so every sign inside reverses: +12 becomes −12 and +10 becomes −10.
2. 14 − (12 + 10) = 14 − 12 − 10.
3. 14 − 12 − 10 = −8.

Answer14 − 12 − 10, which is −8

(c) 14 + (12 – 10)

1. The bracket has + in front, so the signs inside stay as they are.
2. 14 + (12 − 10) = 14 + 12 − 10.
3. 14 + 12 − 10 = 16.

Answer14 + 12 − 10, which is 16

(d) 14 – (12 – 10)

1. The bracket has − in front, so every sign inside reverses: +12 becomes −12 and −10 becomes +10.
2. 14 − (12 − 10) = 14 − 12 + 10.
3. 14 − 12 + 10 = 12.

Answer14 − 12 + 10, which is 12

(e) –14 + (12 – 10)

1. The bracket has + in front, so the signs inside stay as they are.
2. −14 + (12 − 10) = −14 + 12 − 10.
3. −14 + 12 − 10 = −12.

Answer−14 + 12 − 10, which is −12

(f) 14 – (–12 – 10)

1. The bracket has − in front, so every sign inside reverses: −12 becomes +12 and −10 becomes +10.
2. 14 − (−12 − 10) = 14 + 12 + 10.
3. 14 + 12 + 10 = 36.

Answer14 + 12 + 10, which is 36

Watch this explained “Work it out, do not remember it”, 5:57 into Removing a bracket after a minus sign flips every term inside · हिंदी में देखें

Open NCERT p. 37Matches NCERT’s answer

(a) (6 + 10) – 2 and 6 + (10 – 2)

1. (6 + 10) − 2 = 16 − 2 = 14.
2. 6 + (10 − 2) = 6 + 8 = 14.
3. Both are 14. Without brackets both are 6 + 10 − 2, because a bracket with + in front (or at the start) can simply be removed.

Answer14 and 14, yes, they are equal

(b) 16 – (8 – 3) and (16 – 8) – 3

1. 16 − (8 − 3) = 16 − 5 = 11.
2. (16 − 8) − 3 = 8 − 3 = 5.
3. Not equal. Removing the brackets: 16 − (8 − 3) = 16 − 8 + 3, but (16 − 8) − 3 = 16 − 8 − 3. The 3 is given back in the first and taken away in the second.

Answer11 and 5, no, they are not equal

(c) 27 – (18 + 4) and 27 + (–18 – 4)

1. 27 − (18 + 4) = 27 − 22 = 5.
2. 27 + (−18 − 4) = 27 + (−22) = 5.
3. Both are 5. Without brackets both are 27 − 18 − 4: taking away (18 + 4) is the same as adding −18 and −4.

Answer5 and 5, yes, they are equal

When are they equal?

1. Two expressions are equal when they become the same expression once the brackets are removed correctly.
2. A bracket with + in front comes off with no change; a bracket with − in front comes off with every sign inside reversed.

AnswerWhen removing the brackets correctly gives the same terms, as in (a) and (c)

Watch this explained “The check that separates them”, 3:51 into Removing a bracket after a minus sign flips every term inside · हिंदी में देखें

Open NCERT p. 37Checked by computer

(a) 319 + 537, 319 – 537, – 537 + 319, 537 – 319

1. Number the four expressions 1 to 4 in the order printed.
2. 319 − 537 has terms 319 and −537; −537 + 319 has terms −537 and 319 — the same two terms, just swapped.
3. So the 2nd and 3rd expressions are equal by the commutative property; the 1st and 4th are different from these and from each other.

Answerthe 2nd and 3rd expressions (319 − 537 and −537 + 319) are equal

(b) 87 + 46 – 109, … (87 – 46) + 109

1. Number the six expressions 1 to 6 in the order printed.
2. The 1st, 2nd and 3rd are printed identically (87 + 46 − 109), so they are trivially equal.
3. The 4th, 87 − 46 + 109, has terms 87, −46, 109.
4. The 6th, (87 − 46) + 109, removes a bracket behind a +, so it also has terms 87, −46, 109 — same as the 4th.
5. The 5th, 87 − (46 + 109), has terms 87, −46, −109 — a different set of terms, so it stands alone.

Answerexpressions 1, 2, 3 are equal; expressions 4 and 6 are equal; expression 5 is different

Watch this explained “Swapping the two terms”, 0:45 into Commutative and associative: why order and grouping are free · हिंदी में देखें

Open NCERT p. 38Checked by computerAnswers can differ: one example

(a) 34 – 9 + 12 = 13

1. Without brackets, 34 − 9 + 12 = 25 + 12 = 37, not 13.
2. Put a bracket around 9 + 12 so that both are taken away: 34 − (9 + 12).
3. 34 − 21 = 13.

Answer34 − (9 + 12) = 13

(b) 56 – 14 – 8 = 34

1. Without brackets, 56 − 14 − 8 = 42 − 8 = 34 already.
2. So a bracket must not change the order of working: (56 − 14) − 8.
3. 42 − 8 = 34.
4. (A bracket around 14 − 8 would give 56 − 6 = 50, which is wrong.)

Answer(56 − 14) − 8 = 34

(c) –22 – 12 + 10 + 22 = –22

1. Without brackets, −22 − 12 + 10 + 22 = −2, not −22.
2. Put a bracket around 12 + 10 so that both are taken away: −22 − (12 + 10) + 22.
3. −22 − 22 + 22 = −22.

Answer−22 − (12 + 10) + 22 = −22

Watch this explained “The tempting route”, 0:52 into Removing a bracket after a minus sign flips every term inside · हिंदी में देखें

Open NCERT p. 38Checked by computerAnswers can differ: one example

(a) 423 + ______= 419 + ______

1. 419 is 4 less than 423.
2. So the number added to 419 must be 4 more than the number added to 423, to make up the difference.
3. Any such pair works, for example 0 and 4, 1 and 5, or 10 and 14.
4. One answer: 423 + 0 = 423 and 419 + 4 = 423.

Answer423 + 0 = 419 + 4 (any pair where the second number is 4 more than the first also works)

(b) 207 – 68 = 210 – ______

1. 210 is 3 more than 207.
2. To end on the same value, 3 more must be taken away from 210 than from 207.
3. 68 + 3 = 71, so 207 − 68 = 210 − 71.
4. Check: both sides are 139.

Answer71

Watch this explained “Nudging one term”, 6:55 into Removing a bracket after a minus sign flips every term inside · हिंदी में देखें

Open NCERT p. 38Checked by computerAnswers can differ: one example

1. There are many correct lists; here is one that reaches every possible value.
2. 2 + 3 + 5 = 10
3. 3 − 2 + 5 = 6
4. 2 − 3 + 5 = 4
5. 2 + 3 − 5 = 0
6. 3 − (2 + 5) = 3 − 2 − 5 = −4 (a bracket after − takes away both numbers inside)
7. 2 − (3 + 5) = 2 − 3 − 5 = −6
8. Each value is 2, 3 and 5 with a + or − in front of each, and the first number written is never taken away, so no other value is possible. Brackets only move the signs around; they never give a new value.
9. (If you also allow a minus sign in front of the first number, −2 − 3 − 5 = −10 is a seventh value.)

AnswerSix different values: 10, 6, 4, 0, −4, −6

Watch this explained “Two routes, one answer”, 0:00 into Removing a bracket after a minus sign flips every term inside · हिंदी में देखें

Open NCERT p. 38One way to think about it

(a) Do you think she always gets the correct answer? Why?

1. Subtracting 9 is the same as subtracting 10 and then adding back 1, because 9 = 10 − 1.
2. So subtracting 9 = subtracting (10 − 1) = subtracting 10, then adding 1 (removing a bracket behind a minus flips the sign of the 1).
3. This works for any number, not just 36, so yes, she always gets the correct answer.

In shortYes — subtracting 9 always equals subtracting 10 and adding 1 back, because 9 = 10 − 1.

(b) Can you think of other similar strategies?

1. The same idea works for subtracting any number that is 1 less than a round number.
2. To subtract 19: subtract 20, then add 1. For example, 52 − 19 = 32 + 1 = 33.
3. To subtract 8: subtract 10, then add 2 (since 8 = 10 − 2). For example, 45 − 8 = 35 + 2 = 37.

In shortExample: subtract 19 by subtracting 20 and adding 1; subtract 8 by subtracting 10 and adding 2.

Watch this explained “Taking away too much, and giving it back”, 2:48 into Removing a bracket after a minus sign flips every term inside · हिंदी में देखें

Open NCERT p. 38Matches NCERT’s answer

a) 73 − 14 + 1

1. Terms of the target: 73, −14, 1.
2. (b) 73 − (14 − 1): bracket behind minus flips both signs inside, giving terms 73, −14, +1 — matches.
3. (c) 73 + (−14 + 1): already terms 73, −14, +1 — matches.
4. (a) and (d) both end up with −1 as the last term instead of +1, so they do not match.

Answer(b) and (c)

b) 73 − 14 − 1

1. Terms of the target: 73, −14, −1.
2. (a) 73 − (14 + 1): bracket behind minus flips both, giving 73, −14, −1 — matches.
3. (d) 73 + (−14 − 1): already terms 73, −14, −1 — matches.
4. (b) and (c) both end up with +1 as the last term instead of −1, so they do not match.

Answer(a) and (d)

Watch this explained “Taking away too much, and giving it back”, 2:48 into Removing a bracket after a minus sign flips every term inside · हिंदी में देखें

Open NCERT p. 41Checked by computer

(c) 3 × (5 + 8) = 3 × 5

1. Multiplying a sum means multiplying each part and adding: 3 × (5 + 8) = 3 × 5 + 3 × 8.
2. Check: 3 × 13 = 39 and 15 + 24 = 39.

Answerbox: +, blank: 8

(d) (9 + 2) × 4 = 9 × 4

1. (9 + 2) × 4 = 9 × 4 + 2 × 4.
2. Check: 11 × 4 = 44 and 36 + 8 = 44.

Answerbox: +, blank: 4

(e) 3 × (____ + 4) = 3 ____+____

1. The page prints '3 ____' on the right; read it as 3 × ____, like the other parts.
2. Choose any number for the bracket, say 6: 3 × (6 + 4) = 3 × 6 + 3 × 4 = 3 × 6 + 12.
3. Check: 3 × 10 = 30 and 18 + 12 = 30.
4. Any number works in the bracket, as long as the same number goes after 3 ×; the last blank is always 3 × 4 = 12.

Answer6, 6, 12, so 3 × (6 + 4) = 3 × 6 + 12

(f) (____+ 6) × 4 = 13 × 4 + ____

1. The right side starts with 13 × 4, so multiplying out (13 + 6) × 4 gives it: (13 + 6) × 4 = 13 × 4 + 6 × 4.
2. 6 × 4 = 24.
3. Check: 19 × 4 = 76 and 52 + 24 = 76.

Answer13, 24

(g) 3 × (____+____) = 3 × 5 + 3 × 2

1. The right side 3 × 5 + 3 × 2 is 3 times each of 5 and 2, so 3 × (5 + 2).
2. Check: 3 × 7 = 21 and 15 + 6 = 21.
3. (Any two numbers adding to 7, such as 3 and 4, also make both sides equal, but 5 and 2 match the right side.)

Answer5, 2

(h) (____+____)×____= 2 × 4 + 3 × 4

1. 2 × 4 + 3 × 4 is 4 times each of 2 and 3, so (2 + 3) × 4.
2. Check: 5 × 4 = 20 and 8 + 12 = 20.

Answer2, 3, 4

(i) 5 × (9 – 2) = 5 × 9 – 5 ×

1. Multiplying a difference means multiplying each part and subtracting: 5 × (9 − 2) = 5 × 9 − 5 × 2.
2. Check: 5 × 7 = 35 and 45 − 10 = 35.

Answer2

(j) (5 – 2) × 7 = 5 × 7 – 2

1. (5 − 2) × 7 = 5 × 7 − 2 × 7.
2. Check: 3 × 7 = 21 and 35 − 14 = 21.

Answer7

(k) 5 × (8 – 3) = 5 × 8

1. 5 × (8 − 3) = 5 × 8 − 5 × 3.
2. Check: 5 × 5 = 25 and 40 − 15 = 25.

Answerbox: −, blank: 3

(l) (8 – 3) × 7 = 8 × 7

1. (8 − 3) × 7 = 8 × 7 − 3 × 7.
2. Check: 5 × 7 = 35 and 56 − 21 = 35.

Answerbox: −

(m) 5 × (12 –____) =____ 5 ×____

1. Choose any number for the bracket, say 3: 5 × (12 − 3) = 5 × 12 − 5 × 3.
2. 5 × 12 = 60, so 5 × (12 − 3) = 60 − 5 × 3.
3. Check: 5 × 9 = 45 and 60 − 15 = 45.
4. Any number works in the bracket, as long as the same number goes after 5 ×.

Answer3, 60, box: −, 3, so 5 × (12 − 3) = 60 − 5 × 3

(n) (15 –____) × 7 =____ 6 × 7

1. The right side ends with 6 × 7, so the bracket is (15 − 6).
2. (15 − 6) × 7 = 15 × 7 − 6 × 7 = 105 − 6 × 7.
3. Check: 9 × 7 = 63 and 105 − 42 = 63.

Answer6, 105, box: −

(o) 5 × (____–____) = 5 × 9 – 5 × 4

1. 5 × 9 − 5 × 4 is 5 times each of 9 and 4, subtracted, so 5 × (9 − 4).
2. Check: 5 × 5 = 25 and 45 − 20 = 25.

Answer9, 4

(p) (____–____) × ____= 17 × 7 – 9 × 7

1. 17 × 7 − 9 × 7 is 7 times each of 17 and 9, subtracted, so (17 − 9) × 7.
2. Check: 8 × 7 = 56 and 119 − 63 = 56.

Answer17, 9, 7

Watch this explained “The property, in one line”, 5:21 into The distributive property, and using it to compute faster · हिंदी में देखें

Open NCERT p. 42Matches NCERT’s answer

(a) (8 – 3) × 29

1. 8 − 3 is 5, a positive number; 3 − 8 is −5, a negative number.
2. 29 lots of a positive number is more than 29 lots of a negative number.

Answer(8 − 3) × 29 > (3 − 8) × 29

(b) 15 + 9 × 18

1. By the distributive property, (15 + 9) × 18 = 15 × 18 + 9 × 18.
2. Both sides have the term 9 × 18. The other term is 15 on the left and 15 × 18 on the right.
3. 15 × 18 is bigger than 15, so the right side is bigger.

Answer15 + 9 × 18 < (15 + 9) × 18

(c) 23 × (17 – 9)

1. By the distributive property, 23 × (17 − 9) = 23 × 17 − 23 × 9.
2. The right side is 23 × 17 + 23 × 9: it adds 23 × 9 where the left side takes it away.
3. So the right side is bigger.

Answer23 × (17 − 9) < 23 × 17 + 23 × 9

(d) (34 – 28) × 42

1. By the distributive property, (34 − 28) × 42 = 34 × 42 − 28 × 42.
2. That is exactly the right side.

Answer(34 − 28) × 42 = 34 × 42 − 28 × 42

Watch this explained “The near miss”, 2:48 into The distributive property, and using it to compute faster · हिंदी में देखें

Open NCERT p. 42Checked by computerAnswers can differ: one example

1. 14 = 1 × 14 = 2 × 7 = 7 × 2 = 14 × 1, so pick a multiplier that divides 14, then split the other factor into two parts.
2. (a) 1 × (6 + 8) = 1 × 14 = 14.
3. (b) 7 × (1 + 1) = 7 × 2 = 14.
4. (c) 2 × (3 + 4) = 2 × 7 = 14.
5. (d) 1 × (2 + 12) = 1 × 14 = 14.

Answer1×(6+8), 7×(1+1), 2×(3+4), 1×(2+12) — four of the many possible ways

Watch the lesson The distributive property, and using it to compute faster · हिंदी में देखें

Open NCERT p. 42Matches NCERT’s answer

first picture 4, 8, 4 / 8, 4, 8 / 4, 8, 4

1. Way 1, row by row: (4+8+4) + (8+4+8) + (4+8+4) = 16+20+16 = 52.
2. Way 2, by counting equal numbers: there are five 4's and four 8's, so 5×4 + 4×8 = 20+32 = 52.

Answer52

second picture 5, 6, 6, 5 / 6, 5, 5, 6 / …

1. Way 1, row by row: (5+6+6+5)+(6+5+5+6)+(6+5+5+6)+(5+6+6+5) = 22+22+22+22 = 88.
2. Way 2, by counting equal numbers: there are eight 5's and eight 6's, so 8×5 + 8×6 = 40+48 = 88.

Answer88

Watch this explained “One crowd, counted twice”, 1:49 into The distributive property, and using it to compute faster · हिंदी में देखें

Open NCERT p. 42Matches NCERT’s answer

(a) Rahim supplies 9 kg of mangoes each day

1. Each day the market gets 9+11 kg.
2. There are 7 days in a week: 7 × (9 + 11).
3. 7 × 20 = 140 kg.

Answer140 kg

(b) Binu earns ₹20,000 per month

1. Binu saves 20000 − 5000 − 5000 − 2000 every month.
2. For 12 months: 12 × (20000 − 5000 − 5000 − 2000).
3. 12 × 8000 = ₹96,000.

Answer₹96,000

(c) a snail climbs 3 cm up a post

1. Each full day-night cycle, the snail gains 3 − 2 = 1 cm net.
2. After 7 full cycles it has climbed 7 × 1 = 7 cm and it is day 8.
3. On day 8 it climbs 3 more cm: 7 + 3 = 10 cm — exactly the top, so it does not slip back that night.
4. 7 × (3 − 2) + 3 = 10 cm, reached on the 8th day.

Answer8 days

Watch this explained “Two ways that both work”, 0:53 into The distributive property, and using it to compute faster · हिंदी में देखें

Open NCERT p. 43Checked by computer

1. Days in a week: 7
2. Days Melvin does NOT read: 2 (Tuesday and Saturday)
3. Days Melvin reads per week: 7 − 2 = 5
4. Stories per reading day: 1 (given as 'a two-page story' = 1 story)
5. Stories in 8 weeks: 5 × 8 = 40
6. Check expressions:
7. (a) 5 × 2 × 8 = 80 ✗
8. (b) (7 − 2) × 8 = 5 × 8 = 40 ✓
9. (c) 8 × 7 = 56 ✗
10. (d) 7 × 2 × 8 = 112 ✗
11. (e) 7 × 5 − 2 = 33 ✗
12. (f) (7 + 2) × 8 = 72 ✗
13. (g) 7 × 8 − 2 × 8 = 56 − 16 = 40 ✓
14. (h) (7 − 5) × 8 = 16 ✗

Answer40 stories. Expressions (b) and (g) describe this scenario.

Watch this explained “The same argument, for a difference”, 4:38 into The distributive property, and using it to compute faster · हिंदी में देखें

Open NCERT p. 43Checked by computer

(a) 1 – 2 + 3 – 4 + 5 – 6 + 7 – 8 + 9 – 10

1. Method 1 - Pairing consecutive terms:
2. (1 − 2) + (3 − 4) + (5 − 6) + (7 − 8) + (9 − 10)
3. = (−1) + (−1) + (−1) + (−1) + (−1)
4. = −5
5. Method 2 - Left to right:
6. 1 − 2 = −1
7. −1 + 3 = 2
8. 2 − 4 = −2
9. −2 + 5 = 3
10. 3 − 6 = −3
11. −3 + 7 = 4
12. 4 − 8 = −4
13. −4 + 9 = 5
14. 5 − 10 = −5

Answer−5

(b) 1 – 1 + 1 – 1 + 1 – 1 + 1 – 1 + 1 – 1

1. Method 1 - Pairing consecutive terms:
2. (1 − 1) + (1 − 1) + (1 − 1) + (1 − 1) + (1 − 1)
3. = 0 + 0 + 0 + 0 + 0
4. = 0
5. Method 2 - Grouping different way:
6. 1 + (−1 + 1) + (−1 + 1) + (−1 + 1) + (−1 + 1) + (−1)
7. = 1 + 0 + 0 + 0 + 0 − 1
8. = 0

Answer0

Watch this explained “Three terms, two groupings”, 3:21 into Commutative and associative: why order and grouping are free · हिंदी में देखें

Open NCERT p. 43Matches NCERT’s answer

(a) 49 – 7 + 8

1. Both sides are printed identically.

Answer=

(b) 83 × 42 – 18

1. 42 > 40, and the same 18 is subtracted from both, so the left is bigger.

Answer>

(c) 145 – 17 × 8

1. 17×8 > 17×6, so subtracting the bigger amount from 145 leaves less.

Answer<

(d) 23 × 48 – 35

1. 23×(48−35) = 23×48 − 23×35 by distribution, which subtracts far more than just 35.
2. So 23×48 − 35 is bigger.

Answer>

(e) (16 – 11) × 12

1. (16−11)×12 distributes exactly to −11×12 + 16×12.

Answer=

(f) (76 – 53) × 88

1. (76−53) is positive; 88×(53−76) is negative (since 53−76 is negative).
2. A positive value beats a negative one.

Answer>

(g) 25 × (42 + 16)

1. 42+16 = 58 and 43+15 = 58 — the same sum, multiplied by the same 25.

Answer=

(h) 36 × (28 – 16)

1. 28−16=12 and 27−15=12, the same bracket value, but the left multiplies by the bigger number 36 instead of 35.

Answer>

Watch this explained “The property, in one line”, 5:21 into The distributive property, and using it to compute faster · हिंदी में देखें

Open NCERT p. 44Matches NCERT’s answer

(a) 83 − 37 − 12

1. The terms of 83 − 37 − 12 are 83, −37 and −12.
2. (i) 84 − 38 − 12: 84 is 1 more than 83 and 38 is 1 more taken away than 37, so the two changes cancel. Equal.
3. (ii) 84 − (37 + 12) is 84 − 37 − 12, which starts 1 higher and takes away the same. Not equal (1 more).
4. (iii) 83 − 38 − 13 takes away 1 more twice. Not equal (2 less).
5. (iv) −37 + 83 − 12 has the same terms 83, −37, −12 in a different order. Equal.

Answer(i) and (iv)

(b) 93 + 37 × 44 + 76

1. The terms of 93 + 37 × 44 + 76 are 93, 37 × 44 and 76.
2. (iv) 37 × 44 + 93 + 76 has the same three terms in a different order. Equal.
3. (i) 37 + 93 × 44 + 76 multiplies 93 by 44 instead of 37 by 44; 93 × 44 is much bigger than 37 × 44, and the other terms are smaller by only 56 in total. Not equal.
4. (ii) 93 + 37 × 76 + 44 multiplies 37 by 76 instead of 44; 37 × 76 is 37 × 32 more than 37 × 44, while 44 is only 32 less than 76. Not equal.
5. (iii) (93 + 37) × (44 + 76) multiplies every number by two others; it is far bigger than the given sum. Not equal.

Answer(iv) only

Watch this explained “Every order, every grouping”, 4:10 into Commutative and associative: why order and grouping are free · हिंदी में देखें

Open NCERT p. 44Checked by computerAnswers can differ: one example

1. Any number can be chosen, and any ten different expressions with that value are correct. Here is one example, using 24.
2. With addition: 20 + 4 = 24 and 12 + 12 = 24.
3. With subtraction: 30 − 6 = 24, 100 − 76 = 24 and 25 − 1 = 24.
4. With multiplication: 4 × 6 = 24 and 3 × 8 = 24.
5. With division: 48 ÷ 2 = 24 and 96 ÷ 4 = 24.
6. With a bracket: 2 × (10 + 2) = 2 × 12 = 24.

AnswerFor 24: 20 + 4, 30 − 6, 4 × 6, 48 ÷ 2, 12 + 12, 100 − 76, 3 × 8, 2 × (10 + 2), 96 ÷ 4, 25 − 1

Watch this explained “Twelve, under four names”, 4:57 into Writing a situation as an expression before computing it · हिंदी में देखें