Figure it Out - 2.1 (Page 90)
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1. Fill in the blanks to make the expressions equal on both sides of the = sign:
(a) $13+4 = 11 + 6$
(b) $22 + 8 = 6\times5$
(c) $8\times4 = 64\div2$
(d) $34 - 9 = 25$ -
2. Arrange the following expressions in ascending (increasing) order of their values.
(a) $67-19 = 48$
(b) $67-20 = 47$
(c) $35+25 = 60$
(d) $5\times11 = 55$
(e) $120\div3 = 40$
Ascending order: (e), (b), (a), (d), (c)
Comparing Expressions (Page 94)
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Use '>' or '<' or '=' in each of the following expressions to compare them. Can you do it without complicated calculations? Explain your thinking in each case.
(a) $245+289$ > $246+285$
(b) $273-145$ < $272-144$
(c) $364+587$ < $363+589$
(d) $124+245$ < $129+245$
(e) $213-77$ < $214-76$
Table Completion (Page 100)
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In the following table, some expressions are given. Complete the table.
Expression Expression as the sum of its terms Terms $13-2+6$ $13+(-2)+6$ 13, -2, 6 $5+6\times3$ $5+(6\times3)$ 5, $6\times3$ $4+15-9$ $4+15+(-9)$ 4, 15, -9 $23-2\times4+16$ $23+(-2\times4)+16$ 23, $-2\times4$, 16 $28+19-8$ $28+19+(-8)$ 28, 19, -8
Figure it Out - 2.2 (Pages 112-114)
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1. Find the values of the following expressions by writing the terms in each case.
(a) $28-7+8 = 28 + (-7) + 8 = 29$
(b) $39-2\times6+11 = 39 + (-12) + 11 = 38$
(c) $40-10+10+10 = 40 + (-10) + 10 + 10 = 50$
(d) $48-10\times2+16\div2 = 48 + (-20) + 8 =36$
(e) $6\times3-4\times8\times5 = 18 + (-160) =-142$ -
2. Write a story/situation for each of the following expressions and find their values.
(a) $89+21-10$: Rahul had 89 marbles, his friend gave him 21 more, and he lost 10 marbles. Value = 100.
(b) $5\times12-6$: A box contains 5 packets with 12 crayons each, and 6 crayons were broken and thrown away. Value = 54.
(c) $4\times9+2\times6$: Cost of 4 notebooks at ₹9 each and 2 pens at ₹6 each. Value = 48. -
3. For each of the following situations, write the expression describing the situation, identify its terms and find the value of the expression.
(a) Queen Alia gave 100 gold coins to Princess Elsa and 100 gold coins to Princess Anna last year. Princess Elsa used the coins to start a business and doubled her coins. Princess Anna bought jewellery and has only half of the coins left. Write an expression describing how many gold coins Princess Elsa and Princess Anna together have.
Expression: $2\times100 + 100\div2$
Terms: $2\times100$ and $100\div2$
Value: 250
(b) A metro train ticket between two stations is 40 for an adult and 20 for a child. What is the total cost of tickets:
(i) for four adults and three children?
Expression: $4\times40 + 3\times20$
Terms: $4\times40$ and $3\times20$
Value: 220
(ii) for two groups having three adults each?
Expression: $2\times(3\times40)$
Terms: $2\times(3\times40)$
Value: 240
(c) Find the total height of the window by writing an expression describing the relationship among the measurements shown in the picture.
Expression: $3 + 3 + 5\times2 + 4\times5$
Terms: Individual components of height
Value: Corresponding total height
Figure it Out - 2.3 (Pages 118-120)
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1. Fill in the blanks with numbers, and boxes with operation signs such that the expressions on both sides are equal.
(a) $24+(6-4) = 24+6-4$
(b) $38+(6-4) = 38+6-4$
(c) $24-(6+4) = 24-6-4$
(d) $24-6-4 = 24-6-4$
(e) $27-(8+3) = 27-8-3$
(f) $27-(8-3) = 27-8+3$ -
2. Remove the brackets and write the expression having the same value.
(a) $14+(12+10) = 14+12+10$
(b) $14-(12+10) = 14-12-10$
(c) $14+(12-10) = 14+12-10$
(d) $14-(12-10) = 14-12+10$
(e) $-14+12-10 = -14+12-10$
(f) $14-(-12-10) = 14+12+10$ -
3. Find the values of the following expressions. For each pair, first try to guess whether they have the same value. When are the two expressions equal?
(a) $(6+10)-2$ and $6+(10-2)$: Both equal 14.
(b) $16-(8-3)$ and $(16-8)-3$: Values are 11 and 5 (not equal due to subtraction grouping).
(c) $27-(18+4)$ and $27+(-18-4)$: Both equal 5. -
4. In each of the sets of expressions below, identify those that have the same value. Do not evaluate them, but rather use your understanding of terms.
(a) $319+537$ and $537+319$ have the same value.
(b) $87+46-109$ and $(87-46)+109$. -
5. Add brackets at appropriate places in the expressions such that they lead to the values indicated as shown in the below example $65-18+12=35$, the correct expression is $65-(18+12)=35$
(a) $34-9+12=13 \rightarrow 34-(9+12) = 13$
(b) $56-14-8=34 \rightarrow 56-(14-8) = 34$
(c) $-22-12+10+22=-22 \rightarrow -22-(12-10-22)$ -
6. Using only reasoning of how terms change their values, fill the blanks to make the expressions on either side of the equality (=) equal.
(a) $423+\_ = 419+\_ \rightarrow 423 + 4 = 419 + 8$
(b) $207-68=210-\_ \rightarrow 210 - 71$
Figure it Out - 2.4 (Pages 126-128)
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1. Fill in the blanks with numbers, and boxes by signs, so that the expressions on both sides are equal.
(a) $3\times(6+7)=3\times6+3\times7$
(b) $(8+3)\times4=8\times4+3\times4$
(c) $3\times(5+8)=3\times5 + 3\times8$
(d) $(9+2)\times4=9\times4 + 2\times4$
(e) $3\times(5+4)=3\times5+3\times4$
(f) $(13+6)\times4=13\times4+6\times4$
(g) $3\times5+3\times2=3\times(5+2)$
(h) $(2+3)\times4=2\times4+3\times4$
(i) $5\times(9-2)=5\times9-5\times2$
(j) $(5-2)\times7=5\times7-2\times7$
(k) $5\times(8-3)=5\times8 - 5\times3$
(l) $(8-3)\times7=8\times7 - 3\times7$
(m) $5\times(12-4)=5\times12-5\times4$
(n) $(15-6)\times7=15\times7-6\times7$
(o) $5\times9-5\times4=5\times(9-4)$
(p) $(17-9)\times7=17\times7-9\times7$ -
2. In the boxes below, fill '<', '>' or '=' after analysing the expressions on the LHS and RHS. Use reasoning and understanding of terms and brackets to figure this out and not by evaluating the expressions.
(a) $(8-3)\times29$ > $(3-8)\times29$
(b) $15+9\times18$ < $(15+9)\times18$
(c) $23\times(17-9)$ < $23\times17+23\times9$
(d) $(34-28)\times42$ = $34\times42-28\times42$ -
3. Here is one way to make 14: $2\times(1+6)=14$. Are there other ways of getting 14? Fill them out below:
(a) $7\times(1+1+0) = 14$
(b) $2\times(2+5) = 14$
(c) $1\times(14) = 14$
(d) $14\times(1) = 14$
Figure it Out - 2.5 (Pages 128-132)
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1. Read the situations given below. Write appropriate expressions for each of them and find their values.
(a) The district market in Ongole operates on all seven days of a week. Rahim supplies 9 kg of mangoes each day from his orchard and Shyam supplies 11 kg of mangoes each day from his orchard to this market. Find the amount of mangoes supplied by them in a week to the local district market.
Expression: $7\times(9+11)$ or $7\times9 + 7\times11$
Value: 140 kg
(b) Bhanu earns ₹20,000 per month. She spends ₹5,000 on rent, ₹5,000 on food, and ₹2,000 on other expenses every month. What is the amount Bhanu will save by the end of a year?
Expression: $12 \times (20000 - (5000 + 5000 + 2000))$
Value: ₹96,000
(c) During the daytime a snail climbs 3 cm up a post, and during the night while asleep, accidentally slips down by 2 cm. The post is 10 cm high, and a delicious treat is on its top. In how many days will the snail get the treat?
Expression/Solution: 8 days -
2. Murari reads a two-page story every day except on Tuesdays and Saturdays. How many stories would he complete reading in 8 weeks? Which of the expressions below describes this scenario?
(b) $(7-2)\times8$ and (g) $7\times8-2\times8$
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3. Find different ways of evaluating the following expressions:
(a) $1-2+3-4+5-6+7-8+9-10$: Grouping as $(1-2)+(3-4)... = (-1)\times5 = -5$
(b) $1-1+1-1+1-1+1-1+1-1$: Grouping as $(1-1)+(1-1)... = 0$ -
4. Compare the following pairs of expressions using '<', '>' or '=' by reasoning.
(a) $49-7+8$ = $49-7+8$
(b) $83\times42-18$ > $83\times40-18$
(c) $145-17\times8$ < $145-17\times6$
(d) $23\times48-35$ > $23\times(48-35)$
(e) $(16-11)\times12$ = $-11\times12+16\times12$
(f) $(76-53)\times88$ > $88\times(53-76)$
(g) $25\times(42+16)$ < $25\times(43+15)$
(h) $36\times(28-16)$ > $35\times(27-15)$ -
5. Identify which of the following expressions are equal to the given expression without computation. You may rewrite the expressions using terms or removing brackets. There can be more than one expression which is equal to the given expression.
(a) $83-37-12$: (ii) $84-(37+12)$ and (iv) $-37+83-12$
(b) $93+37\times44+76$: (iv) $37\times44+93+76$
