Figure it Out - 4.1 (Pages 214-215)
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1. Write formulas for the perimeter of:
(a) triangle with all sides equal: $3s$ (where $s$ is the side length)
(b) a regular pentagon: $5s$
(c) a regular hexagon: $6s$ -
2. Munirathna has a 20 m long pipe. However, he wants a longer watering pipe for his garden. He joins another pipe of some length to this one. Give the expression for the combined length of the pipe. Use the letter-number 'k' to denote the length in meters of the other pipe.
$20 + k$
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3. What is the total amount Krithika has, if she has the following numbers of notes of ₹100, ₹20 and ₹5? Complete the following table:
No. of 100 notes No. of 20 notes No. of 5 notes Expression and total amount 3 5 6 $3\times100 + 5\times20 + 6\times5 = 430$ 6 4 3 $6\times100 + 4\times20 + 3\times5 = 695$ 8 4 7 $8\times100 + 4\times20 + 7\times5 = 915$ x y z $100x + 20y + 5z$ -
4. Venkatalakshmi owns a flour mill. It takes 10 seconds for the roller mill to start running. Once it is running, each kg of grain takes 8 seconds to grind into powder. Which of the expressions below describes the time taken to complete grind 'y' kg of grain, assuming the machine is off initially?
(d) $10 + 8 \times y$
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5. Write algebraic expressions using letters of your choice.
(a) 5 more than a number: $x + 5$
(b) 4 less than a number: $x - 4$
(c) 2 less than 13 times a number: $13x - 2$
(d) 13 less than 2 times a number: $2x - 13$ -
6. Describe situations corresponding to the following algebraic expressions:
(a) $8\times x + 3\times y$: Total cost of 8 items of type x and 3 items of type y.
(b) $15\times j - 2\times k$: Remaining quantity after subtracting 2 times k from 15 times j. -
7. In a calendar month, if any $2\times3$ grid full of dates is chosen as shown in the picture, write expressions for the dates in the blank cells if the bottom middle cell has date 'w'.
Top-left: $w - 8$, Top-middle: $w - 7$, Top-right: $w - 6$, Bottom-left: $w - 1$, Bottom-middle: $w$, Bottom-right: $w + 1$.
Figure it Out - 4.2 (Pages 232-234)
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1. Add the numbers in each picture below. Write their corresponding expressions and simplify them. Try adding the numbers in each picture in a couple different ways and see that you get the same thing.
Expressions and simplified forms corresponding to the grid elements (e.g., $5y - 6 + x + 2p + 3q - 2 + 3 - 5g + 5k + \dots$).
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2. Simplify each of the following expressions:
(a) $p+p+p+p$ = $4p$; $p+p+p+q$ = $3p+q$; $p+q+p-q$ = $2p$
(b) $p-q+p-q$ = $2p-2q$; $p+q-p+q$ = $2q$
(c) $p+q-(p+q)$ = $0$; $p-q-p-q$ = $-2q$
(d) $2d-d-d-d$ = $-d$; $2d-d-d-c$ = $-c$
(e) $2d-d-(d-c)$ = $c$; $2d-(d-d)-c$ = $d-c$
(f) $2d-d-c-c$ = $d-2c$
Figure it Out - 4.3 (Pages 250-253)
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1. One plate of Jowar roti costs ₹30 and one plate of Pulao costs ₹20. If x plates of Jowar roti and y plates of pulao were ordered in a day, which expression(s) describe the total amount in rupees earned that day?
(a) $30x + 20y$
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2. Pushpita sells two types of flowers on Independence day: champak and marigold. 'p' customers only bought champak, 'q' customers only bought marigold, and 'r' customers bought both. On the same day, she gave away a tiny national flag to every customer. How many flags did she give away that day?
(a) $p + q + r$
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3. A snail is trying to climb along the wall of a deep well. During the day it climbs up 'u' cm and during the night it slowly slips down 'd' cm. This happens for 10 days and 10 nights.
(a) Expression for distance: $10(u - d)$
(b) If $d > u$: The snail moves further down into the well overall. -
4. Radha is preparing for a cycling race and practices daily. The first week she cycles 5 km every day. Every week she increases the daily distance cycled by 'z' km. How many kilometers would Radha have cycled after 3 weeks?
$7(5) + 7(5 + z) + 7(5 + 2z) = 35 + 35 + 7z + 35 + 14z = 105 + 21z$
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6. A local train from Yahapur to Vahapur stops at three stations at equal distances along the way. The time taken in minutes to travel from one station to the next station is the same and is denoted by t. The train stops for 2 minutes at each of the three stations.
(a) If $t=4$ what is the time taken to travel from Yahapur to Vahapur? There are 4 segments of travel and 3 stops, so $4(4) + 3(2) = 16 + 6 = 22$ minutes.
(b) What is the algebraic expression for the time taken to travel from Yahapur to Vahapur? $4t + 6$ -
7. Simplify the following expressions:
(a) $3a+9b-6+8a-4b-7a+16 = 4a + 5b + 10$
(b) $3(3a - 3b) - 8a - 4b - 16 = a - 13b - 16$
(c) $(2x-3)+8x+12 = 10x + 9$
(d) $8x-(2x-3)+12 = 6x + 15$
(e) $8h-(5+7h)+9 = h + 4$
(f) $23 + 4(6m-3n) - 8n - 3m - 18 = 21m - 20n + 5$ -
8. Add the expressions given below:
(a) $4d-7c+9$ and $8c-11+9d$: $13d + c - 2$
(b) $6f-19-8s$ and $-23+13f+12s$: $19f + 4s - 42$
(c) $8d-14c+9$ and $16c-(11+9d)$: $-d + 2c - 2$
(d) $6f-20+8s$ and $23-13f-12s$: $-7f - 4s + 3$
(e) $13m-12n$ and $12n-13m$: $0$
(f) $-26m+24n$ and $26m-24n$: $0$ -
9. Subtract the expressions given below:
(a) $9a-6b+14$ from $6a+9b-18$: $-3a + 15b - 32$
(b) $-15x+13-9y$ from $7y-10+3x$: $18x + 16y - 23$
(c) $17g+9-7h$ from $11-10g+3h$: $-27g + 10h + 2$
(d) $9a-6b+14$ from $6a-(9b+18)$: $-3a - 3b - 32$
(e) $10x+2+10y$ from $-3y+8-3x$: $-13x - 13y + 6$
(f) $8g+4h-10$ from $7h-8g+20$: $-16g + 3h + 30$
